mdirt fits a variety of item response models with discrete latent variables.
These include, but are not limited to, latent class analysis, multidimensional latent
class models, multidimensional discrete latent class models, DINA/DINO models,
grade of measurement models, C-RUM, and so on. If response models are not defined explicitly
then customized models can defined using the createItem function.
Usage
mdirt(
data,
model,
customTheta = NULL,
structure = NULL,
item.Q = NULL,
nruns = 1,
method = "EM",
covdata = NULL,
formula = NULL,
itemtype = "lca",
optimizer = "nlminb",
return_max = TRUE,
group = NULL,
GenRandomPars = FALSE,
verbose = TRUE,
pars = NULL,
technical = list(),
...
)Arguments
- data
a
matrixordata.framethat consists of numerically ordered data, organized in the form of integers, with missing data coded asNA- model
number of mutually exclusive classes to fit, or alternatively a more specific
mirt.modeldefinition (which reflects the so-called Q-matrix). Note that when using amirt.model, the order with which the syntax factors/attributes are defined are associated with the columns in thecustomThetainput- customTheta
input passed to
technical = list(customTheta = ...), but is included directly in this function for convenience. This input is most interesting for discrete latent models because it allows customized patterns of latent classes (i.e., defines the possible combinations of the latent attribute profile). The default builds the patterncustomTheta = diag(model), which is the typical pattern for the traditional latent class analysis whereby class membership mutually distinct and exhaustive. SeethetaCombfor a quick method to generate a matrix with all possible combinations- structure
an R formula allowing the profile probability patterns (i.e., the structural component of the model) to be fitted according to a log-linear model. When
NULL, all profile probabilities (except one) will be estimated. Use of this input requires that thecustomThetainput is supplied, and that the column names in this matrix match the names found within this formula- item.Q
a list of item-level Q-matrices indicating how the respective categories should be modeled by the underlying attributes. Each matrix must represent a \(K_i \times A\) matrix, where \(K_i\) represents the number of categories for the ith item, and \(A\) is the number of attributes included in the
Thetamatrix; otherwise, a value ofNULLwill default to a matrix consisting of 1's for each \(K_i \times A\) element except for the first row, which contains only 0's for proper identification. Incidentally, the first row of each matrixmustcontain only 0's so that the first category represents the reference category for identification- nruns
a numeric value indicating how many times the model should be fit to the data when using random starting values. If greater than 1,
GenRandomParsis set to true by default- method
estimation method. Can be 'EM' or 'BL' (see
mirtfor more details)- covdata
a data.frame of data used for latent regression models
- formula
an R formula (or list of formulas) indicating how the latent traits can be regressed using external covariates in
covdata. If a named list of formulas is supplied (where the names correspond to the latent trait/attribute names inmodel) then specific regression effects can be estimated for each factor. Supplying a single formula will estimate the regression parameters for all latent variables by default- itemtype
a vector indicating the itemtype associated with each item. For discrete models this is limited to only 'lca' or items defined using a
createItemdefinition- optimizer
optimizer used for the M-step, set to
'nlminb'by default. Seemirtfor more details- return_max
logical; when
nruns > 1, return the model that has the most optimal maximum likelihood criteria? If FALSE, returns a list of all the estimated objects- group
a factor variable indicating group membership used for multiple group analyses
- GenRandomPars
logical; use random starting values
- verbose
logical; turn on messages to the R console
- pars
used for modifying starting values; see
mirtfor details- technical
list of lower-level inputs. See
mirtfor details- ...
additional arguments to be passed to the estimation engine. See
mirtfor more details and examples
Details
Posterior classification accuracy for each response pattern may be obtained
via the fscores function. The summary() function will display
the category probability values given the class membership, which can also
be displayed graphically with plot(), while coef()
displays the raw coefficient values (and their standard errors, if estimated). Finally,
anova() is used to compare nested models, while
M2 and itemfit may be used for model fitting purposes.
'lca' model definition
The latent class IRT model with two latent classes has the form
$$P(x = k|\theta_1, \theta_2, a1, a2) = \frac{exp(a1 \theta_1 + a2 \theta_2)}{ \sum_j^K exp(a1 \theta_1 + a2 \theta_2)}$$
where the \(\theta\) values generally take on discrete points (such as 0 or 1). For proper identification, the first category slope parameters (\(a1\) and \(a2\)) are never freely estimated. Alternatively, supplying a different grid of \(\theta\) values will allow the estimation of similar models (multidimensional discrete models, grade of membership, etc.). See the examples below.
When the item.Q for is utilized, the above equation can be understood as
$$P(x = k|\theta_1, \theta_2, a1, a2) = \frac{exp(a1 \theta_1 Q_{j1} + a2 \theta_2 Q_{j2})}{ \sum_j^K exp(a1 \theta_1 Q_{j1} + a2 \theta_2 Q_{j2})}$$
where by construction Q is a \(K_i \times A\) matrix indicating whether the category should
be modeled according to the latent class structure. For the standard latent class model, the Q-matrix
has as many rows as categories, as many columns as the number of classes/attributes modeled,
and consist of 0's in the first row and 1's elsewhere. This of course can be over-written by passing
an alternative item.Q definition for each respective item.
References
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.
Proctor, C. H. (1970). A probabilistic formulation and statistical analysis for Guttman scaling. Psychometrika, 35, 73-78. doi:10.18637/jss.v048.i06
Author
Phil Chalmers rphilip.chalmers@gmail.com
Examples
# LSAT6 dataset
dat <- expand.table(LSAT6)
# fit with 2-3 latent classes
(mod2 <- mdirt(dat, 2))
#>
Iteration: 1, Log-Lik: -3209.317, Max-Change: 2.67790
Iteration: 2, Log-Lik: -2475.451, Max-Change: 0.21401
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#>
#> Call:
#> mdirt(data = dat, model = 2)
#>
#> Latent class model with 2 classes and 2 profiles.
#> Converged within 1e-04 tolerance after 363 EM iterations.
#> mirt version: 1.44.4
#> M-step optimizer: nlminb
#> EM acceleration: Ramsay
#> Latent density type: discrete
#>
#> Log-likelihood = -2467.408
#> Estimated parameters: 11
#> AIC = 4956.816
#> BIC = 5010.802; SABIC = 4975.865
#> G2 (20) = 22.74, p = 0.3018, RMSEA = 0.012
# \donttest{
(mod3 <- mdirt(dat, 3))
#>
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#> Warning: EM cycles terminated after 500 iterations.
#>
#> Call:
#> mdirt(data = dat, model = 3)
#>
#> Latent class model with 3 classes and 3 profiles.
#> FAILED TO CONVERGE within 1e-04 tolerance after 500 EM iterations.
#> mirt version: 1.44.4
#> M-step optimizer: nlminb
#> EM acceleration: Ramsay
#> Latent density type: discrete
#>
#> Log-likelihood = -2465.249
#> Estimated parameters: 17
#> AIC = 4964.499
#> BIC = 5047.931; SABIC = 4993.938
#> G2 (14) = 18.42, p = 0.1882, RMSEA = 0.018
summary(mod2)
#> $Item_1
#> category_1 category_2
#> P[1 0] 0.156 0.844
#> P[0 1] 0.037 0.963
#>
#> $Item_2
#> category_1 category_2
#> P[1 0] 0.485 0.515
#> P[0 1] 0.196 0.804
#>
#> $Item_3
#> category_1 category_2
#> P[1 0] 0.713 0.287
#> P[0 1] 0.317 0.683
#>
#> $Item_4
#> category_1 category_2
#> P[1 0] 0.401 0.599
#> P[0 1] 0.157 0.843
#>
#> $Item_5
#> category_1 category_2
#> P[1 0] 0.232 0.768
#> P[0 1] 0.080 0.920
#>
#> $Class.Probability
#> F1 F2 prob
#> Profile_1 1 0 0.329
#> Profile_2 0 1 0.671
#>
residuals(mod2)
#> Item_1 Item_2 Item_3 Item_4 Item_5
#> Item_1 NA 0.010 0.020 -0.011 -0.018
#> Item_2 0.109 NA 0.003 -0.018 0.022
#> Item_3 0.412 0.009 NA 0.008 -0.026
#> Item_4 0.132 0.313 0.060 NA 0.040
#> Item_5 0.331 0.487 0.680 1.566 NA
residuals(mod2, type = 'exp')
#> Item_1 Item_2 Item_3 Item_4 Item_5 freq exp std.res
#> 1 0 0 0 0 0 3 1.662 1.038
#> 2 0 0 0 0 1 6 5.673 0.137
#> 3 0 0 0 1 0 2 2.556 -0.348
#> 4 0 0 0 1 1 11 9.333 0.546
#> 5 0 0 1 0 0 1 0.702 0.356
#> 6 0 0 1 0 1 1 2.670 -1.022
#> 7 0 0 1 1 0 3 1.211 1.626
#> 8 0 0 1 1 1 4 5.855 -0.767
#> 9 0 1 0 0 0 1 1.826 -0.611
#> 10 0 1 0 0 1 8 6.708 0.499
#> 11 0 1 0 1 1 16 13.561 0.662
#> 12 0 1 1 0 1 3 4.297 -0.625
#> 13 0 1 1 1 0 2 1.972 0.020
#> 14 0 1 1 1 1 15 14.075 0.247
#> 15 1 0 0 0 0 10 9.422 0.188
#> 16 1 0 0 0 1 29 35.372 -1.071
#> 17 1 0 0 1 0 14 16.027 -0.506
#> 18 1 0 0 1 1 81 75.302 0.657
#> 19 1 0 1 0 0 3 4.672 -0.773
#> 20 1 0 1 0 1 28 24.369 0.736
#> 21 1 0 1 1 0 15 11.213 1.131
#> 22 1 0 1 1 1 80 84.968 -0.539
#> 23 1 1 0 0 0 16 11.551 1.309
#> 24 1 1 0 0 1 56 55.154 0.114
#> 25 1 1 0 1 0 21 25.287 -0.853
#> 26 1 1 0 1 1 173 174.541 -0.117
#> 27 1 1 1 0 0 11 8.273 0.948
#> 28 1 1 1 0 1 61 63.783 -0.348
#> 29 1 1 1 1 0 28 29.723 -0.316
#> 30 1 1 1 1 1 298 294.334 0.214
anova(mod2, mod3)
#> AIC SABIC HQ BIC logLik X2 df p
#> mod2 4956.816 4975.865 4977.335 5010.802 -2467.408
#> mod3 4964.499 4993.938 4996.209 5047.931 -2465.249 4.317 6 0.634
M2(mod2)
#> M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI
#> stats 4.603509 4 0.3304498 0.01228935 0 0.05069941 0.02122285 0.973442
#> CFI
#> stats 0.9893768
itemfit(mod2)
#> item S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1 Item_1 0.433 2 0 0.805
#> 2 Item_2 1.702 2 0 0.427
#> 3 Item_3 0.747 1 0 0.387
#> 4 Item_4 0.184 2 0 0.912
#> 5 Item_5 0.145 2 0 0.930
# generate classification plots
plot(mod2)
plot(mod2, facet_items = FALSE)
plot(mod2, profile = TRUE)
# available for polytomous data
mod <- mdirt(Science, 2)
#>
Iteration: 1, Log-Lik: -2133.040, Max-Change: 3.99217
Iteration: 2, Log-Lik: -1667.867, Max-Change: 0.47159
Iteration: 3, Log-Lik: -1665.172, Max-Change: 0.40175
Iteration: 4, Log-Lik: -1661.788, Max-Change: 0.27779
Iteration: 5, Log-Lik: -1660.833, Max-Change: 1.64134
Iteration: 6, Log-Lik: -1659.967, Max-Change: 0.31011
Iteration: 7, Log-Lik: -1659.792, Max-Change: 0.27820
Iteration: 8, Log-Lik: -1658.952, Max-Change: 0.32539
Iteration: 9, Log-Lik: -1658.063, Max-Change: 0.36664
Iteration: 10, Log-Lik: -1656.416, Max-Change: 0.26079
Iteration: 11, Log-Lik: -1653.692, Max-Change: 0.20173
Iteration: 12, Log-Lik: -1652.583, Max-Change: 0.19055
Iteration: 13, Log-Lik: -1650.246, Max-Change: 0.25533
Iteration: 14, Log-Lik: -1647.565, Max-Change: 0.16300
Iteration: 15, Log-Lik: -1646.126, Max-Change: 0.17178
Iteration: 16, Log-Lik: -1644.823, Max-Change: 0.33650
Iteration: 17, Log-Lik: -1638.825, Max-Change: 0.09071
Iteration: 18, Log-Lik: -1637.429, Max-Change: 0.08408
Iteration: 19, Log-Lik: -1635.601, Max-Change: 0.19727
Iteration: 20, Log-Lik: -1633.311, Max-Change: 0.07325
Iteration: 21, Log-Lik: -1632.525, Max-Change: 0.09317
Iteration: 22, Log-Lik: -1631.860, Max-Change: 0.17304
Iteration: 23, Log-Lik: -1629.988, Max-Change: 0.09287
Iteration: 24, Log-Lik: -1629.616, Max-Change: 0.09446
Iteration: 25, Log-Lik: -1629.299, Max-Change: 0.13409
Iteration: 26, Log-Lik: -1628.115, Max-Change: 0.06696
Iteration: 27, Log-Lik: -1627.890, Max-Change: 0.07090
Iteration: 28, Log-Lik: -1627.433, Max-Change: 0.10071
Iteration: 29, Log-Lik: -1626.732, Max-Change: 0.08868
Iteration: 30, Log-Lik: -1626.521, Max-Change: 0.09459
Iteration: 31, Log-Lik: -1625.973, Max-Change: 0.11444
Iteration: 32, Log-Lik: -1625.506, Max-Change: 0.15564
Iteration: 33, Log-Lik: -1625.364, Max-Change: 0.16043
Iteration: 34, Log-Lik: -1625.124, Max-Change: 0.10570
Iteration: 35, Log-Lik: -1624.892, Max-Change: 0.10894
Iteration: 36, Log-Lik: -1624.853, Max-Change: 0.04399
Iteration: 37, Log-Lik: -1624.833, Max-Change: 0.05116
Iteration: 38, Log-Lik: -1624.807, Max-Change: 0.03840
Iteration: 39, Log-Lik: -1624.786, Max-Change: 0.12813
Iteration: 40, Log-Lik: -1624.756, Max-Change: 0.00947
Iteration: 41, Log-Lik: -1624.743, Max-Change: 0.01283
Iteration: 42, Log-Lik: -1624.732, Max-Change: 0.00870
Iteration: 43, Log-Lik: -1624.722, Max-Change: 0.00901
Iteration: 44, Log-Lik: -1624.714, Max-Change: 0.00714
Iteration: 45, Log-Lik: -1624.708, Max-Change: 0.00716
Iteration: 46, Log-Lik: -1624.702, Max-Change: 0.01670
Iteration: 47, Log-Lik: -1624.685, Max-Change: 0.00446
Iteration: 48, Log-Lik: -1624.683, Max-Change: 0.00523
Iteration: 49, Log-Lik: -1624.680, Max-Change: 0.00410
Iteration: 50, Log-Lik: -1624.678, Max-Change: 0.13939
Iteration: 51, Log-Lik: -1624.669, Max-Change: 0.00245
Iteration: 52, Log-Lik: -1624.669, Max-Change: 0.00267
Iteration: 53, Log-Lik: -1624.668, Max-Change: 0.00234
Iteration: 54, Log-Lik: -1624.668, Max-Change: 0.00220
Iteration: 55, Log-Lik: -1624.667, Max-Change: 0.00182
Iteration: 56, Log-Lik: -1624.666, Max-Change: 0.00198
Iteration: 57, Log-Lik: -1624.666, Max-Change: 0.00162
Iteration: 58, Log-Lik: -1624.665, Max-Change: 0.00246
Iteration: 59, Log-Lik: -1624.665, Max-Change: 0.00150
Iteration: 60, Log-Lik: -1624.665, Max-Change: 0.00140
Iteration: 61, Log-Lik: -1624.664, Max-Change: 0.00110
Iteration: 62, Log-Lik: -1624.664, Max-Change: 0.00117
Iteration: 63, Log-Lik: -1624.664, Max-Change: 0.00110
Iteration: 64, Log-Lik: -1624.664, Max-Change: 0.00167
Iteration: 65, Log-Lik: -1624.664, Max-Change: 0.00106
Iteration: 66, Log-Lik: -1624.664, Max-Change: 0.00097
Iteration: 67, Log-Lik: -1624.663, Max-Change: 0.00132
Iteration: 68, Log-Lik: -1624.663, Max-Change: 0.00000
summary(mod)
#> $Comfort
#> category_1 category_2 category_3 category_4
#> P[1 0] 0.021 0.097 0.773 0.109
#> P[0 1] 0.000 0.059 0.535 0.407
#>
#> $Work
#> category_1 category_2 category_3 category_4
#> P[1 0] 0.125 0.339 0.504 0.033
#> P[0 1] 0.023 0.115 0.559 0.303
#>
#> $Future
#> category_1 category_2 category_3 category_4
#> P[1 0] 0.058 0.305 0.637 0.000
#> P[0 1] 0.001 0.000 0.382 0.616
#>
#> $Benefit
#> category_1 category_2 category_3 category_4
#> P[1 0] 0.074 0.339 0.508 0.079
#> P[0 1] 0.022 0.128 0.469 0.382
#>
#> $Class.Probability
#> F1 F2 prob
#> Profile_1 1 0 0.603
#> Profile_2 0 1 0.397
#>
plot(mod)
plot(mod, profile=TRUE)
# classification based on response patterns
fscores(mod2, full.scores = FALSE)
