| fscores {mirt} | R Documentation |
Computes MAP, EAP, ML (Embretson & Reise, 2000), EAP for sum-scores (Thissen et al., 1995),
or WLE (Warm, 1989) factor scores with a multivariate normal
prior distribution using equally spaced quadrature. EAP scores for models with more than
three factors are generally not recommended since the integration grid becomes very large,
resulting in slower estimation and less precision if the quadpts are too low.
Therefore, MAP scores should be used instead of EAP scores for higher dimensional models.
Multiple imputation variants are possible for each estimator if a parameter
information matrix was computed, which are useful if the sample size/number of items were small.
As well, if the model contained latent regression predictors this information will
be used in computing MAP and EAP estimates (for these models, full.scores=TRUE
will always be used). Finally, plausible value imputation is also available, and will also account
for latent regression predictor effects.
fscores(
object,
method = "EAP",
full.scores = TRUE,
rotate = "oblimin",
Target = NULL,
response.pattern = NULL,
append_response.pattern = FALSE,
na.rm = FALSE,
plausible.draws = 0,
plausible.type = "normal",
quadpts = NULL,
item_weights = rep(1, extract.mirt(object, "nitems")),
returnER = FALSE,
T_as_X = FALSE,
EAPsum.scores = FALSE,
return.acov = FALSE,
mean = NULL,
cov = NULL,
covdata = NULL,
verbose = TRUE,
full.scores.SE = FALSE,
theta_lim = c(-6, 6),
MI = 0,
use_dentype_estimate = FALSE,
QMC = FALSE,
custom_den = NULL,
custom_theta = NULL,
min_expected = 1,
max_theta = 20,
start = NULL,
...
)
object |
a computed model object of class |
method |
type of factor score estimation method. Can be:
|
full.scores |
if |
rotate |
prior rotation to be used when estimating the factor scores. See
|
Target |
target rotation; see |
response.pattern |
an optional argument used to calculate the factor scores and standard errors for a given response vector or matrix/data.frame |
append_response.pattern |
logical; should the inputs from |
na.rm |
logical; remove rows with any missing values? This is generally not required due to the nature of computing factors scores, however for the "EAPsum" method this may be necessary to ensure that the sum-scores correspond to the same composite score |
plausible.draws |
number of plausible values to draw for future researchers
to perform secondary analyses of the latent trait scores. Typically used in conjunction
with latent regression predictors (see |
plausible.type |
type of plausible values to obtain. Can be either |
quadpts |
number of quadrature to use per dimension. If not specified, a suitable
one will be created which decreases as the number of dimensions increases
(and therefore for estimates such as EAP, will be less accurate). This is determined from
the switch statement
|
item_weights |
a user-defined weight vector used in the likelihood expressions to add more/less weight for a given observed response. Default is a vector of 1's, indicating that all the items receive the same weight |
returnER |
logical; return empirical reliability (also known as marginal reliability) estimates as a numeric values? |
T_as_X |
logical; should the observed variance be equal to
|
EAPsum.scores |
logical; include the model-implied expected values and variance for the item
and total scores when using |
return.acov |
logical; return a list containing covariance matrices instead of factors
scores? |
mean |
a vector for custom latent variable means. If NULL, the default for 'group' values from the computed mirt object will be used |
cov |
a custom matrix of the latent variable covariance matrix. If NULL, the default for 'group' values from the computed mirt object will be used |
covdata |
when latent regression model has been fitted, and the |
verbose |
logical; print verbose output messages? |
full.scores.SE |
logical; when |
theta_lim |
lower and upper range to evaluate latent trait integral for each dimension. If omitted, a range will be generated automatically based on the number of dimensions |
MI |
a number indicating how many multiple imputation draws to perform. Default is 0, indicating that no MI draws will be performed |
use_dentype_estimate |
logical; if the density of the latent trait was estimated in the model (e.g., via Davidian curves or empirical histograms), should this information be used to compute the latent trait estimates? Only applicable for EAP-based estimates (EAP, EAPsum, and plausible) |
QMC |
logical; use quasi-Monte Carlo integration? If |
custom_den |
a function used to define the integration density (if required). The NULL default assumes that the multivariate normal distribution with the 'GroupPars' hyper-parameters are used. At the minimum must be of the form:
where Theta is a matrix of latent trait values (will be a grid of values
if |
custom_theta |
a matrix of custom integration nodes to use instead of the default, where each column corresponds to the respective dimension in the model |
min_expected |
when computing goodness of fit tests when |
max_theta |
the maximum/minimum value any given factor score estimate will achieve using any modal estimator method (e.g., MAP, WLE, ML) |
start |
a matrix of starting values to use for iterative estimation methods. Default
will start at a vector of 0's for each response pattern, or will start at the EAP
estimates (unidimensional models only). Must be in the form that matches
|
... |
additional arguments to be passed to |
The function will return either a table with the computed scores and standard errors,
the original data matrix with scores appended to the rightmost column, or the scores only. By
default the latent means and covariances are determined from the estimated object,
though these can be overwritten. Iterative estimation methods can be estimated
in parallel to decrease estimation times if a mirtCluster object is available.