#> Item_1 Item_2 Item_3 Item_4 Item_5 Class_1 Class_2
#> [1,] 0 0 0 0 0 0.98832539 0.01167461
#> [2,] 0 0 0 0 1 0.96080421 0.03919579
#> [3,] 0 0 0 1 0 0.95911420 0.04088580
#> [4,] 0 0 0 1 1 0.87167305 0.12832695
#> [5,] 0 0 1 0 0 0.94030147 0.05969853
#> [6,] 0 0 1 0 1 0.82016986 0.17983014
#> [7,] 0 0 1 1 0 0.81359256 0.18640744
#> [8,] 0 0 1 1 1 0.55826672 0.44173328
#> [9,] 0 1 0 0 0 0.95646627 0.04353373
#> [10,] 0 1 0 0 1 0.86416411 0.13583589
#> [11,] 0 1 0 1 1 0.63805843 0.36194157
#> [12,] 0 1 1 0 1 0.54205358 0.45794642
#> [13,] 0 1 1 1 0 0.53111944 0.46888056
#> [14,] 0 1 1 1 1 0.24698538 0.75301462
#> [15,] 1 0 0 0 0 0.94648118 0.05351882
#> [16,] 1 0 0 0 1 0.83662440 0.16337560
#> [17,] 1 0 0 1 0 0.83052457 0.16947543
#> [18,] 1 0 0 1 1 0.58660671 0.41339329
#> [19,] 1 0 1 0 0 0.76692257 0.23307743
#> [20,] 1 0 1 0 1 0.48790756 0.51209244
#> [21,] 1 0 1 1 0 0.47692814 0.52307186
#> [22,] 1 0 1 1 1 0.20887048 0.79112952
#> [23,] 1 1 0 0 0 0.82110202 0.17889798
#> [24,] 1 1 0 0 1 0.57063375 0.42936625
#> [25,] 1 1 0 1 0 0.55982786 0.44017214
#> [26,] 1 1 0 1 1 0.26915168 0.73084832
#> [27,] 1 1 1 0 0 0.46061404 0.53938596
#> [28,] 1 1 1 0 1 0.19825043 0.80174957
#> [29,] 1 1 1 1 0 0.19135355 0.80864645
#> [30,] 1 1 1 1 1 0.06412585 0.93587415
# classify individuals either with the largest posterior probability.....
fs <- fscores(mod2)
head(fs)
#> Class_1 Class_2
#> 1 0.9883254 0.01167461
#> 2 0.9883254 0.01167461
#> 3 0.9883254 0.01167461
#> 4 0.9608042 0.03919579
#> 5 0.9608042 0.03919579
#> 6 0.9608042 0.03919579
classes <- 1:2
class_max <- classes[apply(apply(fs, 1, max) == fs, 1, which)]
table(class_max)
#> class_max
#> 1 2
#> 291 709
# ... or by probability sampling (i.e., plausible value draws)
class_prob <- apply(fs, 1, function(x) sample(1:2, 1, prob=x))
table(class_prob)
#> class_prob
#> 1 2
#> 325 675
# plausible value imputations for stochastic classification in both classes
pvs <- fscores(mod2, plausible.draws=10)
tabs <- lapply(pvs, function(x) apply(x, 2, table))
tabs[[1]]
#> [,1] [,2]
#> 0 678 306
#> 1 322 694
# fit with random starting points (run in parallel to save time)
if(interactive()) mirtCluster()
mod <- mdirt(dat, 2, nruns=10)
#> Model log-likelihoods:
#> [1] -2467.408 -2467.408 -2467.408 -2467.408 -2467.408 -2467.408 -2467.408
#> [8] -2467.408 -2467.408 -2467.408
#--------------------------
# Grade of measurement model
# define a custom Theta grid for including a 'fuzzy' class membership
(Theta <- matrix(c(1, 0, .5, .5, 0, 1), nrow=3 , ncol=2, byrow=TRUE))
#> [,1] [,2]
#> [1,] 1.0 0.0
#> [2,] 0.5 0.5
#> [3,] 0.0 1.0
(mod_gom <- mdirt(dat, 2, customTheta = Theta))
#>
Iteration: 1, Log-Lik: -3135.540, Max-Change: 2.42774
Iteration: 2, Log-Lik: -2471.362, Max-Change: 0.16596
Iteration: 3, Log-Lik: -2468.100, Max-Change: 0.08347
Iteration: 4, Log-Lik: -2467.443, Max-Change: 0.05135
Iteration: 5, Log-Lik: -2467.182, Max-Change: 0.03074
Iteration: 6, Log-Lik: -2467.090, Max-Change: 0.01952
Iteration: 7, Log-Lik: -2467.036, Max-Change: 0.01266
Iteration: 8, Log-Lik: -2467.017, Max-Change: 0.01065
Iteration: 9, Log-Lik: -2467.003, Max-Change: 0.01105
Iteration: 10, Log-Lik: -2466.983, Max-Change: 0.00631
Iteration: 11, Log-Lik: -2466.975, Max-Change: 0.00878
Iteration: 12, Log-Lik: -2466.970, Max-Change: 0.00526
Iteration: 13, Log-Lik: -2466.964, Max-Change: 0.00372
Iteration: 14, Log-Lik: -2466.959, Max-Change: 0.00517
Iteration: 15, Log-Lik: -2466.954, Max-Change: 0.00410
Iteration: 16, Log-Lik: -2466.948, Max-Change: 0.00625
Iteration: 17, Log-Lik: -2466.944, Max-Change: 0.00288
Iteration: 18, Log-Lik: -2466.941, Max-Change: 0.00367
Iteration: 19, Log-Lik: -2466.937, Max-Change: 0.00376
Iteration: 20, Log-Lik: -2466.933, Max-Change: 0.00349
Iteration: 21, Log-Lik: -2466.930, Max-Change: 0.00407
Iteration: 22, Log-Lik: -2466.926, Max-Change: 0.00285
Iteration: 23, Log-Lik: -2466.923, Max-Change: 0.00391
Iteration: 24, Log-Lik: -2466.920, Max-Change: 0.00277
Iteration: 25, Log-Lik: -2466.917, Max-Change: 0.00345
Iteration: 26, Log-Lik: -2466.914, Max-Change: 0.00384
Iteration: 27, Log-Lik: -2466.910, Max-Change: 0.00364
Iteration: 28, Log-Lik: -2466.907, Max-Change: 0.00334
Iteration: 29, Log-Lik: -2466.904, Max-Change: 0.00265
Iteration: 30, Log-Lik: -2466.901, Max-Change: 0.00367
Iteration: 31, Log-Lik: -2466.898, Max-Change: 0.00321
Iteration: 32, Log-Lik: -2466.895, Max-Change: 0.00339
Iteration: 33, Log-Lik: -2466.892, Max-Change: 0.00383
Iteration: 34, Log-Lik: -2466.889, Max-Change: 0.00333
Iteration: 35, Log-Lik: -2466.886, Max-Change: 0.00327
Iteration: 36, Log-Lik: -2466.883, Max-Change: 0.00374
Iteration: 37, Log-Lik: -2466.880, Max-Change: 0.00322
Iteration: 38, Log-Lik: -2466.878, Max-Change: 0.00319
Iteration: 39, Log-Lik: -2466.875, Max-Change: 0.00366
Iteration: 40, Log-Lik: -2466.872, Max-Change: 0.00319
Iteration: 41, Log-Lik: -2466.869, Max-Change: 0.00311
Iteration: 42, Log-Lik: -2466.866, Max-Change: 0.00359
Iteration: 43, Log-Lik: -2466.864, Max-Change: 0.00312
Iteration: 44, Log-Lik: -2466.861, Max-Change: 0.00304
Iteration: 45, Log-Lik: -2466.859, Max-Change: 0.00350
Iteration: 46, Log-Lik: -2466.856, Max-Change: 0.00335
Iteration: 47, Log-Lik: -2466.854, Max-Change: 0.00297
Iteration: 48, Log-Lik: -2466.851, Max-Change: 0.00344
Iteration: 49, Log-Lik: -2466.849, Max-Change: 0.00308
Iteration: 50, Log-Lik: -2466.846, Max-Change: 0.00254
Iteration: 51, Log-Lik: -2466.844, Max-Change: 0.00251
Iteration: 52, Log-Lik: -2466.842, Max-Change: 0.00363
Iteration: 53, Log-Lik: -2466.840, Max-Change: 0.00387
Iteration: 54, Log-Lik: -2466.837, Max-Change: 0.00266
Iteration: 55, Log-Lik: -2466.835, Max-Change: 0.00245
Iteration: 56, Log-Lik: -2466.833, Max-Change: 0.00230
Iteration: 57, Log-Lik: -2466.831, Max-Change: 0.00224
Iteration: 58, Log-Lik: -2466.829, Max-Change: 0.00281
Iteration: 59, Log-Lik: -2466.827, Max-Change: 0.00376
Iteration: 60, Log-Lik: -2466.825, Max-Change: 0.00282
Iteration: 61, Log-Lik: -2466.822, Max-Change: 0.00330
Iteration: 62, Log-Lik: -2466.820, Max-Change: 0.00237
Iteration: 63, Log-Lik: -2466.819, Max-Change: 0.00259
Iteration: 64, Log-Lik: -2466.816, Max-Change: 0.00359
Iteration: 65, Log-Lik: -2466.814, Max-Change: 0.00365
Iteration: 66, Log-Lik: -2466.812, Max-Change: 0.00269
Iteration: 67, Log-Lik: -2466.810, Max-Change: 0.00311
Iteration: 68, Log-Lik: -2466.808, Max-Change: 0.00263
Iteration: 69, Log-Lik: -2466.806, Max-Change: 0.00226
Iteration: 70, Log-Lik: -2466.804, Max-Change: 0.00351
Iteration: 71, Log-Lik: -2466.801, Max-Change: 0.00263
Iteration: 72, Log-Lik: -2466.799, Max-Change: 0.00238
Iteration: 73, Log-Lik: -2466.798, Max-Change: 0.00326
Iteration: 74, Log-Lik: -2466.795, Max-Change: 0.00250
Iteration: 75, Log-Lik: -2466.794, Max-Change: 0.00235
Iteration: 76, Log-Lik: -2466.793, Max-Change: 0.00365
Iteration: 77, Log-Lik: -2466.789, Max-Change: 0.00243
Iteration: 78, Log-Lik: -2466.788, Max-Change: 0.00218
Iteration: 79, Log-Lik: -2466.786, Max-Change: 0.00196
Iteration: 80, Log-Lik: -2466.785, Max-Change: 0.00196
Iteration: 81, Log-Lik: -2466.783, Max-Change: 0.00194
Iteration: 82, Log-Lik: -2466.783, Max-Change: 0.00325
Iteration: 83, Log-Lik: -2466.780, Max-Change: 0.00204
Iteration: 84, Log-Lik: -2466.779, Max-Change: 0.00236
Iteration: 85, Log-Lik: -2466.777, Max-Change: 0.00236
Iteration: 86, Log-Lik: -2466.776, Max-Change: 0.00168
Iteration: 87, Log-Lik: -2466.775, Max-Change: 0.00225
Iteration: 88, Log-Lik: -2466.773, Max-Change: 0.00237
Iteration: 89, Log-Lik: -2466.772, Max-Change: 0.00233
Iteration: 90, Log-Lik: -2466.770, Max-Change: 0.00193
Iteration: 91, Log-Lik: -2466.769, Max-Change: 0.00287
Iteration: 92, Log-Lik: -2466.767, Max-Change: 0.00206
Iteration: 93, Log-Lik: -2466.766, Max-Change: 0.00187
Iteration: 94, Log-Lik: -2466.765, Max-Change: 0.00173
Iteration: 95, Log-Lik: -2466.764, Max-Change: 0.00175
Iteration: 96, Log-Lik: -2466.763, Max-Change: 0.00176
Iteration: 97, Log-Lik: -2466.762, Max-Change: 0.00325
Iteration: 98, Log-Lik: -2466.759, Max-Change: 0.00217
Iteration: 99, Log-Lik: -2466.758, Max-Change: 0.00155
Iteration: 100, Log-Lik: -2466.757, Max-Change: 0.00172
Iteration: 101, Log-Lik: -2466.756, Max-Change: 0.00207
Iteration: 102, Log-Lik: -2466.755, Max-Change: 0.00149
Iteration: 103, Log-Lik: -2466.754, Max-Change: 0.00164
Iteration: 104, Log-Lik: -2466.753, Max-Change: 0.00199
Iteration: 105, Log-Lik: -2466.752, Max-Change: 0.00206
Iteration: 106, Log-Lik: -2466.751, Max-Change: 0.00187
Iteration: 107, Log-Lik: -2466.750, Max-Change: 0.00172
Iteration: 108, Log-Lik: -2466.749, Max-Change: 0.00186
Iteration: 109, Log-Lik: -2466.749, Max-Change: 0.00289
Iteration: 110, Log-Lik: -2466.747, Max-Change: 0.00195
Iteration: 111, Log-Lik: -2466.746, Max-Change: 0.00143
Iteration: 112, Log-Lik: -2466.745, Max-Change: 0.00161
Iteration: 113, Log-Lik: -2466.744, Max-Change: 0.00188
Iteration: 114, Log-Lik: -2466.743, Max-Change: 0.00193
Iteration: 115, Log-Lik: -2466.742, Max-Change: 0.00178
Iteration: 116, Log-Lik: -2466.741, Max-Change: 0.00164
Iteration: 117, Log-Lik: -2466.740, Max-Change: 0.00175
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Iteration: 431, Log-Lik: -2466.621, Max-Change: 0.00079
Iteration: 432, Log-Lik: -2466.621, Max-Change: 0.00091
Iteration: 433, Log-Lik: -2466.620, Max-Change: 0.00247
Iteration: 434, Log-Lik: -2466.620, Max-Change: 0.00060
Iteration: 435, Log-Lik: -2466.620, Max-Change: 0.00087
Iteration: 436, Log-Lik: -2466.619, Max-Change: 0.00129
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Iteration: 440, Log-Lik: -2466.618, Max-Change: 0.00077
Iteration: 441, Log-Lik: -2466.618, Max-Change: 0.00093
Iteration: 442, Log-Lik: -2466.618, Max-Change: 0.00139
Iteration: 443, Log-Lik: -2466.617, Max-Change: 0.00076
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Iteration: 445, Log-Lik: -2466.617, Max-Change: 0.00130
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Iteration: 448, Log-Lik: -2466.616, Max-Change: 0.00143
Iteration: 449, Log-Lik: -2466.616, Max-Change: 0.00077
Iteration: 450, Log-Lik: -2466.616, Max-Change: 0.00094
Iteration: 451, Log-Lik: -2466.615, Max-Change: 0.00128
Iteration: 452, Log-Lik: -2466.615, Max-Change: 0.00078
Iteration: 453, Log-Lik: -2466.615, Max-Change: 0.00091
Iteration: 454, Log-Lik: -2466.615, Max-Change: 0.00146
Iteration: 455, Log-Lik: -2466.614, Max-Change: 0.00078
Iteration: 456, Log-Lik: -2466.614, Max-Change: 0.00095
Iteration: 457, Log-Lik: -2466.614, Max-Change: 0.00126
Iteration: 458, Log-Lik: -2466.614, Max-Change: 0.00078
Iteration: 459, Log-Lik: -2466.613, Max-Change: 0.00091
Iteration: 460, Log-Lik: -2466.613, Max-Change: 0.00239
Iteration: 461, Log-Lik: -2466.613, Max-Change: 0.00061
Iteration: 462, Log-Lik: -2466.612, Max-Change: 0.00087
Iteration: 463, Log-Lik: -2466.612, Max-Change: 0.00130
Iteration: 464, Log-Lik: -2466.612, Max-Change: 0.00077
Iteration: 465, Log-Lik: -2466.612, Max-Change: 0.00092
Iteration: 466, Log-Lik: -2466.611, Max-Change: 0.00133
Iteration: 467, Log-Lik: -2466.611, Max-Change: 0.00077
Iteration: 468, Log-Lik: -2466.611, Max-Change: 0.00092
Iteration: 469, Log-Lik: -2466.611, Max-Change: 0.00139
Iteration: 470, Log-Lik: -2466.610, Max-Change: 0.00076
Iteration: 471, Log-Lik: -2466.610, Max-Change: 0.00093
Iteration: 472, Log-Lik: -2466.610, Max-Change: 0.00129
Iteration: 473, Log-Lik: -2466.610, Max-Change: 0.00077
Iteration: 474, Log-Lik: -2466.609, Max-Change: 0.00091
Iteration: 475, Log-Lik: -2466.609, Max-Change: 0.00143
Iteration: 476, Log-Lik: -2466.609, Max-Change: 0.00077
Iteration: 477, Log-Lik: -2466.609, Max-Change: 0.00094
Iteration: 478, Log-Lik: -2466.608, Max-Change: 0.00127
Iteration: 479, Log-Lik: -2466.608, Max-Change: 0.00077
Iteration: 480, Log-Lik: -2466.608, Max-Change: 0.00091
Iteration: 481, Log-Lik: -2466.608, Max-Change: 0.00145
Iteration: 482, Log-Lik: -2466.607, Max-Change: 0.00077
Iteration: 483, Log-Lik: -2466.607, Max-Change: 0.00094
Iteration: 484, Log-Lik: -2466.607, Max-Change: 0.00126
Iteration: 485, Log-Lik: -2466.607, Max-Change: 0.00077
Iteration: 486, Log-Lik: -2466.606, Max-Change: 0.00091
Iteration: 487, Log-Lik: -2466.606, Max-Change: 0.00147
Iteration: 488, Log-Lik: -2466.606, Max-Change: 0.00078
Iteration: 489, Log-Lik: -2466.606, Max-Change: 0.00094
Iteration: 490, Log-Lik: -2466.605, Max-Change: 0.00125
Iteration: 491, Log-Lik: -2466.605, Max-Change: 0.00077
Iteration: 492, Log-Lik: -2466.605, Max-Change: 0.00090
Iteration: 493, Log-Lik: -2466.605, Max-Change: 0.00239
Iteration: 494, Log-Lik: -2466.604, Max-Change: 0.00060
Iteration: 495, Log-Lik: -2466.604, Max-Change: 0.00086
Iteration: 496, Log-Lik: -2466.604, Max-Change: 0.00129
Iteration: 497, Log-Lik: -2466.603, Max-Change: 0.00076
Iteration: 498, Log-Lik: -2466.603, Max-Change: 0.00091
Iteration: 499, Log-Lik: -2466.603, Max-Change: 0.00133
Iteration: 500, Log-Lik: -2466.603, Max-Change: 0.00076
#> Warning: EM cycles terminated after 500 iterations.
#>
#> Call:
#> mdirt(data = dat, model = 2, customTheta = Theta)
#>
#> Latent class model with 2 classes and 3 profiles.
#> FAILED TO CONVERGE within 1e-04 tolerance after 500 EM iterations.
#> mirt version: 1.44.4
#> M-step optimizer: nlminb
#> EM acceleration: Ramsay
#> Latent density type: discrete
#>
#> Log-likelihood = -2466.602
#> Estimated parameters: 12
#> AIC = 4957.205
#> BIC = 5016.098; SABIC = 4977.985
#> G2 (19) = 21.13, p = 0.3298, RMSEA = 0.011
summary(mod_gom)
#> $Item_1
#> category_1 category_2
#> P[1 0] 0.322 0.678
#> P[0.5 0.5] 0.102 0.898
#> P[0 1] 0.026 0.974
#>
#> $Item_2
#> category_1 category_2
#> P[1 0] 0.692 0.308
#> P[0.5 0.5] 0.386 0.614
#> P[0 1] 0.150 0.850
#>
#> $Item_3
#> category_1 category_2
#> P[1 0] 0.866 0.134
#> P[0.5 0.5] 0.592 0.408
#> P[0 1] 0.247 0.753
#>
#> $Item_4
#> category_1 category_2
#> P[1 0] 0.603 0.397
#> P[0.5 0.5] 0.313 0.687
#> P[0 1] 0.120 0.880
#>
#> $Item_5
#> category_1 category_2
#> P[1 0] 0.398 0.602
#> P[0.5 0.5] 0.171 0.829
#> P[0 1] 0.061 0.939
#>
#> $Class.Probability
#> F1 F2 prob
#> Profile_1 1.0 0.0 0.037
#> Profile_2 0.5 0.5 0.513
#> Profile_3 0.0 1.0 0.450
#>
#-----------------
# Multidimensional discrete latent class model
dat <- key2binary(SAT12,
key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
# define Theta grid for three latent classes
(Theta <- thetaComb(0:1, 3))
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 1 0 0
#> [3,] 0 1 0
#> [4,] 1 1 0
#> [5,] 0 0 1
#> [6,] 1 0 1
#> [7,] 0 1 1
#> [8,] 1 1 1
(mod_discrete <- mdirt(dat, 3, customTheta = Theta))
#>
Iteration: 1, Log-Lik: -13095.734, Max-Change: 3.22686
Iteration: 2, Log-Lik: -9755.059, Max-Change: 2.71698
Iteration: 3, Log-Lik: -9579.691, Max-Change: 1.25062
Iteration: 4, Log-Lik: -9553.061, Max-Change: 0.65725
Iteration: 5, Log-Lik: -9541.293, Max-Change: 0.44295
Iteration: 6, Log-Lik: -9533.462, Max-Change: 0.32826
Iteration: 7, Log-Lik: -9526.302, Max-Change: 0.23613
Iteration: 8, Log-Lik: -9518.892, Max-Change: 0.22465
Iteration: 9, Log-Lik: -9511.816, Max-Change: 0.25353
Iteration: 10, Log-Lik: -9505.855, Max-Change: 0.19403
Iteration: 11, Log-Lik: -9501.226, Max-Change: 0.18620
Iteration: 12, Log-Lik: -9497.328, Max-Change: 0.19801
Iteration: 13, Log-Lik: -9485.632, Max-Change: 0.12541
Iteration: 14, Log-Lik: -9481.386, Max-Change: 0.14234
Iteration: 15, Log-Lik: -9478.520, Max-Change: 0.11810
Iteration: 16, Log-Lik: -9470.621, Max-Change: 0.12233
Iteration: 17, Log-Lik: -9467.373, Max-Change: 0.08084
Iteration: 18, Log-Lik: -9465.136, Max-Change: 0.11006
Iteration: 19, Log-Lik: -9458.281, Max-Change: 0.09830
Iteration: 20, Log-Lik: -9455.141, Max-Change: 0.18132
Iteration: 21, Log-Lik: -9452.372, Max-Change: 0.13551
Iteration: 22, Log-Lik: -9445.887, Max-Change: 0.15291
Iteration: 23, Log-Lik: -9443.501, Max-Change: 0.17948
Iteration: 24, Log-Lik: -9441.744, Max-Change: 0.15519
Iteration: 25, Log-Lik: -9437.171, Max-Change: 0.15811
Iteration: 26, Log-Lik: -9435.024, Max-Change: 0.07509
Iteration: 27, Log-Lik: -9434.613, Max-Change: 0.57613
Iteration: 28, Log-Lik: -9434.091, Max-Change: 0.14597
Iteration: 29, Log-Lik: -9433.822, Max-Change: 0.84837
Iteration: 30, Log-Lik: -9433.503, Max-Change: 0.02450
Iteration: 31, Log-Lik: -9433.477, Max-Change: 0.02663
Iteration: 32, Log-Lik: -9433.318, Max-Change: 0.02154
Iteration: 33, Log-Lik: -9433.194, Max-Change: 0.01903
Iteration: 34, Log-Lik: -9432.941, Max-Change: 0.06555
Iteration: 35, Log-Lik: -9432.746, Max-Change: 0.02253
Iteration: 36, Log-Lik: -9432.709, Max-Change: 0.01798
Iteration: 37, Log-Lik: -9432.656, Max-Change: 0.02955
Iteration: 38, Log-Lik: -9432.620, Max-Change: 0.01746
Iteration: 39, Log-Lik: -9432.600, Max-Change: 0.01500
Iteration: 40, Log-Lik: -9432.568, Max-Change: 0.02499
Iteration: 41, Log-Lik: -9432.546, Max-Change: 0.01582
Iteration: 42, Log-Lik: -9432.530, Max-Change: 0.01441
Iteration: 43, Log-Lik: -9432.507, Max-Change: 0.03430
Iteration: 44, Log-Lik: -9432.470, Max-Change: 0.01997
Iteration: 45, Log-Lik: -9432.454, Max-Change: 0.01578
Iteration: 46, Log-Lik: -9432.431, Max-Change: 0.02496
Iteration: 47, Log-Lik: -9432.411, Max-Change: 0.01744
Iteration: 48, Log-Lik: -9432.395, Max-Change: 0.01587
Iteration: 49, Log-Lik: -9432.371, Max-Change: 0.04101
Iteration: 50, Log-Lik: -9432.326, Max-Change: 0.02314
Iteration: 51, Log-Lik: -9432.303, Max-Change: 0.01994
Iteration: 52, Log-Lik: -9432.268, Max-Change: 0.04015
Iteration: 53, Log-Lik: -9432.227, Max-Change: 0.02473
Iteration: 54, Log-Lik: -9432.203, Max-Change: 0.02234
Iteration: 55, Log-Lik: -9432.167, Max-Change: 0.02883
Iteration: 56, Log-Lik: -9432.138, Max-Change: 0.02439
Iteration: 57, Log-Lik: -9432.111, Max-Change: 0.02335
Iteration: 58, Log-Lik: -9432.066, Max-Change: 0.03093
Iteration: 59, Log-Lik: -9432.034, Max-Change: 0.02890
Iteration: 60, Log-Lik: -9431.999, Max-Change: 0.02733
Iteration: 61, Log-Lik: -9431.935, Max-Change: 0.05068
Iteration: 62, Log-Lik: -9431.879, Max-Change: 0.03640
Iteration: 63, Log-Lik: -9431.839, Max-Change: 0.03343
Iteration: 64, Log-Lik: -9431.780, Max-Change: 0.03968
Iteration: 65, Log-Lik: -9431.731, Max-Change: 0.03738
Iteration: 66, Log-Lik: -9431.681, Max-Change: 0.03700
Iteration: 67, Log-Lik: -9431.612, Max-Change: 0.09519
Iteration: 68, Log-Lik: -9431.469, Max-Change: 0.05397
Iteration: 69, Log-Lik: -9431.407, Max-Change: 0.04807
Iteration: 70, Log-Lik: -9431.321, Max-Change: 0.06880
Iteration: 71, Log-Lik: -9431.246, Max-Change: 0.05308
Iteration: 72, Log-Lik: -9431.181, Max-Change: 0.05092
Iteration: 73, Log-Lik: -9431.093, Max-Change: 0.11416
Iteration: 74, Log-Lik: -9430.937, Max-Change: 0.06476
Iteration: 75, Log-Lik: -9430.869, Max-Change: 0.06480
Iteration: 76, Log-Lik: -9430.781, Max-Change: 0.06873
Iteration: 77, Log-Lik: -9430.716, Max-Change: 0.05743
Iteration: 78, Log-Lik: -9430.658, Max-Change: 0.06035
Iteration: 79, Log-Lik: -9430.570, Max-Change: 0.09839
Iteration: 80, Log-Lik: -9430.473, Max-Change: 0.07400
Iteration: 81, Log-Lik: -9430.416, Max-Change: 0.06223
Iteration: 82, Log-Lik: -9430.350, Max-Change: 0.09178
Iteration: 83, Log-Lik: -9430.282, Max-Change: 0.06842
Iteration: 84, Log-Lik: -9430.238, Max-Change: 0.05465
Iteration: 85, Log-Lik: -9430.191, Max-Change: 0.06697
Iteration: 86, Log-Lik: -9430.152, Max-Change: 0.05672
Iteration: 87, Log-Lik: -9430.122, Max-Change: 0.05414
Iteration: 88, Log-Lik: -9430.093, Max-Change: 0.07441
Iteration: 89, Log-Lik: -9430.040, Max-Change: 0.05108
Iteration: 90, Log-Lik: -9430.018, Max-Change: 0.04561
Iteration: 91, Log-Lik: -9429.998, Max-Change: 0.06249
Iteration: 92, Log-Lik: -9429.967, Max-Change: 0.04110
Iteration: 93, Log-Lik: -9429.952, Max-Change: 0.05644
Iteration: 94, Log-Lik: -9429.935, Max-Change: 0.05073
Iteration: 95, Log-Lik: -9429.914, Max-Change: 0.03645
Iteration: 96, Log-Lik: -9429.902, Max-Change: 0.05490
Iteration: 97, Log-Lik: -9429.884, Max-Change: 0.04800
Iteration: 98, Log-Lik: -9429.871, Max-Change: 0.05109
Iteration: 99, Log-Lik: -9429.858, Max-Change: 0.03139
Iteration: 100, Log-Lik: -9429.849, Max-Change: 0.03078
Iteration: 101, Log-Lik: -9429.841, Max-Change: 0.02435
Iteration: 102, Log-Lik: -9429.835, Max-Change: 0.02368
Iteration: 103, Log-Lik: -9429.829, Max-Change: 0.04141
Iteration: 104, Log-Lik: -9429.817, Max-Change: 0.02622
Iteration: 105, Log-Lik: -9429.812, Max-Change: 0.03805
Iteration: 106, Log-Lik: -9429.805, Max-Change: 0.03118
Iteration: 107, Log-Lik: -9429.798, Max-Change: 0.03604
Iteration: 108, Log-Lik: -9429.791, Max-Change: 0.01818
Iteration: 109, Log-Lik: -9429.787, Max-Change: 0.02078
Iteration: 110, Log-Lik: -9429.783, Max-Change: 0.01713
Iteration: 111, Log-Lik: -9429.780, Max-Change: 0.01950
Iteration: 112, Log-Lik: -9429.778, Max-Change: 0.03393
Iteration: 113, Log-Lik: -9429.770, Max-Change: 0.02654
Iteration: 114, Log-Lik: -9429.766, Max-Change: 0.01733
Iteration: 115, Log-Lik: -9429.763, Max-Change: 0.01288
Iteration: 116, Log-Lik: -9429.761, Max-Change: 0.02667
Iteration: 117, Log-Lik: -9429.757, Max-Change: 0.01562
Iteration: 118, Log-Lik: -9429.755, Max-Change: 0.01216
Iteration: 119, Log-Lik: -9429.753, Max-Change: 0.01525
Iteration: 120, Log-Lik: -9429.751, Max-Change: 0.01493
Iteration: 121, Log-Lik: -9429.749, Max-Change: 0.02219
Iteration: 122, Log-Lik: -9429.745, Max-Change: 0.01601
Iteration: 123, Log-Lik: -9429.743, Max-Change: 0.01460
Iteration: 124, Log-Lik: -9429.743, Max-Change: 0.00940
Iteration: 125, Log-Lik: -9429.739, Max-Change: 0.02407
Iteration: 126, Log-Lik: -9429.736, Max-Change: 0.01375
Iteration: 127, Log-Lik: -9429.734, Max-Change: 0.01029
Iteration: 128, Log-Lik: -9429.733, Max-Change: 0.01660
Iteration: 129, Log-Lik: -9429.731, Max-Change: 0.00641
Iteration: 130, Log-Lik: -9429.730, Max-Change: 0.00865
Iteration: 131, Log-Lik: -9429.729, Max-Change: 0.00640
Iteration: 132, Log-Lik: -9429.728, Max-Change: 0.01738
Iteration: 133, Log-Lik: -9429.726, Max-Change: 0.00608
Iteration: 134, Log-Lik: -9429.725, Max-Change: 0.02071
Iteration: 135, Log-Lik: -9429.723, Max-Change: 0.00615
Iteration: 136, Log-Lik: -9429.722, Max-Change: 0.01189
Iteration: 137, Log-Lik: -9429.721, Max-Change: 0.00257
Iteration: 138, Log-Lik: -9429.720, Max-Change: 0.01938
Iteration: 139, Log-Lik: -9429.718, Max-Change: 0.01593
Iteration: 140, Log-Lik: -9429.716, Max-Change: 0.00365
Iteration: 141, Log-Lik: -9429.716, Max-Change: 0.00240
Iteration: 142, Log-Lik: -9429.715, Max-Change: 0.00000
#>
#> Call:
#> mdirt(data = dat, model = 3, customTheta = Theta)
#>
#> Latent class model with 3 classes and 8 profiles.
#> Converged within 1e-04 tolerance after 142 EM iterations.
#> mirt version: 1.44.4
#> M-step optimizer: nlminb
#> EM acceleration: Ramsay
#> Latent density type: discrete
#>
#> Log-likelihood = -9429.715
#> Estimated parameters: 103
#> AIC = 19065.43
#> BIC = 19518.31; SABIC = 19191.32
#> G2 (4294967192) = 11189.71, p = 1, RMSEA = 0
summary(mod_discrete)
#> $Item.1
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.868 0.132
#> P[0 1 0] 0.460 0.540
#> P[1 1 0] 0.849 0.151
#> P[0 0 1] 0.341 0.659
#> P[1 0 1] 0.773 0.227
#> P[0 1 1] 0.306 0.694
#> P[1 1 1] 0.744 0.256
#>
#> $Item.2
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.945 0.055
#> P[0 1 0] 0.165 0.835
#> P[1 1 0] 0.774 0.226
#> P[0 0 1] 0.072 0.928
#> P[1 0 1] 0.575 0.425
#> P[0 1 1] 0.015 0.985
#> P[1 1 1] 0.211 0.789
#>
#> $Item.3
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.929 0.071
#> P[0 1 0] 0.337 0.663
#> P[1 1 0] 0.870 0.130
#> P[0 0 1] 0.271 0.729
#> P[1 0 1] 0.830 0.170
#> P[0 1 1] 0.159 0.841
#> P[1 1 1] 0.713 0.287
#>
#> $Item.4
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.844 0.156
#> P[0 1 0] 0.223 0.777
#> P[1 1 0] 0.609 0.391
#> P[0 0 1] 0.428 0.572
#> P[1 0 1] 0.802 0.198
#> P[0 1 1] 0.177 0.823
#> P[1 1 1] 0.538 0.462
#>
#> $Item.5
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.837 0.163
#> P[0 1 0] 0.263 0.737
#> P[1 1 0] 0.647 0.353
#> P[0 0 1] 0.137 0.863
#> P[1 0 1] 0.449 0.551
#> P[0 1 1] 0.053 0.947
#> P[1 1 1] 0.225 0.775
#>
#> $Item.6
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.943 0.057
#> P[0 1 0] 0.334 0.666
#> P[1 1 0] 0.893 0.107
#> P[0 0 1] 0.473 0.527
#> P[1 0 1] 0.937 0.063
#> P[0 1 1] 0.311 0.689
#> P[1 1 1] 0.882 0.118
#>
#> $Item.7
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.766 0.234
#> P[0 1 0] 0.283 0.717
#> P[1 1 0] 0.563 0.437
#> P[0 0 1] 0.088 0.912
#> P[1 0 1] 0.240 0.760
#> P[0 1 1] 0.037 0.963
#> P[1 1 1] 0.111 0.889
#>
#> $Item.8
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.866 0.134
#> P[0 1 0] 0.573 0.427
#> P[1 1 0] 0.897 0.103
#> P[0 0 1] 0.422 0.578
#> P[1 0 1] 0.825 0.175
#> P[0 1 1] 0.495 0.505
#> P[1 1 1] 0.864 0.136
#>
#> $Item.9
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.457 0.543
#> P[0 1 0] 0.252 0.748
#> P[1 1 0] 0.221 0.779
#> P[0 0 1] 0.144 0.856
#> P[1 0 1] 0.124 0.876
#> P[0 1 1] 0.054 0.946
#> P[1 1 1] 0.046 0.954
#>
#> $Item.10
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.904 0.096
#> P[0 1 0] 0.298 0.702
#> P[1 1 0] 0.800 0.200
#> P[0 0 1] 0.189 0.811
#> P[1 0 1] 0.686 0.314
#> P[0 1 1] 0.090 0.910
#> P[1 1 1] 0.482 0.518
#>
#> $Item.11
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.989 0.011
#> P[0 1 0] 0.000 1.000
#> P[1 1 0] 0.039 0.961
#> P[0 0 1] 0.000 1.000
#> P[1 0 1] 0.014 0.986
#> P[0 1 1] 0.000 1.000
#> P[1 1 1] 0.000 1.000
#>
#> $Item.12
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.621 0.379
#> P[0 1 0] 0.434 0.566
#> P[1 1 0] 0.557 0.443
#> P[0 0 1] 0.523 0.477
#> P[1 0 1] 0.643 0.357
#> P[0 1 1] 0.457 0.543
#> P[1 1 1] 0.580 0.420
#>
#> $Item.13
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.849 0.151
#> P[0 1 0] 0.316 0.684
#> P[1 1 0] 0.722 0.278
#> P[0 0 1] 0.087 0.913
#> P[1 0 1] 0.348 0.652
#> P[0 1 1] 0.042 0.958
#> P[1 1 1] 0.198 0.802
#>
#> $Item.14
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.857 0.143
#> P[0 1 0] 0.108 0.892
#> P[1 1 0] 0.421 0.579
#> P[0 0 1] 0.112 0.888
#> P[1 0 1] 0.432 0.568
#> P[0 1 1] 0.015 0.985
#> P[1 1 1] 0.085 0.915
#>
#> $Item.15
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.742 0.258
#> P[0 1 0] 0.289 0.711
#> P[1 1 0] 0.539 0.461
#> P[0 0 1] 0.054 0.946
#> P[1 0 1] 0.141 0.859
#> P[0 1 1] 0.023 0.977
#> P[1 1 1] 0.062 0.938
#>
#> $Item.16
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.846 0.154
#> P[0 1 0] 0.298 0.702
#> P[1 1 0] 0.700 0.300
#> P[0 0 1] 0.315 0.685
#> P[1 0 1] 0.716 0.284
#> P[0 1 1] 0.164 0.836
#> P[1 1 1] 0.517 0.483
#>
#> $Item.17
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.695 0.305
#> P[0 1 0] 0.061 0.939
#> P[1 1 0] 0.130 0.870
#> P[0 0 1] 0.008 0.992
#> P[1 0 1] 0.018 0.982
#> P[0 1 1] 0.001 0.999
#> P[1 1 1] 0.001 0.999
#>
#> $Item.18
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.977 0.023
#> P[0 1 0] 0.217 0.783
#> P[1 1 0] 0.922 0.078
#> P[0 0 1] 0.090 0.910
#> P[1 0 1] 0.808 0.192
#> P[0 1 1] 0.027 0.973
#> P[1 1 1] 0.539 0.461
#>
#> $Item.19
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.830 0.170
#> P[0 1 0] 0.291 0.709
#> P[1 1 0] 0.668 0.332
#> P[0 0 1] 0.200 0.800
#> P[1 0 1] 0.550 0.450
#> P[0 1 1] 0.093 0.907
#> P[1 1 1] 0.334 0.666
#>
#> $Item.20
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.918 0.082
#> P[0 1 0] 0.038 0.962
#> P[1 1 0] 0.306 0.694
#> P[0 0 1] 0.017 0.983
#> P[1 0 1] 0.164 0.836
#> P[0 1 1] 0.001 0.999
#> P[1 1 1] 0.008 0.992
#>
#> $Item.21
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.434 0.566
#> P[0 1 0] 0.223 0.777
#> P[1 1 0] 0.180 0.820
#> P[0 0 1] 0.110 0.890
#> P[1 0 1] 0.086 0.914
#> P[0 1 1] 0.034 0.966
#> P[1 1 1] 0.026 0.974
#>
#> $Item.22
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.997 0.003
#> P[0 1 0] 0.001 0.999
#> P[1 1 0] 0.209 0.791
#> P[0 0 1] 0.000 1.000
#> P[1 0 1] 0.055 0.945
#> P[0 1 1] 0.000 1.000
#> P[1 1 1] 0.000 1.000
#>
#> $Item.23
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.864 0.136
#> P[0 1 0] 0.284 0.716
#> P[1 1 0] 0.717 0.283
#> P[0 0 1] 0.422 0.578
#> P[1 0 1] 0.823 0.177
#> P[0 1 1] 0.225 0.775
#> P[1 1 1] 0.649 0.351
#>
#> $Item.24
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.825 0.175
#> P[0 1 0] 0.300 0.700
#> P[1 1 0] 0.668 0.332
#> P[0 0 1] 0.068 0.932
#> P[1 0 1] 0.256 0.744
#> P[0 1 1] 0.030 0.970
#> P[1 1 1] 0.129 0.871
#>
#> $Item.25
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.869 0.131
#> P[0 1 0] 0.350 0.650
#> P[1 1 0] 0.782 0.218
#> P[0 0 1] 0.280 0.720
#> P[1 0 1] 0.721 0.279
#> P[0 1 1] 0.174 0.826
#> P[1 1 1] 0.583 0.417
#>
#> $Item.26
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.967 0.033
#> P[0 1 0] 0.140 0.860
#> P[1 1 0] 0.825 0.175
#> P[0 0 1] 0.093 0.907
#> P[1 0 1] 0.748 0.252
#> P[0 1 1] 0.016 0.984
#> P[1 1 1] 0.326 0.674
#>
#> $Item.27
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.839 0.161
#> P[0 1 0] 0.136 0.864
#> P[1 1 0] 0.451 0.549
#> P[0 0 1] 0.023 0.977
#> P[1 0 1] 0.110 0.890
#> P[0 1 1] 0.004 0.996
#> P[1 1 1] 0.019 0.981
#>
#> $Item.28
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.888 0.112
#> P[0 1 0] 0.222 0.778
#> P[1 1 0] 0.693 0.307
#> P[0 0 1] 0.163 0.837
#> P[1 0 1] 0.606 0.394
#> P[0 1 1] 0.053 0.947
#> P[1 1 1] 0.305 0.695
#>
#> $Item.29
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.893 0.107
#> P[0 1 0] 0.292 0.708
#> P[1 1 0] 0.774 0.226
#> P[0 0 1] 0.323 0.677
#> P[1 0 1] 0.799 0.201
#> P[0 1 1] 0.164 0.836
#> P[1 1 1] 0.620 0.380
#>
#> $Item.30
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.698 0.302
#> P[0 1 0] 0.455 0.545
#> P[1 1 0] 0.659 0.341
#> P[0 0 1] 0.378 0.622
#> P[1 0 1] 0.584 0.416
#> P[0 1 1] 0.336 0.664
#> P[1 1 1] 0.540 0.460
#>
#> $Item.31
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.977 0.023
#> P[0 1 0] 0.024 0.976
#> P[1 1 0] 0.509 0.491
#> P[0 0 1] 0.005 0.995
#> P[1 0 1] 0.166 0.834
#> P[0 1 1] 0.000 1.000
#> P[1 1 1] 0.005 0.995
#>
#> $Item.32
#> category_1 category_2
#> P[0 0 0] 0.500 0.500
#> P[1 0 0] 0.728 0.272
#> P[0 1 0] 0.568 0.432
#> P[1 1 0] 0.779 0.221
#> P[0 0 1] 0.702 0.298
#> P[1 0 1] 0.863 0.137
#> P[0 1 1] 0.755 0.245
#> P[1 1 1] 0.892 0.108
#>
#> $Class.Probability
#> F1 F2 F3 prob
#> Profile_1 0 0 0 0.000
#> Profile_2 1 0 0 0.004
#> Profile_3 0 1 0 0.002
#> Profile_4 1 1 0 0.194
#> Profile_5 0 0 1 0.084
#> Profile_6 1 0 1 0.368
#> Profile_7 0 1 1 0.058
#> Profile_8 1 1 1 0.290
#>
# Located latent class model
model <- mirt.model('C1 = 1-32
C2 = 1-32
C3 = 1-32
CONSTRAIN = (1-32, a1), (1-32, a2), (1-32, a3)')
(mod_located <- mdirt(dat, model, customTheta = diag(3)))
#>
Iteration: 1, Log-Lik: -13258.809, Max-Change: 1.94332
Iteration: 2, Log-Lik: -12792.570, Max-Change: 0.18446
Iteration: 3, Log-Lik: -12783.893, Max-Change: 0.13917
Iteration: 4, Log-Lik: -12779.420, Max-Change: 0.09224
Iteration: 5, Log-Lik: -12777.102, Max-Change: 0.08104
Iteration: 6, Log-Lik: -12775.794, Max-Change: 0.06339
Iteration: 7, Log-Lik: -12774.879, Max-Change: 0.08224
Iteration: 8, Log-Lik: -12774.265, Max-Change: 0.04692
Iteration: 9, Log-Lik: -12774.073, Max-Change: 0.03533
Iteration: 10, Log-Lik: -12774.012, Max-Change: 0.09661
Iteration: 11, Log-Lik: -12773.613, Max-Change: 0.03324
Iteration: 12, Log-Lik: -12773.535, Max-Change: 0.02356
Iteration: 13, Log-Lik: -12773.451, Max-Change: 0.03011
Iteration: 14, Log-Lik: -12773.389, Max-Change: 0.02693
Iteration: 15, Log-Lik: -12773.332, Max-Change: 0.02030
Iteration: 16, Log-Lik: -12773.261, Max-Change: 0.05565
Iteration: 17, Log-Lik: -12773.149, Max-Change: 0.02016
Iteration: 18, Log-Lik: -12773.110, Max-Change: 0.01920
Iteration: 19, Log-Lik: -12773.073, Max-Change: 0.05678
Iteration: 20, Log-Lik: -12772.954, Max-Change: 0.01618
Iteration: 21, Log-Lik: -12772.926, Max-Change: 0.01470
Iteration: 22, Log-Lik: -12772.886, Max-Change: 0.03411
Iteration: 23, Log-Lik: -12772.833, Max-Change: 0.01341
Iteration: 24, Log-Lik: -12772.810, Max-Change: 0.01334
Iteration: 25, Log-Lik: -12772.789, Max-Change: 0.04585
Iteration: 26, Log-Lik: -12772.710, Max-Change: 0.01097
Iteration: 27, Log-Lik: -12772.690, Max-Change: 0.01197
Iteration: 28, Log-Lik: -12772.663, Max-Change: 0.02144
Iteration: 29, Log-Lik: -12772.637, Max-Change: 0.01091
Iteration: 30, Log-Lik: -12772.620, Max-Change: 0.01119
Iteration: 31, Log-Lik: -12772.595, Max-Change: 0.02159
Iteration: 32, Log-Lik: -12772.567, Max-Change: 0.01006
Iteration: 33, Log-Lik: -12772.553, Max-Change: 0.01012
Iteration: 34, Log-Lik: -12772.541, Max-Change: 0.03370
Iteration: 35, Log-Lik: -12772.488, Max-Change: 0.00925
Iteration: 36, Log-Lik: -12772.475, Max-Change: 0.01061
Iteration: 37, Log-Lik: -12772.454, Max-Change: 0.01352
Iteration: 38, Log-Lik: -12772.439, Max-Change: 0.00892
Iteration: 39, Log-Lik: -12772.428, Max-Change: 0.01086
Iteration: 40, Log-Lik: -12772.409, Max-Change: 0.01147
Iteration: 41, Log-Lik: -12772.397, Max-Change: 0.00829
Iteration: 42, Log-Lik: -12772.386, Max-Change: 0.00747
Iteration: 43, Log-Lik: -12772.382, Max-Change: 0.03189
Iteration: 44, Log-Lik: -12772.332, Max-Change: 0.00750
Iteration: 45, Log-Lik: -12772.322, Max-Change: 0.00937
Iteration: 46, Log-Lik: -12772.304, Max-Change: 0.01608
Iteration: 47, Log-Lik: -12772.287, Max-Change: 0.00935
Iteration: 48, Log-Lik: -12772.277, Max-Change: 0.00597
Iteration: 49, Log-Lik: -12772.264, Max-Change: 0.01103
Iteration: 50, Log-Lik: -12772.253, Max-Change: 0.00949
Iteration: 51, Log-Lik: -12772.243, Max-Change: 0.00586
Iteration: 52, Log-Lik: -12772.230, Max-Change: 0.01034
Iteration: 53, Log-Lik: -12772.219, Max-Change: 0.00647
Iteration: 54, Log-Lik: -12772.211, Max-Change: 0.00652
Iteration: 55, Log-Lik: -12772.200, Max-Change: 0.02111
Iteration: 56, Log-Lik: -12772.175, Max-Change: 0.00644
Iteration: 57, Log-Lik: -12772.167, Max-Change: 0.00636
Iteration: 58, Log-Lik: -12772.157, Max-Change: 0.02092
Iteration: 59, Log-Lik: -12772.132, Max-Change: 0.00768
Iteration: 60, Log-Lik: -12772.125, Max-Change: 0.00558
Iteration: 61, Log-Lik: -12772.113, Max-Change: 0.00882
Iteration: 62, Log-Lik: -12772.104, Max-Change: 0.01088
Iteration: 63, Log-Lik: -12772.098, Max-Change: 0.00357
Iteration: 64, Log-Lik: -12772.089, Max-Change: 0.00453
Iteration: 65, Log-Lik: -12772.081, Max-Change: 0.00749
Iteration: 66, Log-Lik: -12772.074, Max-Change: 0.00525
Iteration: 67, Log-Lik: -12772.064, Max-Change: 0.00779
Iteration: 68, Log-Lik: -12772.055, Max-Change: 0.00631
Iteration: 69, Log-Lik: -12772.048, Max-Change: 0.00772
Iteration: 70, Log-Lik: -12772.037, Max-Change: 0.00585
Iteration: 71, Log-Lik: -12772.030, Max-Change: 0.00753
Iteration: 72, Log-Lik: -12772.022, Max-Change: 0.00598
Iteration: 73, Log-Lik: -12772.011, Max-Change: 0.01712
Iteration: 74, Log-Lik: -12771.994, Max-Change: 0.00572
Iteration: 75, Log-Lik: -12771.986, Max-Change: 0.00591
Iteration: 76, Log-Lik: -12771.980, Max-Change: 0.02070
Iteration: 77, Log-Lik: -12771.952, Max-Change: 0.00744
Iteration: 78, Log-Lik: -12771.945, Max-Change: 0.00690
Iteration: 79, Log-Lik: -12771.935, Max-Change: 0.01384
Iteration: 80, Log-Lik: -12771.918, Max-Change: 0.00650
Iteration: 81, Log-Lik: -12771.911, Max-Change: 0.00690
Iteration: 82, Log-Lik: -12771.900, Max-Change: 0.00763
Iteration: 83, Log-Lik: -12771.892, Max-Change: 0.00647
Iteration: 84, Log-Lik: -12771.886, Max-Change: 0.00526
Iteration: 85, Log-Lik: -12771.875, Max-Change: 0.00920
Iteration: 86, Log-Lik: -12771.867, Max-Change: 0.00515
Iteration: 87, Log-Lik: -12771.861, Max-Change: 0.00518
Iteration: 88, Log-Lik: -12771.850, Max-Change: 0.01377
Iteration: 89, Log-Lik: -12771.837, Max-Change: 0.00628
Iteration: 90, Log-Lik: -12771.830, Max-Change: 0.00665
Iteration: 91, Log-Lik: -12771.823, Max-Change: 0.01414
Iteration: 92, Log-Lik: -12771.804, Max-Change: 0.00508
Iteration: 93, Log-Lik: -12771.797, Max-Change: 0.00520
Iteration: 94, Log-Lik: -12771.790, Max-Change: 0.01992
Iteration: 95, Log-Lik: -12771.767, Max-Change: 0.00571
Iteration: 96, Log-Lik: -12771.761, Max-Change: 0.00538
Iteration: 97, Log-Lik: -12771.752, Max-Change: 0.01715
Iteration: 98, Log-Lik: -12771.734, Max-Change: 0.00517
Iteration: 99, Log-Lik: -12771.727, Max-Change: 0.00517
Iteration: 100, Log-Lik: -12771.718, Max-Change: 0.01465
Iteration: 101, Log-Lik: -12771.702, Max-Change: 0.00611
Iteration: 102, Log-Lik: -12771.695, Max-Change: 0.00507
Iteration: 103, Log-Lik: -12771.688, Max-Change: 0.00536
Iteration: 104, Log-Lik: -12771.683, Max-Change: 0.00528
Iteration: 105, Log-Lik: -12771.677, Max-Change: 0.00446
Iteration: 106, Log-Lik: -12771.667, Max-Change: 0.00872
Iteration: 107, Log-Lik: -12771.660, Max-Change: 0.00517
Iteration: 108, Log-Lik: -12771.654, Max-Change: 0.00520
Iteration: 109, Log-Lik: -12771.647, Max-Change: 0.01701
Iteration: 110, Log-Lik: -12771.627, Max-Change: 0.00528
Iteration: 111, Log-Lik: -12771.621, Max-Change: 0.00438
Iteration: 112, Log-Lik: -12771.612, Max-Change: 0.00727
Iteration: 113, Log-Lik: -12771.605, Max-Change: 0.00507
Iteration: 114, Log-Lik: -12771.600, Max-Change: 0.00514
Iteration: 115, Log-Lik: -12771.592, Max-Change: 0.01542
Iteration: 116, Log-Lik: -12771.575, Max-Change: 0.00511
Iteration: 117, Log-Lik: -12771.570, Max-Change: 0.00425
Iteration: 118, Log-Lik: -12771.562, Max-Change: 0.00579
Iteration: 119, Log-Lik: -12771.556, Max-Change: 0.00495
Iteration: 120, Log-Lik: -12771.551, Max-Change: 0.00502
Iteration: 121, Log-Lik: -12771.542, Max-Change: 0.01399
Iteration: 122, Log-Lik: -12771.529, Max-Change: 0.00400
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Iteration: 135, Log-Lik: -12771.448, Max-Change: 0.00486
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Iteration: 137, Log-Lik: -12771.427, Max-Change: 0.00461
Iteration: 138, Log-Lik: -12771.422, Max-Change: 0.00374
Iteration: 139, Log-Lik: -12771.415, Max-Change: 0.00614
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Iteration: 143, Log-Lik: -12771.395, Max-Change: 0.00449
Iteration: 144, Log-Lik: -12771.391, Max-Change: 0.00325
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Iteration: 149, Log-Lik: -12771.364, Max-Change: 0.00433
Iteration: 150, Log-Lik: -12771.360, Max-Change: 0.00286
Iteration: 151, Log-Lik: -12771.355, Max-Change: 0.00434
Iteration: 152, Log-Lik: -12771.350, Max-Change: 0.00447
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Iteration: 156, Log-Lik: -12771.332, Max-Change: 0.00441
Iteration: 157, Log-Lik: -12771.327, Max-Change: 0.00514
Iteration: 158, Log-Lik: -12771.322, Max-Change: 0.00350
Iteration: 159, Log-Lik: -12771.319, Max-Change: 0.00424
Iteration: 160, Log-Lik: -12771.314, Max-Change: 0.00370
Iteration: 161, Log-Lik: -12771.310, Max-Change: 0.00426
Iteration: 162, Log-Lik: -12771.306, Max-Change: 0.00309
Iteration: 163, Log-Lik: -12771.301, Max-Change: 0.00572
Iteration: 164, Log-Lik: -12771.296, Max-Change: 0.00412
Iteration: 165, Log-Lik: -12771.293, Max-Change: 0.00266
Iteration: 166, Log-Lik: -12771.289, Max-Change: 0.00387
Iteration: 167, Log-Lik: -12771.285, Max-Change: 0.00419
Iteration: 168, Log-Lik: -12771.282, Max-Change: 0.00271
Iteration: 169, Log-Lik: -12771.278, Max-Change: 0.00434
Iteration: 170, Log-Lik: -12771.274, Max-Change: 0.00268
Iteration: 171, Log-Lik: -12771.271, Max-Change: 0.00396
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Iteration: 364, Log-Lik: -12771.077, Max-Change: 0.00000
#>
#> Call:
#> mdirt(data = dat, model = model, customTheta = diag(3))
#>
#> Latent class model with 3 classes and 3 profiles.
#> Converged within 1e-04 tolerance after 364 EM iterations.
#> mirt version: 1.44.4
#> M-step optimizer: nlminb
#> EM acceleration: Ramsay
#> Latent density type: discrete
#>
#> Log-likelihood = -12771.08
#> Estimated parameters: 5
#> AIC = 25552.15
#> BIC = 25574.14; SABIC = 25558.26
#> G2 (4294967290) = 17872.43, p = 1, RMSEA = 0
summary(mod_located)
#> $Item.1
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.2
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.3
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.4
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.5
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.6
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.7
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.8
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.9
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.10
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.11
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.12
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.13
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.14
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.15
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.16
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.17
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.18
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.19
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.20
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.21
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.22
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.23
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.24
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.25
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.26
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.27
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.28
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.29
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.30
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.31
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Item.32
#> category_1 category_2
#> P[1 0 0] 0.578 0.422
#> P[0 1 0] 0.410 0.590
#> P[0 0 1] 0.190 0.810
#>
#> $Class.Probability
#> C1 C2 C3 prob
#> Profile_1 1 0 0 0.339
#> Profile_2 0 1 0 0.498
#> Profile_3 0 0 1 0.164
#>
#-----------------
### DINA model example
# generate some suitable data for a two dimensional DINA application
# (first columns are intercepts)
set.seed(1)
Theta <- expand.table(matrix(c(1,0,0,0,
1,1,0,0,
1,0,1,0,
1,1,1,1), 4, 4, byrow=TRUE),
freq = c(200,200,100,500))
a <- matrix(c(rnorm(15, -1.5, .5), rlnorm(5, .2, .3), numeric(15), rlnorm(5, .2, .3),
numeric(15), rlnorm(5, .2, .3)), 15, 4)
guess <- plogis(a[11:15,1]) # population guess
slip <- 1 - plogis(rowSums(a[11:15,])) # population slip
dat <- simdata(a, Theta=Theta, itemtype = 'lca')
# first column is the intercept, 2nd and 3rd are attributes
theta <- cbind(1, thetaComb(0:1, 2))
theta <- cbind(theta, theta[,2] * theta[,3]) #DINA interaction of main attributes
model <- mirt.model('Intercept = 1-15
A1 = 1-5
A2 = 6-10
A1A2 = 11-15')
# last 5 items are DINA (first 10 are unidimensional C-RUMs)
DINA <- mdirt(dat, model, customTheta = theta)
#>
Iteration: 1, Log-Lik: -13247.652, Max-Change: 2.92936
Iteration: 2, Log-Lik: -9318.778, Max-Change: 0.35829
Iteration: 3, Log-Lik: -9294.365, Max-Change: 0.28513
Iteration: 4, Log-Lik: -9281.914, Max-Change: 0.21152
Iteration: 5, Log-Lik: -9272.301, Max-Change: 0.18434
Iteration: 6, Log-Lik: -9263.063, Max-Change: 0.18260
Iteration: 7, Log-Lik: -9253.943, Max-Change: 0.18190
Iteration: 8, Log-Lik: -9245.572, Max-Change: 0.16797
Iteration: 9, Log-Lik: -9238.782, Max-Change: 0.14236
Iteration: 10, Log-Lik: -9233.874, Max-Change: 0.11263
Iteration: 11, Log-Lik: -9230.580, Max-Change: 0.08422
Iteration: 12, Log-Lik: -9228.425, Max-Change: 0.06077
Iteration: 13, Log-Lik: -9226.341, Max-Change: 0.07998
Iteration: 14, Log-Lik: -9225.386, Max-Change: 0.05160
Iteration: 15, Log-Lik: -9224.797, Max-Change: 0.04726
Iteration: 16, Log-Lik: -9224.586, Max-Change: 0.08829
Iteration: 17, Log-Lik: -9223.521, Max-Change: 0.04078
Iteration: 18, Log-Lik: -9223.207, Max-Change: 0.03739
Iteration: 19, Log-Lik: -9223.195, Max-Change: 0.06968
Iteration: 20, Log-Lik: -9222.520, Max-Change: 0.03113
Iteration: 21, Log-Lik: -9222.352, Max-Change: 0.02879
Iteration: 22, Log-Lik: -9222.265, Max-Change: 0.04934
Iteration: 23, Log-Lik: -9221.983, Max-Change: 0.02420
Iteration: 24, Log-Lik: -9221.882, Max-Change: 0.02269
Iteration: 25, Log-Lik: -9221.793, Max-Change: 0.03204
Iteration: 26, Log-Lik: -9221.676, Max-Change: 0.01949
Iteration: 27, Log-Lik: -9221.611, Max-Change: 0.01871
Iteration: 28, Log-Lik: -9221.600, Max-Change: 0.03308
Iteration: 29, Log-Lik: -9221.449, Max-Change: 0.01563
Iteration: 30, Log-Lik: -9221.406, Max-Change: 0.01483
Iteration: 31, Log-Lik: -9221.365, Max-Change: 0.02025
Iteration: 32, Log-Lik: -9221.319, Max-Change: 0.01280
Iteration: 33, Log-Lik: -9221.289, Max-Change: 0.01186
Iteration: 34, Log-Lik: -9221.281, Max-Change: 0.02219
Iteration: 35, Log-Lik: -9221.213, Max-Change: 0.01096
Iteration: 36, Log-Lik: -9221.191, Max-Change: 0.00972
Iteration: 37, Log-Lik: -9221.177, Max-Change: 0.01454
Iteration: 38, Log-Lik: -9221.145, Max-Change: 0.00787
Iteration: 39, Log-Lik: -9221.130, Max-Change: 0.00815
Iteration: 40, Log-Lik: -9221.116, Max-Change: 0.01169
Iteration: 41, Log-Lik: -9221.095, Max-Change: 0.00645
Iteration: 42, Log-Lik: -9221.082, Max-Change: 0.00715
Iteration: 43, Log-Lik: -9221.069, Max-Change: 0.00891
Iteration: 44, Log-Lik: -9221.057, Max-Change: 0.00584
Iteration: 45, Log-Lik: -9221.047, Max-Change: 0.00621
Iteration: 46, Log-Lik: -9221.039, Max-Change: 0.00553
Iteration: 47, Log-Lik: -9221.030, Max-Change: 0.00617
Iteration: 48, Log-Lik: -9221.021, Max-Change: 0.00522
Iteration: 49, Log-Lik: -9221.013, Max-Change: 0.00495
Iteration: 50, Log-Lik: -9221.007, Max-Change: 0.00522
Iteration: 51, Log-Lik: -9221.000, Max-Change: 0.00498
Iteration: 52, Log-Lik: -9220.993, Max-Change: 0.00495
Iteration: 53, Log-Lik: -9220.988, Max-Change: 0.00425
Iteration: 54, Log-Lik: -9220.983, Max-Change: 0.00443
Iteration: 55, Log-Lik: -9220.978, Max-Change: 0.00432
Iteration: 56, Log-Lik: -9220.973, Max-Change: 0.00450
Iteration: 57, Log-Lik: -9220.968, Max-Change: 0.00412
Iteration: 58, Log-Lik: -9220.964, Max-Change: 0.00401
Iteration: 59, Log-Lik: -9220.960, Max-Change: 0.00397
Iteration: 60, Log-Lik: -9220.956, Max-Change: 0.00380
Iteration: 61, Log-Lik: -9220.952, Max-Change: 0.00456
Iteration: 62, Log-Lik: -9220.947, Max-Change: 0.00384
Iteration: 63, Log-Lik: -9220.944, Max-Change: 0.00351
Iteration: 64, Log-Lik: -9220.942, Max-Change: 0.00477
Iteration: 65, Log-Lik: -9220.937, Max-Change: 0.00371
Iteration: 66, Log-Lik: -9220.934, Max-Change: 0.00335
Iteration: 67, Log-Lik: -9220.934, Max-Change: 0.00564
Iteration: 68, Log-Lik: -9220.928, Max-Change: 0.00352
Iteration: 69, Log-Lik: -9220.925, Max-Change: 0.00320
Iteration: 70, Log-Lik: -9220.923, Max-Change: 0.00304
Iteration: 71, Log-Lik: -9220.921, Max-Change: 0.00278
Iteration: 72, Log-Lik: -9220.919, Max-Change: 0.00298
Iteration: 73, Log-Lik: -9220.918, Max-Change: 0.00333
Iteration: 74, Log-Lik: -9220.915, Max-Change: 0.00257
Iteration: 75, Log-Lik: -9220.914, Max-Change: 0.00267
Iteration: 76, Log-Lik: -9220.913, Max-Change: 0.00300
Iteration: 77, Log-Lik: -9220.911, Max-Change: 0.00235
Iteration: 78, Log-Lik: -9220.910, Max-Change: 0.00221
Iteration: 79, Log-Lik: -9220.909, Max-Change: 0.00322
Iteration: 80, Log-Lik: -9220.907, Max-Change: 0.00208
Iteration: 81, Log-Lik: -9220.906, Max-Change: 0.00213
Iteration: 82, Log-Lik: -9220.905, Max-Change: 0.00275
Iteration: 83, Log-Lik: -9220.903, Max-Change: 0.00216
Iteration: 84, Log-Lik: -9220.902, Max-Change: 0.00203
Iteration: 85, Log-Lik: -9220.902, Max-Change: 0.00190
Iteration: 86, Log-Lik: -9220.901, Max-Change: 0.00175
Iteration: 87, Log-Lik: -9220.900, Max-Change: 0.00167
Iteration: 88, Log-Lik: -9220.900, Max-Change: 0.00246
Iteration: 89, Log-Lik: -9220.898, Max-Change: 0.00166
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Iteration: 91, Log-Lik: -9220.898, Max-Change: 0.00236
Iteration: 92, Log-Lik: -9220.897, Max-Change: 0.00186
Iteration: 93, Log-Lik: -9220.896, Max-Change: 0.00156
Iteration: 94, Log-Lik: -9220.896, Max-Change: 0.00193
Iteration: 95, Log-Lik: -9220.895, Max-Change: 0.00116
Iteration: 96, Log-Lik: -9220.895, Max-Change: 0.00110
Iteration: 97, Log-Lik: -9220.894, Max-Change: 0.00163
Iteration: 98, Log-Lik: -9220.894, Max-Change: 0.00132
Iteration: 99, Log-Lik: -9220.893, Max-Change: 0.00108
Iteration: 100, Log-Lik: -9220.893, Max-Change: 0.00109
Iteration: 101, Log-Lik: -9220.893, Max-Change: 0.00101
Iteration: 102, Log-Lik: -9220.893, Max-Change: 0.00095
Iteration: 103, Log-Lik: -9220.892, Max-Change: 0.00081
Iteration: 104, Log-Lik: -9220.892, Max-Change: 0.00105
Iteration: 105, Log-Lik: -9220.892, Max-Change: 0.00094
Iteration: 106, Log-Lik: -9220.892, Max-Change: 0.00122
Iteration: 107, Log-Lik: -9220.892, Max-Change: 0.00096
Iteration: 108, Log-Lik: -9220.891, Max-Change: 0.00085
Iteration: 109, Log-Lik: -9220.891, Max-Change: 0.00062
Iteration: 110, Log-Lik: -9220.891, Max-Change: 0.00104
Iteration: 111, Log-Lik: -9220.891, Max-Change: 0.00098
Iteration: 112, Log-Lik: -9220.891, Max-Change: 0.00079
Iteration: 113, Log-Lik: -9220.891, Max-Change: 0.00068
Iteration: 114, Log-Lik: -9220.890, Max-Change: 0.00064
Iteration: 115, Log-Lik: -9220.890, Max-Change: 0.00104
Iteration: 116, Log-Lik: -9220.890, Max-Change: 0.00000
coef(DINA, simplify=TRUE)
#> $items
#> a1 a2 a3 a4
#> Item_1 -1.630 1.115 0.000 0.000
#> Item_2 -1.052 0.841 0.000 0.000
#> Item_3 -1.582 1.271 0.000 0.000
#> Item_4 -0.388 1.229 0.000 0.000
#> Item_5 -1.054 1.340 0.000 0.000
#> Item_6 -2.569 0.000 2.500 0.000
#> Item_7 -1.100 0.000 1.435 0.000
#> Item_8 -1.103 0.000 1.054 0.000
#> Item_9 -1.474 0.000 1.041 0.000
#> Item_10 -1.620 0.000 1.359 0.000
#> Item_11 -0.542 0.000 0.000 0.997
#> Item_12 -1.584 0.000 0.000 1.609
#> Item_13 -1.881 0.000 0.000 0.934
#> Item_14 -2.663 0.000 0.000 0.912
#> Item_15 -0.813 0.000 0.000 1.005
#>
#> $group.intercepts
#> c1 c2 c3
#> par -0.545 -1.53 -1.468
#>
summary(DINA)
#> $Item_1
#> category_1 category_2
#> P[1 0 0 0] 0.836 0.164
#> P[1 1 0 0] 0.626 0.374
#> P[1 0 1 0] 0.836 0.164
#> P[1 1 1 1] 0.626 0.374
#>
#> $Item_2
#> category_1 category_2
#> P[1 0 0 0] 0.741 0.259
#> P[1 1 0 0] 0.553 0.447
#> P[1 0 1 0] 0.741 0.259
#> P[1 1 1 1] 0.553 0.447
#>
#> $Item_3
#> category_1 category_2
#> P[1 0 0 0] 0.829 0.171
#> P[1 1 0 0] 0.577 0.423
#> P[1 0 1 0] 0.829 0.171
#> P[1 1 1 1] 0.577 0.423
#>
#> $Item_4
#> category_1 category_2
#> P[1 0 0 0] 0.596 0.404
#> P[1 1 0 0] 0.301 0.699
#> P[1 0 1 0] 0.596 0.404
#> P[1 1 1 1] 0.301 0.699
#>
#> $Item_5
#> category_1 category_2
#> P[1 0 0 0] 0.742 0.258
#> P[1 1 0 0] 0.429 0.571
#> P[1 0 1 0] 0.742 0.258
#> P[1 1 1 1] 0.429 0.571
#>
#> $Item_6
#> category_1 category_2
#> P[1 0 0 0] 0.929 0.071
#> P[1 1 0 0] 0.929 0.071
#> P[1 0 1 0] 0.517 0.483
#> P[1 1 1 1] 0.517 0.483
#>
#> $Item_7
#> category_1 category_2
#> P[1 0 0 0] 0.750 0.250
#> P[1 1 0 0] 0.750 0.250
#> P[1 0 1 0] 0.417 0.583
#> P[1 1 1 1] 0.417 0.583
#>
#> $Item_8
#> category_1 category_2
#> P[1 0 0 0] 0.751 0.249
#> P[1 1 0 0] 0.751 0.249
#> P[1 0 1 0] 0.512 0.488
#> P[1 1 1 1] 0.512 0.488
#>
#> $Item_9
#> category_1 category_2
#> P[1 0 0 0] 0.814 0.186
#> P[1 1 0 0] 0.814 0.186
#> P[1 0 1 0] 0.607 0.393
#> P[1 1 1 1] 0.607 0.393
#>
#> $Item_10
#> category_1 category_2
#> P[1 0 0 0] 0.835 0.165
#> P[1 1 0 0] 0.835 0.165
#> P[1 0 1 0] 0.565 0.435
#> P[1 1 1 1] 0.565 0.435
#>
#> $Item_11
#> category_1 category_2
#> P[1 0 0 0] 0.632 0.368
#> P[1 1 0 0] 0.632 0.368
#> P[1 0 1 0] 0.632 0.368
#> P[1 1 1 1] 0.388 0.612
#>
#> $Item_12
#> category_1 category_2
#> P[1 0 0 0] 0.830 0.170
#> P[1 1 0 0] 0.830 0.170
#> P[1 0 1 0] 0.830 0.170
#> P[1 1 1 1] 0.494 0.506
#>
#> $Item_13
#> category_1 category_2
#> P[1 0 0 0] 0.868 0.132
#> P[1 1 0 0] 0.868 0.132
#> P[1 0 1 0] 0.868 0.132
#> P[1 1 1 1] 0.720 0.280
#>
#> $Item_14
#> category_1 category_2
#> P[1 0 0 0] 0.935 0.065
#> P[1 1 0 0] 0.935 0.065
#> P[1 0 1 0] 0.935 0.065
#> P[1 1 1 1] 0.852 0.148
#>
#> $Item_15
#> category_1 category_2
#> P[1 0 0 0] 0.693 0.307
#> P[1 1 0 0] 0.693 0.307
#> P[1 0 1 0] 0.693 0.307
#> P[1 1 1 1] 0.452 0.548
#>
#> $Class.Probability
#> Intercept A1 A2 A1A2 prob
#> Profile_1 1 0 0 0 0.286
#> Profile_2 1 1 0 0 0.107
#> Profile_3 1 0 1 0 0.114
#> Profile_4 1 1 1 1 0.493
#>
M2(DINA) # fits well (as it should)
#> M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI
#> stats 96.49206 87 0.2281074 0.01045052 0 0.02080658 0.02972262 0.9655028
#> CFI
#> stats 0.9714166
cfs <- coef(DINA, simplify=TRUE)$items[11:15,]
cbind(guess, estguess = plogis(cfs[,1]))
#> guess estguess
#> Item_11 0.32210618 0.36762331
#> Item_12 0.21331157 0.17019244
#> Item_13 0.14056317 0.13232904
#> Item_14 0.06866689 0.06517149
#> Item_15 0.28139862 0.30727217
cbind(slip, estslip = 1 - plogis(rowSums(cfs)))
#> slip estslip
#> Item_11 0.3877218 0.3883873
#> Item_12 0.5348058 0.4937323
#> Item_13 0.7359368 0.7203743
#> Item_14 0.8247931 0.8520713
#> Item_15 0.3900682 0.4520799
### DINO model example
theta <- cbind(1, thetaComb(0:1, 2))
# define theta matrix with negative interaction term
(theta <- cbind(theta, -theta[,2] * theta[,3]))
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 0
#> [2,] 1 1 0 0
#> [3,] 1 0 1 0
#> [4,] 1 1 1 -1
model <- mirt.model('Intercept = 1-15
A1 = 1-5, 11-15
A2 = 6-15
Yoshi = 11-15
CONSTRAIN = (11,a2,a3,a4), (12,a2,a3,a4), (13,a2,a3,a4),
(14,a2,a3,a4), (15,a2,a3,a4)')
# last five items are DINOs (first 10 are unidimensional C-RUMs)
DINO <- mdirt(dat, model, customTheta = theta)
#>
Iteration: 1, Log-Lik: -13202.556, Max-Change: 2.96768
Iteration: 2, Log-Lik: -9286.842, Max-Change: 0.40444
Iteration: 3, Log-Lik: -9273.016, Max-Change: 0.33735
Iteration: 4, Log-Lik: -9265.501, Max-Change: 0.23786
Iteration: 5, Log-Lik: -9261.963, Max-Change: 0.16654
Iteration: 6, Log-Lik: -9260.080, Max-Change: 0.12920
Iteration: 7, Log-Lik: -9258.136, Max-Change: 0.08895
Iteration: 8, Log-Lik: -9257.440, Max-Change: 0.06591
Iteration: 9, Log-Lik: -9257.001, Max-Change: 0.06272
Iteration: 10, Log-Lik: -9256.678, Max-Change: 0.07456
Iteration: 11, Log-Lik: -9256.119, Max-Change: 0.04974
Iteration: 12, Log-Lik: -9255.905, Max-Change: 0.04532
Iteration: 13, Log-Lik: -9255.791, Max-Change: 0.06246
Iteration: 14, Log-Lik: -9255.476, Max-Change: 0.03647
Iteration: 15, Log-Lik: -9255.350, Max-Change: 0.03427
Iteration: 16, Log-Lik: -9255.304, Max-Change: 0.05321
Iteration: 17, Log-Lik: -9255.070, Max-Change: 0.03079
Iteration: 18, Log-Lik: -9254.983, Max-Change: 0.02901
Iteration: 19, Log-Lik: -9254.955, Max-Change: 0.05358
Iteration: 20, Log-Lik: -9254.773, Max-Change: 0.02626
Iteration: 21, Log-Lik: -9254.713, Max-Change: 0.02507
Iteration: 22, Log-Lik: -9254.683, Max-Change: 0.04663
Iteration: 23, Log-Lik: -9254.559, Max-Change: 0.02431
Iteration: 24, Log-Lik: -9254.513, Max-Change: 0.02401
Iteration: 25, Log-Lik: -9254.501, Max-Change: 0.04438
Iteration: 26, Log-Lik: -9254.383, Max-Change: 0.02212
Iteration: 27, Log-Lik: -9254.347, Max-Change: 0.02106
Iteration: 28, Log-Lik: -9254.324, Max-Change: 0.03269
Iteration: 29, Log-Lik: -9254.255, Max-Change: 0.02146
Iteration: 30, Log-Lik: -9254.224, Max-Change: 0.02021
Iteration: 31, Log-Lik: -9254.209, Max-Change: 0.03449
Iteration: 32, Log-Lik: -9254.141, Max-Change: 0.01740
Iteration: 33, Log-Lik: -9254.118, Max-Change: 0.01785
Iteration: 34, Log-Lik: -9254.111, Max-Change: 0.03345
Iteration: 35, Log-Lik: -9254.047, Max-Change: 0.01744
Iteration: 36, Log-Lik: -9254.026, Max-Change: 0.01721
Iteration: 37, Log-Lik: -9254.012, Max-Change: 0.03054
Iteration: 38, Log-Lik: -9253.962, Max-Change: 0.01572
Iteration: 39, Log-Lik: -9253.945, Max-Change: 0.01507
Iteration: 40, Log-Lik: -9253.939, Max-Change: 0.02838
Iteration: 41, Log-Lik: -9253.893, Max-Change: 0.01545
Iteration: 42, Log-Lik: -9253.878, Max-Change: 0.01163
Iteration: 43, Log-Lik: -9253.863, Max-Change: 0.01605
Iteration: 44, Log-Lik: -9253.849, Max-Change: 0.01261
Iteration: 45, Log-Lik: -9253.837, Max-Change: 0.01239
Iteration: 46, Log-Lik: -9253.826, Max-Change: 0.02286
Iteration: 47, Log-Lik: -9253.795, Max-Change: 0.01268
Iteration: 48, Log-Lik: -9253.784, Max-Change: 0.01089
Iteration: 49, Log-Lik: -9253.772, Max-Change: 0.01978
Iteration: 50, Log-Lik: -9253.750, Max-Change: 0.01291
Iteration: 51, Log-Lik: -9253.740, Max-Change: 0.01054
Iteration: 52, Log-Lik: -9253.726, Max-Change: 0.01799
Iteration: 53, Log-Lik: -9253.705, Max-Change: 0.01097
Iteration: 54, Log-Lik: -9253.696, Max-Change: 0.01038
Iteration: 55, Log-Lik: -9253.688, Max-Change: 0.01980
Iteration: 56, Log-Lik: -9253.663, Max-Change: 0.01008
Iteration: 57, Log-Lik: -9253.655, Max-Change: 0.00969
Iteration: 58, Log-Lik: -9253.650, Max-Change: 0.01769
Iteration: 59, Log-Lik: -9253.626, Max-Change: 0.00932
Iteration: 60, Log-Lik: -9253.619, Max-Change: 0.00948
Iteration: 61, Log-Lik: -9253.614, Max-Change: 0.01736
Iteration: 62, Log-Lik: -9253.591, Max-Change: 0.00883
Iteration: 63, Log-Lik: -9253.585, Max-Change: 0.00799
Iteration: 64, Log-Lik: -9253.582, Max-Change: 0.01548
Iteration: 65, Log-Lik: -9253.565, Max-Change: 0.00814
Iteration: 66, Log-Lik: -9253.559, Max-Change: 0.00784
Iteration: 67, Log-Lik: -9253.562, Max-Change: 0.01424
Iteration: 68, Log-Lik: -9253.538, Max-Change: 0.00617
Iteration: 69, Log-Lik: -9253.534, Max-Change: 0.00713
Iteration: 70, Log-Lik: -9253.531, Max-Change: 0.01069
Iteration: 71, Log-Lik: -9253.521, Max-Change: 0.00692
Iteration: 72, Log-Lik: -9253.517, Max-Change: 0.00747
Iteration: 73, Log-Lik: -9253.514, Max-Change: 0.01172
Iteration: 74, Log-Lik: -9253.503, Max-Change: 0.00546
Iteration: 75, Log-Lik: -9253.500, Max-Change: 0.00574
Iteration: 76, Log-Lik: -9253.496, Max-Change: 0.00873
Iteration: 77, Log-Lik: -9253.490, Max-Change: 0.00531
Iteration: 78, Log-Lik: -9253.487, Max-Change: 0.01145
Iteration: 79, Log-Lik: -9253.481, Max-Change: 0.00696
Iteration: 80, Log-Lik: -9253.478, Max-Change: 0.00567
Iteration: 81, Log-Lik: -9253.475, Max-Change: 0.00727
Iteration: 82, Log-Lik: -9253.472, Max-Change: 0.00812
Iteration: 83, Log-Lik: -9253.466, Max-Change: 0.00443
Iteration: 84, Log-Lik: -9253.464, Max-Change: 0.00561
Iteration: 85, Log-Lik: -9253.461, Max-Change: 0.00693
Iteration: 86, Log-Lik: -9253.456, Max-Change: 0.00507
Iteration: 87, Log-Lik: -9253.454, Max-Change: 0.00513
Iteration: 88, Log-Lik: -9253.451, Max-Change: 0.00681
Iteration: 89, Log-Lik: -9253.446, Max-Change: 0.00422
Iteration: 90, Log-Lik: -9253.444, Max-Change: 0.00551
Iteration: 91, Log-Lik: -9253.442, Max-Change: 0.00705
Iteration: 92, Log-Lik: -9253.438, Max-Change: 0.00522
Iteration: 93, Log-Lik: -9253.436, Max-Change: 0.00404
Iteration: 94, Log-Lik: -9253.435, Max-Change: 0.00428
Iteration: 95, Log-Lik: -9253.432, Max-Change: 0.00400
Iteration: 96, Log-Lik: -9253.431, Max-Change: 0.00666
Iteration: 97, Log-Lik: -9253.428, Max-Change: 0.00352
Iteration: 98, Log-Lik: -9253.427, Max-Change: 0.00404
Iteration: 99, Log-Lik: -9253.425, Max-Change: 0.00337
Iteration: 100, Log-Lik: -9253.424, Max-Change: 0.00462
Iteration: 101, Log-Lik: -9253.422, Max-Change: 0.00420
Iteration: 102, Log-Lik: -9253.421, Max-Change: 0.00292
Iteration: 103, Log-Lik: -9253.420, Max-Change: 0.00174
Iteration: 104, Log-Lik: -9253.419, Max-Change: 0.00306
Iteration: 105, Log-Lik: -9253.418, Max-Change: 0.00302
Iteration: 106, Log-Lik: -9253.416, Max-Change: 0.00505
Iteration: 107, Log-Lik: -9253.414, Max-Change: 0.00169
Iteration: 108, Log-Lik: -9253.414, Max-Change: 0.00177
Iteration: 109, Log-Lik: -9253.413, Max-Change: 0.00142
Iteration: 110, Log-Lik: -9253.413, Max-Change: 0.00742
Iteration: 111, Log-Lik: -9253.411, Max-Change: 0.00246
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Iteration: 145, Log-Lik: -9253.395, Max-Change: 0.00071
Iteration: 146, Log-Lik: -9253.394, Max-Change: 0.00178
Iteration: 147, Log-Lik: -9253.394, Max-Change: 0.00357
Iteration: 148, Log-Lik: -9253.393, Max-Change: 0.00128
Iteration: 149, Log-Lik: -9253.393, Max-Change: 0.00148
Iteration: 150, Log-Lik: -9253.393, Max-Change: 0.00000
coef(DINO, simplify=TRUE)
#> $items
#> a1 a2 a3 a4
#> Item_1 -0.742 -1.828 0.000 0.000
#> Item_2 -0.402 -1.136 0.000 0.000
#> Item_3 -0.548 -3.194 0.000 0.000
#> Item_4 0.579 -2.116 0.000 0.000
#> Item_5 -0.046 -1.620 0.000 0.000
#> Item_6 -2.818 0.000 2.659 0.000
#> Item_7 -1.187 0.000 1.457 0.000
#> Item_8 -1.154 0.000 1.055 0.000
#> Item_9 -1.583 0.000 1.121 0.000
#> Item_10 -1.736 0.000 1.427 0.000
#> Item_11 -0.937 1.163 1.163 1.163
#> Item_12 -1.957 1.577 1.577 1.577
#> Item_13 -2.088 0.915 0.915 0.915
#> Item_14 -3.713 1.840 1.840 1.840
#> Item_15 -1.130 1.075 1.075 1.075
#>
#> $group.intercepts
#> c1 c2 c3
#> par 2.029 1.084 2.947
#>
summary(DINO)
#> $Item_1
#> category_1 category_2
#> P[1 0 0 0] 0.678 0.322
#> P[1 1 0 0] 0.929 0.071
#> P[1 0 1 0] 0.678 0.322
#> P[1 1 1 -1] 0.929 0.071
#>
#> $Item_2
#> category_1 category_2
#> P[1 0 0 0] 0.599 0.401
#> P[1 1 0 0] 0.823 0.177
#> P[1 0 1 0] 0.599 0.401
#> P[1 1 1 -1] 0.823 0.177
#>
#> $Item_3
#> category_1 category_2
#> P[1 0 0 0] 0.634 0.366
#> P[1 1 0 0] 0.977 0.023
#> P[1 0 1 0] 0.634 0.366
#> P[1 1 1 -1] 0.977 0.023
#>
#> $Item_4
#> category_1 category_2
#> P[1 0 0 0] 0.359 0.641
#> P[1 1 0 0] 0.823 0.177
#> P[1 0 1 0] 0.359 0.641
#> P[1 1 1 -1] 0.823 0.177
#>
#> $Item_5
#> category_1 category_2
#> P[1 0 0 0] 0.511 0.489
#> P[1 1 0 0] 0.841 0.159
#> P[1 0 1 0] 0.511 0.489
#> P[1 1 1 -1] 0.841 0.159
#>
#> $Item_6
#> category_1 category_2
#> P[1 0 0 0] 0.944 0.056
#> P[1 1 0 0] 0.944 0.056
#> P[1 0 1 0] 0.540 0.460
#> P[1 1 1 -1] 0.540 0.460
#>
#> $Item_7
#> category_1 category_2
#> P[1 0 0 0] 0.766 0.234
#> P[1 1 0 0] 0.766 0.234
#> P[1 0 1 0] 0.433 0.567
#> P[1 1 1 -1] 0.433 0.567
#>
#> $Item_8
#> category_1 category_2
#> P[1 0 0 0] 0.760 0.240
#> P[1 1 0 0] 0.760 0.240
#> P[1 0 1 0] 0.525 0.475
#> P[1 1 1 -1] 0.525 0.475
#>
#> $Item_9
#> category_1 category_2
#> P[1 0 0 0] 0.830 0.170
#> P[1 1 0 0] 0.830 0.170
#> P[1 0 1 0] 0.613 0.387
#> P[1 1 1 -1] 0.613 0.387
#>
#> $Item_10
#> category_1 category_2
#> P[1 0 0 0] 0.850 0.150
#> P[1 1 0 0] 0.850 0.150
#> P[1 0 1 0] 0.577 0.423
#> P[1 1 1 -1] 0.577 0.423
#>
#> $Item_11
#> category_1 category_2
#> P[1 0 0 0] 0.718 0.282
#> P[1 1 0 0] 0.444 0.556
#> P[1 0 1 0] 0.444 0.556
#> P[1 1 1 -1] 0.444 0.556
#>
#> $Item_12
#> category_1 category_2
#> P[1 0 0 0] 0.876 0.124
#> P[1 1 0 0] 0.594 0.406
#> P[1 0 1 0] 0.594 0.406
#> P[1 1 1 -1] 0.594 0.406
#>
#> $Item_13
#> category_1 category_2
#> P[1 0 0 0] 0.890 0.110
#> P[1 1 0 0] 0.764 0.236
#> P[1 0 1 0] 0.764 0.236
#> P[1 1 1 -1] 0.764 0.236
#>
#> $Item_14
#> category_1 category_2
#> P[1 0 0 0] 0.976 0.024
#> P[1 1 0 0] 0.867 0.133
#> P[1 0 1 0] 0.867 0.133
#> P[1 1 1 -1] 0.867 0.133
#>
#> $Item_15
#> category_1 category_2
#> P[1 0 0 0] 0.756 0.244
#> P[1 1 0 0] 0.514 0.486
#> P[1 0 1 0] 0.514 0.486
#> P[1 1 1 -1] 0.514 0.486
#>
#> $Class.Probability
#> Intercept A1 A2 Yoshi prob
#> Profile_1 1 0 0 0 0.249
#> Profile_2 1 1 0 0 0.097
#> Profile_3 1 0 1 0 0.622
#> Profile_4 1 1 1 -1 0.033
#>
M2(DINO) #doesn't fit as well, because not the generating model
#> M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR
#> stats 146.478 87 6.93916e-05 0.02615988 0.01856199 0.03336756 0.04140113
#> TLI CFI
#> stats 0.7838382 0.8208945
## C-RUM (analogous to MIRT model)
theta <- cbind(1, thetaComb(0:1, 2))
model <- mirt.model('Intercept = 1-15
A1 = 1-5, 11-15
A2 = 6-15')
CRUM <- mdirt(dat, model, customTheta = theta)
#>
Iteration: 1, Log-Lik: -11278.364, Max-Change: 2.42560
Iteration: 2, Log-Lik: -9278.962, Max-Change: 0.20224
Iteration: 3, Log-Lik: -9273.128, Max-Change: 0.08935
Iteration: 4, Log-Lik: -9272.086, Max-Change: 0.06370
Iteration: 5, Log-Lik: -9271.754, Max-Change: 0.05108
Iteration: 6, Log-Lik: -9271.609, Max-Change: 0.04160
Iteration: 7, Log-Lik: -9271.452, Max-Change: 0.01738
Iteration: 8, Log-Lik: -9271.439, Max-Change: 0.01400
Iteration: 9, Log-Lik: -9271.431, Max-Change: 0.01085
Iteration: 10, Log-Lik: -9271.419, Max-Change: 0.00701
Iteration: 11, Log-Lik: -9271.410, Max-Change: 0.00585
Iteration: 12, Log-Lik: -9271.397, Max-Change: 0.00780
Iteration: 13, Log-Lik: -9271.281, Max-Change: 0.01993
Iteration: 14, Log-Lik: -9271.135, Max-Change: 0.02881
Iteration: 15, Log-Lik: -9270.840, Max-Change: 0.04114
Iteration: 16, Log-Lik: -9268.379, Max-Change: 0.09280
Iteration: 17, Log-Lik: -9265.443, Max-Change: 0.12546
Iteration: 18, Log-Lik: -9260.293, Max-Change: 0.16137
Iteration: 19, Log-Lik: -9252.354, Max-Change: 0.18968
Iteration: 20, Log-Lik: -9242.406, Max-Change: 0.19538
Iteration: 21, Log-Lik: -9232.937, Max-Change: 0.17147
Iteration: 22, Log-Lik: -9226.224, Max-Change: 0.12844
Iteration: 23, Log-Lik: -9222.454, Max-Change: 0.08492
Iteration: 24, Log-Lik: -9220.507, Max-Change: 0.06664
Iteration: 25, Log-Lik: -9219.278, Max-Change: 0.05996
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Iteration: 192, Log-Lik: -9215.781, Max-Change: 0.00124
Iteration: 193, Log-Lik: -9215.781, Max-Change: 0.00118
Iteration: 194, Log-Lik: -9215.781, Max-Change: 0.00122
Iteration: 195, Log-Lik: -9215.781, Max-Change: 0.00000
coef(CRUM, simplify=TRUE)
#> $items
#> a1 a2 a3
#> Item_1 -1.405 0.996 0.000
#> Item_2 -0.950 0.876 0.000
#> Item_3 -1.328 1.145 0.000
#> Item_4 -0.235 1.309 0.000
#> Item_5 -0.855 1.342 0.000
#> Item_6 -2.592 0.000 2.479
#> Item_7 -1.095 0.000 1.388
#> Item_8 -1.127 0.000 1.061
#> Item_9 -1.505 0.000 1.058
#> Item_10 -1.674 0.000 1.399
#> Item_11 -0.589 0.491 0.500
#> Item_12 -1.730 1.049 0.743
#> Item_13 -2.052 0.255 0.820
#> Item_14 -3.276 -0.695 1.963
#> Item_15 -0.989 -0.008 1.069
#>
#> $group.intercepts
#> c1 c2 c3
#> par -0.225 -2.397 -0.726
#>
summary(CRUM)
#> $Item_1
#> category_1 category_2
#> P[1 0 0] 0.803 0.197
#> P[1 1 0] 0.601 0.399
#> P[1 0 1] 0.803 0.197
#> P[1 1 1] 0.601 0.399
#>
#> $Item_2
#> category_1 category_2
#> P[1 0 0] 0.721 0.279
#> P[1 1 0] 0.519 0.481
#> P[1 0 1] 0.721 0.279
#> P[1 1 1] 0.519 0.481
#>
#> $Item_3
#> category_1 category_2
#> P[1 0 0] 0.791 0.209
#> P[1 1 0] 0.546 0.454
#> P[1 0 1] 0.791 0.209
#> P[1 1 1] 0.546 0.454
#>
#> $Item_4
#> category_1 category_2
#> P[1 0 0] 0.559 0.441
#> P[1 1 0] 0.255 0.745
#> P[1 0 1] 0.559 0.441
#> P[1 1 1] 0.255 0.745
#>
#> $Item_5
#> category_1 category_2
#> P[1 0 0] 0.702 0.298
#> P[1 1 0] 0.381 0.619
#> P[1 0 1] 0.702 0.298
#> P[1 1 1] 0.381 0.619
#>
#> $Item_6
#> category_1 category_2
#> P[1 0 0] 0.930 0.070
#> P[1 1 0] 0.930 0.070
#> P[1 0 1] 0.528 0.472
#> P[1 1 1] 0.528 0.472
#>
#> $Item_7
#> category_1 category_2
#> P[1 0 0] 0.749 0.251
#> P[1 1 0] 0.749 0.251
#> P[1 0 1] 0.427 0.573
#> P[1 1 1] 0.427 0.573
#>
#> $Item_8
#> category_1 category_2
#> P[1 0 0] 0.755 0.245
#> P[1 1 0] 0.755 0.245
#> P[1 0 1] 0.517 0.483
#> P[1 1 1] 0.517 0.483
#>
#> $Item_9
#> category_1 category_2
#> P[1 0 0] 0.818 0.182
#> P[1 1 0] 0.818 0.182
#> P[1 0 1] 0.610 0.390
#> P[1 1 1] 0.610 0.390
#>
#> $Item_10
#> category_1 category_2
#> P[1 0 0] 0.842 0.158
#> P[1 1 0] 0.842 0.158
#> P[1 0 1] 0.568 0.432
#> P[1 1 1] 0.568 0.432
#>
#> $Item_11
#> category_1 category_2
#> P[1 0 0] 0.643 0.357
#> P[1 1 0] 0.525 0.475
#> P[1 0 1] 0.522 0.478
#> P[1 1 1] 0.401 0.599
#>
#> $Item_12
#> category_1 category_2
#> P[1 0 0] 0.849 0.151
#> P[1 1 0] 0.664 0.336
#> P[1 0 1] 0.729 0.271
#> P[1 1 1] 0.485 0.515
#>
#> $Item_13
#> category_1 category_2
#> P[1 0 0] 0.886 0.114
#> P[1 1 0] 0.858 0.142
#> P[1 0 1] 0.774 0.226
#> P[1 1 1] 0.727 0.273
#>
#> $Item_14
#> category_1 category_2
#> P[1 0 0] 0.964 0.036
#> P[1 1 0] 0.981 0.019
#> P[1 0 1] 0.788 0.212
#> P[1 1 1] 0.882 0.118
#>
#> $Item_15
#> category_1 category_2
#> P[1 0 0] 0.729 0.271
#> P[1 1 0] 0.730 0.270
#> P[1 0 1] 0.480 0.520
#> P[1 1 1] 0.482 0.518
#>
#> $Class.Probability
#> Intercept A1 A2 prob
#> Profile_1 1 0 0 0.337
#> Profile_2 1 1 0 0.038
#> Profile_3 1 0 1 0.204
#> Profile_4 1 1 1 0.421
#>
# good fit, but over-saturated (main effects for items 11-15 can be set to 0)
M2(CRUM)
#> M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI
#> stats 85.5485 82 0.3725544 0.006581616 0 0.01905772 0.02788709 0.9863173
#> CFI
#> stats 0.9893144
#------------------
# multidimensional latent class model
dat <- key2binary(SAT12,
key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
# 5 latent classes within 2 different sets of items
model <- mirt.model('C1 = 1-16
C2 = 1-16
C3 = 1-16
C4 = 1-16
C5 = 1-16
C6 = 17-32
C7 = 17-32
C8 = 17-32
C9 = 17-32
C10 = 17-32
CONSTRAIN = (1-16, a1), (1-16, a2), (1-16, a3), (1-16, a4), (1-16, a5),
(17-32, a6), (17-32, a7), (17-32, a8), (17-32, a9), (17-32, a10)')
theta <- diag(10) # defined explicitly. Otherwise, this profile is assumed
mod <- mdirt(dat, model, customTheta = theta)
#>
Iteration: 1, Log-Lik: -13386.899, Max-Change: 2.52965
Iteration: 2, Log-Lik: -12990.924, Max-Change: 0.20224
Iteration: 3, Log-Lik: -12986.575, Max-Change: 0.09718
Iteration: 4, Log-Lik: -12986.113, Max-Change: 0.11289
Iteration: 5, Log-Lik: -12985.895, Max-Change: 0.03901
Iteration: 6, Log-Lik: -12985.799, Max-Change: 0.02791
Iteration: 7, Log-Lik: -12985.658, Max-Change: 0.01556
Iteration: 8, Log-Lik: -12985.627, Max-Change: 0.01397
Iteration: 9, Log-Lik: -12985.600, Max-Change: 0.01273
Iteration: 10, Log-Lik: -12985.496, Max-Change: 0.00802
Iteration: 11, Log-Lik: -12985.477, Max-Change: 0.00918
Iteration: 12, Log-Lik: -12985.460, Max-Change: 0.00800
Iteration: 13, Log-Lik: -12985.409, Max-Change: 0.00683
Iteration: 14, Log-Lik: -12985.396, Max-Change: 0.00714
Iteration: 15, Log-Lik: -12985.384, Max-Change: 0.00676
Iteration: 16, Log-Lik: -12985.348, Max-Change: 0.00620
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Iteration: 228, Log-Lik: -12984.851, Max-Change: 0.00051
Iteration: 229, Log-Lik: -12984.851, Max-Change: 0.00039
Iteration: 230, Log-Lik: -12984.851, Max-Change: 0.00051
Iteration: 231, Log-Lik: -12984.851, Max-Change: 0.00039
Iteration: 232, Log-Lik: -12984.850, Max-Change: 0.00050
Iteration: 233, Log-Lik: -12984.850, Max-Change: 0.00039
Iteration: 234, Log-Lik: -12984.850, Max-Change: 0.00049
Iteration: 235, Log-Lik: -12984.850, Max-Change: 0.00037
Iteration: 236, Log-Lik: -12984.850, Max-Change: 0.00049
Iteration: 237, Log-Lik: -12984.850, Max-Change: 0.00037
Iteration: 238, Log-Lik: -12984.850, Max-Change: 0.00048
Iteration: 239, Log-Lik: -12984.849, Max-Change: 0.00037
Iteration: 240, Log-Lik: -12984.849, Max-Change: 0.00047
Iteration: 241, Log-Lik: -12984.849, Max-Change: 0.00036
Iteration: 242, Log-Lik: -12984.849, Max-Change: 0.00047
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Iteration: 244, Log-Lik: -12984.849, Max-Change: 0.00046
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Iteration: 247, Log-Lik: -12984.848, Max-Change: 0.00034
Iteration: 248, Log-Lik: -12984.848, Max-Change: 0.00045
Iteration: 249, Log-Lik: -12984.848, Max-Change: 0.00034
Iteration: 250, Log-Lik: -12984.848, Max-Change: 0.00045
Iteration: 251, Log-Lik: -12984.848, Max-Change: 0.00034
Iteration: 252, Log-Lik: -12984.848, Max-Change: 0.00044
Iteration: 253, Log-Lik: -12984.848, Max-Change: 0.00033
Iteration: 254, Log-Lik: -12984.848, Max-Change: 0.00043
Iteration: 255, Log-Lik: -12984.847, Max-Change: 0.00033
Iteration: 256, Log-Lik: -12984.847, Max-Change: 0.00043
Iteration: 257, Log-Lik: -12984.847, Max-Change: 0.00033
Iteration: 258, Log-Lik: -12984.847, Max-Change: 0.00042
Iteration: 259, Log-Lik: -12984.847, Max-Change: 0.00031
Iteration: 260, Log-Lik: -12984.847, Max-Change: 0.00042
Iteration: 261, Log-Lik: -12984.847, Max-Change: 0.00032
Iteration: 262, Log-Lik: -12984.847, Max-Change: 0.00041
Iteration: 263, Log-Lik: -12984.847, Max-Change: 0.00032
Iteration: 264, Log-Lik: -12984.847, Max-Change: 0.00041
Iteration: 265, Log-Lik: -12984.846, Max-Change: 0.00030
Iteration: 266, Log-Lik: -12984.846, Max-Change: 0.00040
Iteration: 267, Log-Lik: -12984.846, Max-Change: 0.00031
Iteration: 268, Log-Lik: -12984.846, Max-Change: 0.00040
Iteration: 269, Log-Lik: -12984.846, Max-Change: 0.00031
Iteration: 270, Log-Lik: -12984.846, Max-Change: 0.00039
Iteration: 271, Log-Lik: -12984.846, Max-Change: 0.00029
Iteration: 272, Log-Lik: -12984.846, Max-Change: 0.00039
Iteration: 273, Log-Lik: -12984.846, Max-Change: 0.00029
Iteration: 274, Log-Lik: -12984.846, Max-Change: 0.00038
Iteration: 275, Log-Lik: -12984.845, Max-Change: 0.00029
Iteration: 276, Log-Lik: -12984.845, Max-Change: 0.00038
Iteration: 277, Log-Lik: -12984.845, Max-Change: 0.00028
Iteration: 278, Log-Lik: -12984.845, Max-Change: 0.00037
Iteration: 279, Log-Lik: -12984.845, Max-Change: 0.00028
Iteration: 280, Log-Lik: -12984.845, Max-Change: 0.00037
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Iteration: 282, Log-Lik: -12984.845, Max-Change: 0.00036
Iteration: 283, Log-Lik: -12984.845, Max-Change: 0.00027
Iteration: 284, Log-Lik: -12984.845, Max-Change: 0.00033
Iteration: 285, Log-Lik: -12984.845, Max-Change: 0.00037
Iteration: 286, Log-Lik: -12984.844, Max-Change: 0.00028
Iteration: 287, Log-Lik: -12984.844, Max-Change: 0.00036
Iteration: 288, Log-Lik: -12984.844, Max-Change: 0.00028
Iteration: 289, Log-Lik: -12984.844, Max-Change: 0.00000
coef(mod, simplify=TRUE)
#> $items
#> a1 a2 a3 a4 a5 a6 a7 a8 a9 a10
#> Item.1 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.2 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.3 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.4 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.5 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.6 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.7 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.8 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.9 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.10 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.11 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.12 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.13 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.14 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.15 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.16 -0.921 -0.679 -0.574 -0.542 -0.363 0.00 0.000 0.000 0.000 0.000
#> Item.17 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.18 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.19 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.20 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.21 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.22 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.23 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.24 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.25 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.26 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.27 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.28 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.29 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.30 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.31 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#> Item.32 0.000 0.000 0.000 0.000 0.000 0.31 0.443 1.389 1.396 1.419
#>
#> $group.intercepts
#> c1 c2 c3 c4 c5 c6 c7 c8 c9
#> par -2.737 -1.478 0.137 1.489 2.185 2.882 2.315 2.144 1.112
#>
summary(mod)
#> $Item.1
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.2
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.3
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.4
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.5
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.6
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.7
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.8
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.9
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.10
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.11
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.12
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.13
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.14
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.15
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.16
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.715 0.285
#> P[0 1 0 0 0 0 0 0 0 0] 0.663 0.337
#> P[0 0 1 0 0 0 0 0 0 0] 0.640 0.360
#> P[0 0 0 1 0 0 0 0 0 0] 0.632 0.368
#> P[0 0 0 0 1 0 0 0 0 0] 0.590 0.410
#> P[0 0 0 0 0 1 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 1 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 1 0 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 1 0] 0.500 0.500
#> P[0 0 0 0 0 0 0 0 0 1] 0.500 0.500
#>
#> $Item.17
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.18
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.19
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.20
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.21
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.22
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.23
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.24
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.25
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.26
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.27
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.28
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.29
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.30
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.31
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Item.32
#> category_1 category_2
#> P[1 0 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 1 0 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 1 0 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 1 0 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 1 0 0 0 0 0] 0.500 0.500
#> P[0 0 0 0 0 1 0 0 0 0] 0.423 0.577
#> P[0 0 0 0 0 0 1 0 0 0] 0.391 0.609
#> P[0 0 0 0 0 0 0 1 0 0] 0.200 0.800
#> P[0 0 0 0 0 0 0 0 1 0] 0.198 0.802
#> P[0 0 0 0 0 0 0 0 0 1] 0.195 0.805
#>
#> $Class.Probability
#> C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 prob
#> Profile_1 1 0 0 0 0 0 0 0 0 0 0.001
#> Profile_2 0 1 0 0 0 0 0 0 0 0 0.004
#> Profile_3 0 0 1 0 0 0 0 0 0 0 0.021
#> Profile_4 0 0 0 1 0 0 0 0 0 0 0.080
#> Profile_5 0 0 0 0 1 0 0 0 0 0 0.161
#> Profile_6 0 0 0 0 0 1 0 0 0 0 0.323
#> Profile_7 0 0 0 0 0 0 1 0 0 0 0.183
#> Profile_8 0 0 0 0 0 0 0 1 0 0 0.154
#> Profile_9 0 0 0 0 0 0 0 0 1 0 0.055
#> Profile_10 0 0 0 0 0 0 0 0 0 1 0.018
#>
#------------------
# multiple group with constrained group probabilities
dat <- key2binary(SAT12,
key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
group <- rep(c('G1', 'G2'), each = nrow(SAT12)/2)
Theta <- diag(2)
# the latent class parameters are technically located in the (nitems + 1) location
model <- mirt.model('A1 = 1-32
A2 = 1-32
CONSTRAINB = (33, c1)')
mod <- mdirt(dat, model, group = group, customTheta = Theta)
#>
Iteration: 1, Log-Lik: -15493.466, Max-Change: 6.13505
Iteration: 2, Log-Lik: -9677.768, Max-Change: 0.98177
Iteration: 3, Log-Lik: -9644.068, Max-Change: 1.15366
Iteration: 4, Log-Lik: -9626.468, Max-Change: 1.47114
Iteration: 5, Log-Lik: -9616.567, Max-Change: 0.88718
Iteration: 6, Log-Lik: -9610.915, Max-Change: 0.33640
Iteration: 7, Log-Lik: -9607.307, Max-Change: 0.57463
Iteration: 8, Log-Lik: -9604.763, Max-Change: 0.48688
Iteration: 9, Log-Lik: -9602.959, Max-Change: 0.54477
Iteration: 10, Log-Lik: -9601.136, Max-Change: 0.18248
Iteration: 11, Log-Lik: -9598.577, Max-Change: 0.13304
Iteration: 12, Log-Lik: -9598.469, Max-Change: 0.06085
Iteration: 13, Log-Lik: -9598.418, Max-Change: 0.01602
Iteration: 14, Log-Lik: -9598.376, Max-Change: 0.03559
Iteration: 15, Log-Lik: -9598.340, Max-Change: 0.17129
Iteration: 16, Log-Lik: -9598.284, Max-Change: 0.01484
Iteration: 17, Log-Lik: -9598.262, Max-Change: 0.00972
Iteration: 18, Log-Lik: -9598.248, Max-Change: 0.00848
Iteration: 19, Log-Lik: -9598.227, Max-Change: 0.08765
Iteration: 20, Log-Lik: -9598.208, Max-Change: 0.00651
Iteration: 21, Log-Lik: -9598.203, Max-Change: 0.00653
Iteration: 22, Log-Lik: -9598.191, Max-Change: 0.01732
Iteration: 23, Log-Lik: -9598.184, Max-Change: 0.00500
Iteration: 24, Log-Lik: -9598.182, Max-Change: 0.22187
Iteration: 25, Log-Lik: -9598.155, Max-Change: 0.00340
Iteration: 26, Log-Lik: -9598.153, Max-Change: 0.00451
Iteration: 27, Log-Lik: -9598.151, Max-Change: 0.00342
Iteration: 28, Log-Lik: -9598.149, Max-Change: 0.00000
coef(mod, simplify=TRUE)
#> $G1
#> $items
#> a1 a2
#> Item.1 -1.462 -0.238
#> Item.2 -0.522 1.905
#> Item.3 -1.639 -0.087
#> Item.4 -1.181 0.114
#> Item.5 -0.149 1.966
#> Item.6 -2.913 -1.120
#> Item.7 0.469 2.107
#> Item.8 -1.833 -0.731
#> Item.9 1.888 2.722
#> Item.10 -0.972 0.380
#> Item.11 4.484 9.810
#> Item.12 -0.381 -0.305
#> Item.13 0.008 1.820
#> Item.14 0.411 2.339
#> Item.15 0.737 3.359
#> Item.16 -0.997 0.141
#> Item.17 2.648 4.629
#> Item.18 -1.588 0.582
#> Item.19 -0.415 1.056
#> Item.20 1.253 4.570
#> Item.21 1.959 3.169
#> Item.22 1.965 9.847
#> Item.23 -1.633 -0.393
#> Item.24 0.270 2.349
#> Item.25 -1.224 0.328
#> Item.26 -0.973 1.196
#> Item.27 1.151 9.631
#> Item.28 -0.478 1.176
#> Item.29 -1.235 0.071
#> Item.30 -0.514 0.150
#> Item.31 0.761 9.640
#> Item.32 -1.380 -1.742
#>
#> $group.intercepts
#> c1
#> par 0.416
#>
#>
#> $G2
#> $items
#> a1 a2
#> Item.1 -1.384 -0.426
#> Item.2 -0.490 1.719
#> Item.3 -1.885 -0.062
#> Item.4 -0.826 0.229
#> Item.5 0.001 1.267
#> Item.6 -2.386 -0.601
#> Item.7 0.857 2.666
#> Item.8 -1.887 -0.942
#> Item.9 1.627 2.611
#> Item.10 -1.047 0.943
#> Item.11 3.082 9.727
#> Item.12 -0.487 -0.110
#> Item.13 0.251 1.767
#> Item.14 0.380 2.385
#> Item.15 1.233 2.786
#> Item.16 -0.740 0.606
#> Item.17 2.958 9.692
#> Item.18 -1.969 0.782
#> Item.19 -0.235 1.065
#> Item.20 1.454 5.474
#> Item.21 2.271 2.770
#> Item.22 2.280 6.826
#> Item.23 -1.107 0.202
#> Item.24 0.553 2.564
#> Item.25 -0.869 0.045
#> Item.26 -1.272 1.388
#> Item.27 1.381 3.529
#> Item.28 -0.607 1.313
#> Item.29 -1.391 0.200
#> Item.30 -0.476 0.112
#> Item.31 1.208 4.732
#> Item.32 -2.027 -1.482
#>
#> $group.intercepts
#> c1
#> par 0.416
#>
#>
summary(mod)
#> $G1
#> $Item.1
#> category_1 category_2
#> P[1 0] 0.812 0.188
#> P[0 1] 0.559 0.441
#>
#> $Item.2
#> category_1 category_2
#> P[1 0] 0.628 0.372
#> P[0 1] 0.130 0.870
#>
#> $Item.3
#> category_1 category_2
#> P[1 0] 0.837 0.163
#> P[0 1] 0.522 0.478
#>
#> $Item.4
#> category_1 category_2
#> P[1 0] 0.765 0.235
#> P[0 1] 0.472 0.528
#>
#> $Item.5
#> category_1 category_2
#> P[1 0] 0.537 0.463
#> P[0 1] 0.123 0.877
#>
#> $Item.6
#> category_1 category_2
#> P[1 0] 0.948 0.052
#> P[0 1] 0.754 0.246
#>
#> $Item.7
#> category_1 category_2
#> P[1 0] 0.385 0.615
#> P[0 1] 0.108 0.892
#>
#> $Item.8
#> category_1 category_2
#> P[1 0] 0.862 0.138
#> P[0 1] 0.675 0.325
#>
#> $Item.9
#> category_1 category_2
#> P[1 0] 0.131 0.869
#> P[0 1] 0.062 0.938
#>
#> $Item.10
#> category_1 category_2
#> P[1 0] 0.726 0.274
#> P[0 1] 0.406 0.594
#>
#> $Item.11
#> category_1 category_2
#> P[1 0] 0.011 0.989
#> P[0 1] 0.000 1.000
#>
#> $Item.12
#> category_1 category_2
#> P[1 0] 0.594 0.406
#> P[0 1] 0.576 0.424
#>
#> $Item.13
#> category_1 category_2
#> P[1 0] 0.498 0.502
#> P[0 1] 0.139 0.861
#>
#> $Item.14
#> category_1 category_2
#> P[1 0] 0.399 0.601
#> P[0 1] 0.088 0.912
#>
#> $Item.15
#> category_1 category_2
#> P[1 0] 0.324 0.676
#> P[0 1] 0.034 0.966
#>
#> $Item.16
#> category_1 category_2
#> P[1 0] 0.731 0.269
#> P[0 1] 0.465 0.535
#>
#> $Item.17
#> category_1 category_2
#> P[1 0] 0.066 0.934
#> P[0 1] 0.010 0.990
#>
#> $Item.18
#> category_1 category_2
#> P[1 0] 0.830 0.170
#> P[0 1] 0.358 0.642
#>
#> $Item.19
#> category_1 category_2
#> P[1 0] 0.602 0.398
#> P[0 1] 0.258 0.742
#>
#> $Item.20
#> category_1 category_2
#> P[1 0] 0.222 0.778
#> P[0 1] 0.010 0.990
#>
#> $Item.21
#> category_1 category_2
#> P[1 0] 0.124 0.876
#> P[0 1] 0.040 0.960
#>
#> $Item.22
#> category_1 category_2
#> P[1 0] 0.123 0.877
#> P[0 1] 0.000 1.000
#>
#> $Item.23
#> category_1 category_2
#> P[1 0] 0.837 0.163
#> P[0 1] 0.597 0.403
#>
#> $Item.24
#> category_1 category_2
#> P[1 0] 0.433 0.567
#> P[0 1] 0.087 0.913
#>
#> $Item.25
#> category_1 category_2
#> P[1 0] 0.773 0.227
#> P[0 1] 0.419 0.581
#>
#> $Item.26
#> category_1 category_2
#> P[1 0] 0.726 0.274
#> P[0 1] 0.232 0.768
#>
#> $Item.27
#> category_1 category_2
#> P[1 0] 0.24 0.76
#> P[0 1] 0.00 1.00
#>
#> $Item.28
#> category_1 category_2
#> P[1 0] 0.617 0.383
#> P[0 1] 0.236 0.764
#>
#> $Item.29
#> category_1 category_2
#> P[1 0] 0.775 0.225
#> P[0 1] 0.482 0.518
#>
#> $Item.30
#> category_1 category_2
#> P[1 0] 0.626 0.374
#> P[0 1] 0.463 0.537
#>
#> $Item.31
#> category_1 category_2
#> P[1 0] 0.318 0.682
#> P[0 1] 0.000 1.000
#>
#> $Item.32
#> category_1 category_2
#> P[1 0] 0.799 0.201
#> P[0 1] 0.851 0.149
#>
#> $Class.Probability
#> A1 A2 prob
#> Profile_1 1 0 0.602
#> Profile_2 0 1 0.398
#>
#>
#> $G2
#> $Item.1
#> category_1 category_2
#> P[1 0] 0.800 0.200
#> P[0 1] 0.605 0.395
#>
#> $Item.2
#> category_1 category_2
#> P[1 0] 0.620 0.380
#> P[0 1] 0.152 0.848
#>
#> $Item.3
#> category_1 category_2
#> P[1 0] 0.868 0.132
#> P[0 1] 0.515 0.485
#>
#> $Item.4
#> category_1 category_2
#> P[1 0] 0.696 0.304
#> P[0 1] 0.443 0.557
#>
#> $Item.5
#> category_1 category_2
#> P[1 0] 0.50 0.50
#> P[0 1] 0.22 0.78
#>
#> $Item.6
#> category_1 category_2
#> P[1 0] 0.916 0.084
#> P[0 1] 0.646 0.354
#>
#> $Item.7
#> category_1 category_2
#> P[1 0] 0.298 0.702
#> P[0 1] 0.065 0.935
#>
#> $Item.8
#> category_1 category_2
#> P[1 0] 0.868 0.132
#> P[0 1] 0.719 0.281
#>
#> $Item.9
#> category_1 category_2
#> P[1 0] 0.164 0.836
#> P[0 1] 0.068 0.932
#>
#> $Item.10
#> category_1 category_2
#> P[1 0] 0.74 0.26
#> P[0 1] 0.28 0.72
#>
#> $Item.11
#> category_1 category_2
#> P[1 0] 0.044 0.956
#> P[0 1] 0.000 1.000
#>
#> $Item.12
#> category_1 category_2
#> P[1 0] 0.619 0.381
#> P[0 1] 0.527 0.473
#>
#> $Item.13
#> category_1 category_2
#> P[1 0] 0.438 0.562
#> P[0 1] 0.146 0.854
#>
#> $Item.14
#> category_1 category_2
#> P[1 0] 0.406 0.594
#> P[0 1] 0.084 0.916
#>
#> $Item.15
#> category_1 category_2
#> P[1 0] 0.226 0.774
#> P[0 1] 0.058 0.942
#>
#> $Item.16
#> category_1 category_2
#> P[1 0] 0.677 0.323
#> P[0 1] 0.353 0.647
#>
#> $Item.17
#> category_1 category_2
#> P[1 0] 0.049 0.951
#> P[0 1] 0.000 1.000
#>
#> $Item.18
#> category_1 category_2
#> P[1 0] 0.878 0.122
#> P[0 1] 0.314 0.686
#>
#> $Item.19
#> category_1 category_2
#> P[1 0] 0.558 0.442
#> P[0 1] 0.256 0.744
#>
#> $Item.20
#> category_1 category_2
#> P[1 0] 0.189 0.811
#> P[0 1] 0.004 0.996
#>
#> $Item.21
#> category_1 category_2
#> P[1 0] 0.094 0.906
#> P[0 1] 0.059 0.941
#>
#> $Item.22
#> category_1 category_2
#> P[1 0] 0.093 0.907
#> P[0 1] 0.001 0.999
#>
#> $Item.23
#> category_1 category_2
#> P[1 0] 0.752 0.248
#> P[0 1] 0.450 0.550
#>
#> $Item.24
#> category_1 category_2
#> P[1 0] 0.365 0.635
#> P[0 1] 0.072 0.928
#>
#> $Item.25
#> category_1 category_2
#> P[1 0] 0.705 0.295
#> P[0 1] 0.489 0.511
#>
#> $Item.26
#> category_1 category_2
#> P[1 0] 0.781 0.219
#> P[0 1] 0.200 0.800
#>
#> $Item.27
#> category_1 category_2
#> P[1 0] 0.201 0.799
#> P[0 1] 0.028 0.972
#>
#> $Item.28
#> category_1 category_2
#> P[1 0] 0.647 0.353
#> P[0 1] 0.212 0.788
#>
#> $Item.29
#> category_1 category_2
#> P[1 0] 0.801 0.199
#> P[0 1] 0.450 0.550
#>
#> $Item.30
#> category_1 category_2
#> P[1 0] 0.617 0.383
#> P[0 1] 0.472 0.528
#>
#> $Item.31
#> category_1 category_2
#> P[1 0] 0.230 0.770
#> P[0 1] 0.009 0.991
#>
#> $Item.32
#> category_1 category_2
#> P[1 0] 0.884 0.116
#> P[0 1] 0.815 0.185
#>
#> $Class.Probability
#> A1 A2 prob
#> Profile_1 1 0 0.602
#> Profile_2 0 1 0.398
#>
#>
#------------------
# Probabilistic Guttman Model (Proctor, 1970)
# example analysis can also be found in the sirt package (see ?prob.guttman)
data(data.read, package = 'sirt')
head(data.read)
#> A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4
#> 2 1 1 1 1 1 1 1 1 1 1 1 0
#> 22 1 1 0 0 1 0 1 1 1 0 1 0
#> 23 1 1 0 1 1 0 1 1 1 1 1 1
#> 41 1 1 1 1 1 1 1 1 1 1 1 1
#> 43 1 0 0 1 0 0 1 1 1 0 1 0
#> 63 1 1 0 0 1 0 1 1 1 1 1 1
Theta <- matrix(c(1,0,0,0,
1,1,0,0,
1,1,1,0,
1,1,1,1), 4, byrow=TRUE)
model <- mirt.model("INTERCEPT = 1-12
C1 = 1,7,9,11
C2 = 2,5,8,10,12
C3 = 3,4,6")
mod <- mdirt(data.read, model, customTheta=Theta)
#>
Iteration: 1, Log-Lik: -6782.919, Max-Change: 4.84683
Iteration: 2, Log-Lik: -2028.321, Max-Change: 1.24269
Iteration: 3, Log-Lik: -1982.631, Max-Change: 0.90648
Iteration: 4, Log-Lik: -1968.458, Max-Change: 0.57055
Iteration: 5, Log-Lik: -1964.032, Max-Change: 0.62507
Iteration: 6, Log-Lik: -1961.312, Max-Change: 0.66604
Iteration: 7, Log-Lik: -1960.474, Max-Change: 0.40556
Iteration: 8, Log-Lik: -1957.169, Max-Change: 0.11661
Iteration: 9, Log-Lik: -1956.990, Max-Change: 0.04031
Iteration: 10, Log-Lik: -1956.920, Max-Change: 0.03167
Iteration: 11, Log-Lik: -1956.871, Max-Change: 0.02919
Iteration: 12, Log-Lik: -1956.836, Max-Change: 0.02705
Iteration: 13, Log-Lik: -1956.812, Max-Change: 0.04865
Iteration: 14, Log-Lik: -1956.748, Max-Change: 0.01675
Iteration: 15, Log-Lik: -1956.739, Max-Change: 0.01536
Iteration: 16, Log-Lik: -1956.731, Max-Change: 0.02328
Iteration: 17, Log-Lik: -1956.718, Max-Change: 0.01444
Iteration: 18, Log-Lik: -1956.713, Max-Change: 0.01422
Iteration: 19, Log-Lik: -1956.713, Max-Change: 0.02398
Iteration: 20, Log-Lik: -1956.697, Max-Change: 0.01187
Iteration: 21, Log-Lik: -1956.694, Max-Change: 0.01352
Iteration: 22, Log-Lik: -1956.690, Max-Change: 0.01440
Iteration: 23, Log-Lik: -1956.685, Max-Change: 0.01045
Iteration: 24, Log-Lik: -1956.683, Max-Change: 0.01204
Iteration: 25, Log-Lik: -1956.680, Max-Change: 0.01449
Iteration: 26, Log-Lik: -1956.676, Max-Change: 0.00943
Iteration: 27, Log-Lik: -1956.674, Max-Change: 0.01093
Iteration: 28, Log-Lik: -1956.672, Max-Change: 0.01256
Iteration: 29, Log-Lik: -1956.669, Max-Change: 0.00919
Iteration: 30, Log-Lik: -1956.667, Max-Change: 0.00925
Iteration: 31, Log-Lik: -1956.665, Max-Change: 0.01110
Iteration: 32, Log-Lik: -1956.663, Max-Change: 0.00954
Iteration: 33, Log-Lik: -1956.661, Max-Change: 0.00834
Iteration: 34, Log-Lik: -1956.660, Max-Change: 0.00952
Iteration: 35, Log-Lik: -1956.658, Max-Change: 0.00849
Iteration: 36, Log-Lik: -1956.657, Max-Change: 0.00789
Iteration: 37, Log-Lik: -1956.655, Max-Change: 0.00715
Iteration: 38, Log-Lik: -1956.654, Max-Change: 0.00707
Iteration: 39, Log-Lik: -1956.653, Max-Change: 0.00674
Iteration: 40, Log-Lik: -1956.652, Max-Change: 0.00663
Iteration: 41, Log-Lik: -1956.651, Max-Change: 0.00599
Iteration: 42, Log-Lik: -1956.650, Max-Change: 0.00627
Iteration: 43, Log-Lik: -1956.650, Max-Change: 0.00582
Iteration: 44, Log-Lik: -1956.649, Max-Change: 0.00567
Iteration: 45, Log-Lik: -1956.648, Max-Change: 0.00555
Iteration: 46, Log-Lik: -1956.647, Max-Change: 0.00551
Iteration: 47, Log-Lik: -1956.647, Max-Change: 0.00496
Iteration: 48, Log-Lik: -1956.646, Max-Change: 0.00514
Iteration: 49, Log-Lik: -1956.645, Max-Change: 0.00481
Iteration: 50, Log-Lik: -1956.645, Max-Change: 0.00466
Iteration: 51, Log-Lik: -1956.644, Max-Change: 0.00455
Iteration: 52, Log-Lik: -1956.644, Max-Change: 0.00454
Iteration: 53, Log-Lik: -1956.643, Max-Change: 0.00404
Iteration: 54, Log-Lik: -1956.643, Max-Change: 0.00418
Iteration: 55, Log-Lik: -1956.642, Max-Change: 0.00391
Iteration: 56, Log-Lik: -1956.642, Max-Change: 0.00379
Iteration: 57, Log-Lik: -1956.642, Max-Change: 0.00370
Iteration: 58, Log-Lik: -1956.641, Max-Change: 0.00266
Iteration: 59, Log-Lik: -1956.641, Max-Change: 0.00239
Iteration: 60, Log-Lik: -1956.641, Max-Change: 0.00226
Iteration: 61, Log-Lik: -1956.641, Max-Change: 0.00446
Iteration: 62, Log-Lik: -1956.640, Max-Change: 0.00203
Iteration: 63, Log-Lik: -1956.640, Max-Change: 0.00328
Iteration: 64, Log-Lik: -1956.640, Max-Change: 0.00212
Iteration: 65, Log-Lik: -1956.640, Max-Change: 0.00194
Iteration: 66, Log-Lik: -1956.639, Max-Change: 0.00186
Iteration: 67, Log-Lik: -1956.639, Max-Change: 0.00237
Iteration: 68, Log-Lik: -1956.639, Max-Change: 0.00180
Iteration: 69, Log-Lik: -1956.639, Max-Change: 0.00170
Iteration: 70, Log-Lik: -1956.639, Max-Change: 0.00200
Iteration: 71, Log-Lik: -1956.639, Max-Change: 0.00162
Iteration: 72, Log-Lik: -1956.639, Max-Change: 0.00156
Iteration: 73, Log-Lik: -1956.638, Max-Change: 0.00195
Iteration: 74, Log-Lik: -1956.638, Max-Change: 0.00151
Iteration: 75, Log-Lik: -1956.638, Max-Change: 0.00144
Iteration: 76, Log-Lik: -1956.638, Max-Change: 0.00180
Iteration: 77, Log-Lik: -1956.638, Max-Change: 0.00138
Iteration: 78, Log-Lik: -1956.638, Max-Change: 0.00133
Iteration: 79, Log-Lik: -1956.638, Max-Change: 0.00166
Iteration: 80, Log-Lik: -1956.638, Max-Change: 0.00127
Iteration: 81, Log-Lik: -1956.637, Max-Change: 0.00000
summary(mod)
#> $A1
#> category_1 category_2
#> P[1 0 0 0] 0.331 0.669
#> P[1 1 0 0] 0.037 0.963
#> P[1 1 1 0] 0.037 0.963
#> P[1 1 1 1] 0.037 0.963
#>
#> $A2
#> category_1 category_2
#> P[1 0 0 0] 0.544 0.456
#> P[1 1 0 0] 0.544 0.456
#> P[1 1 1 0] 0.041 0.959
#> P[1 1 1 1] 0.041 0.959
#>
#> $A3
#> category_1 category_2
#> P[1 0 0 0] 0.687 0.313
#> P[1 1 0 0] 0.687 0.313
#> P[1 1 1 0] 0.687 0.313
#> P[1 1 1 1] 0.097 0.903
#>
#> $A4
#> category_1 category_2
#> P[1 0 0 0] 0.709 0.291
#> P[1 1 0 0] 0.709 0.291
#> P[1 1 1 0] 0.709 0.291
#> P[1 1 1 1] 0.315 0.685
#>
#> $B1
#> category_1 category_2
#> P[1 0 0 0] 0.438 0.562
#> P[1 1 0 0] 0.438 0.562
#> P[1 1 1 0] 0.168 0.832
#> P[1 1 1 1] 0.168 0.832
#>
#> $B2
#> category_1 category_2
#> P[1 0 0 0] 0.628 0.372
#> P[1 1 0 0] 0.628 0.372
#> P[1 1 1 0] 0.628 0.372
#> P[1 1 1 1] 0.317 0.683
#>
#> $B3
#> category_1 category_2
#> P[1 0 0 0] 0.205 0.795
#> P[1 1 0 0] 0.021 0.979
#> P[1 1 1 0] 0.021 0.979
#> P[1 1 1 1] 0.021 0.979
#>
#> $B4
#> category_1 category_2
#> P[1 0 0 0] 0.543 0.457
#> P[1 1 0 0] 0.543 0.457
#> P[1 1 1 0] 0.140 0.860
#> P[1 1 1 1] 0.140 0.860
#>
#> $C1
#> category_1 category_2
#> P[1 0 0 0] 0.175 0.825
#> P[1 1 0 0] 0.000 1.000
#> P[1 1 1 0] 0.000 1.000
#> P[1 1 1 1] 0.000 1.000
#>
#> $C2
#> category_1 category_2
#> P[1 0 0 0] 0.526 0.474
#> P[1 1 0 0] 0.526 0.474
#> P[1 1 1 0] 0.098 0.902
#> P[1 1 1 1] 0.098 0.902
#>
#> $C3
#> category_1 category_2
#> P[1 0 0 0] 0.292 0.708
#> P[1 1 0 0] 0.026 0.974
#> P[1 1 1 0] 0.026 0.974
#> P[1 1 1 1] 0.026 0.974
#>
#> $C4
#> category_1 category_2
#> P[1 0 0 0] 0.425 0.575
#> P[1 1 0 0] 0.425 0.575
#> P[1 1 1 0] 0.140 0.860
#> P[1 1 1 1] 0.140 0.860
#>
#> $Class.Probability
#> INTERCEPT C1 C2 C3 prob
#> Profile_1 1 0 0 0 0.383
#> Profile_2 1 1 0 0 0.057
#> Profile_3 1 1 1 0 0.130
#> Profile_4 1 1 1 1 0.431
#>
M2(mod)
#> M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR
#> stats 145.0553 51 5.876977e-11 0.07509875 0.06080295 0.08947343 0.09158964
#> TLI CFI
#> stats 0.8130941 0.8555727
itemfit(mod)
#> item S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1 A1 27.808 7 0.095 0.000
#> 2 A2 2.984 6 0.000 0.811
#> 3 A3 10.219 6 0.046 0.116
#> 4 A4 5.575 6 0.000 0.472
#> 5 B1 8.168 7 0.023 0.318
#> 6 B2 7.176 6 0.024 0.305
#> 7 B3 9.351 7 0.032 0.228
#> 8 B4 2.359 6 0.000 0.884
#> 9 C1 6.260 5 0.028 0.282
#> 10 C2 6.914 6 0.022 0.329
#> 11 C3 11.734 7 0.045 0.110
#> 12 C4 5.585 7 0.000 0.589
# }