If the input object is a discrete latent class object estimated from mdirt
then the returned results will be with respect to the posterior classification for each
individual. The method inputs for 'DiscreteClass' objects may only be 'EAP',
for posterior classification of each response pattern, or 'EAPsum' for posterior
classification based on the raw sum-score. For more information on these algorithms refer to
the mirtCAT package and the associated JSS paper (Chalmers, 2016).
Phil Chalmers rphilip.chalmers@gmail.com
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
Chalmers, R. P. (2016). Generating Adaptive and Non-Adaptive Test Interfaces for Multidimensional Item Response Theory Applications. Journal of Statistical Software, 71(5), 1-39. doi:10.18637/jss.v071.i05
Embretson, S. E. & Reise, S. P. (2000). Item Response Theory for Psychologists. Erlbaum.
Thissen, D., Pommerich, M., Billeaud, K., & Williams, V. S. L. (1995). Item Response Theory for Scores on Tests Including Polytomous Items with Ordered Responses. Applied Psychological Measurement, 19, 39-49.
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450.
mod <- mirt(Science)
tabscores <- fscores(mod, full.scores = FALSE)
##
## Method: EAP
##
## Empirical Reliability:
##
## F1
## 0.6666
head(tabscores)
## Comfort Work Future Benefit F1 SE_F1
## [1,] 1 1 1 1 -2.7492669 0.6293525
## [2,] 1 3 2 1 -1.4198318 0.5772364
## [3,] 1 4 2 3 -0.7141976 0.6200139
## [4,] 1 4 3 1 -0.4469265 0.6509531
## [5,] 2 1 1 1 -2.5437807 0.5909114
## [6,] 2 1 2 4 -1.2478570 0.5840105
# convert scores into expected total score information with 95% CIs
E.total <- expected.test(mod, Theta=tabscores[,'F1'])
E.total_2.5 <- expected.test(mod, Theta=tabscores[,'F1'] +
tabscores[,'SE_F1'] * qnorm(.05/2))
E.total_97.5 <- expected.test(mod, Theta=tabscores[,'F1'] +
tabscores[,'SE_F1'] * qnorm(1-.05/2))
data.frame(Total_score=rowSums(tabscores[,1:4]),
E.total, E.total_2.5, E.total_97.5) |> head()
## Total_score E.total E.total_2.5 E.total_97.5
## 1 4 6.791606 5.321810 9.084082
## 2 7 9.266018 7.128071 11.296189
## 3 10 10.584682 8.296461 12.504975
## 4 9 11.041648 8.691107 13.034195
## 5 5 7.141179 5.576233 9.330947
## 6 9 9.592533 7.415339 11.582060
## No test:
fullscores <- fscores(mod)
fullscores_with_SE <- fscores(mod, full.scores.SE=TRUE)
head(fullscores)
## F1
## [1,] 0.4015613
## [2,] 0.0520324
## [3,] -0.8906436
## [4,] -0.8906436
## [5,] 0.7653806
## [6,] 0.6695350
head(fullscores_with_SE)
## F1 SE_F1
## [1,] 0.4015613 0.5978747
## [2,] 0.0520324 0.5549554
## [3,] -0.8906436 0.5421855
## [4,] -0.8906436 0.5421855
## [5,] 0.7653806 0.6385998
## [6,] 0.6695350 0.5761860
# convert scores into expected total score information with 95% CIs
E.total <- expected.test(mod, Theta=fullscores[,'F1'])
E.total_2.5 <- expected.test(mod, Theta=fullscores_with_SE[,'F1'] +
fullscores_with_SE[,'SE_F1'] * qnorm(.05/2))
E.total_97.5 <- expected.test(mod, Theta=fullscores_with_SE[,'F1'] +
fullscores_with_SE[,'SE_F1'] * qnorm(1-.05/2))
data.frame(Total_score=rowSums(Science),
E.total, E.total_2.5, E.total_97.5) |> head()
## Total_score E.total E.total_2.5 E.total_97.5
## 1 13 12.34882 10.484432 14.15621
## 2 12 11.81643 9.994252 13.53226
## 3 10 10.26478 8.250620 11.99721
## 4 10 10.26478 8.250620 11.99721
## 5 12 12.93068 10.976668 14.67563
## 6 14 12.77499 11.020512 14.43522
# change method argument to use MAP estimates
fullscores <- fscores(mod, method='MAP')
head(fullscores)
## F1
## [1,] 0.42140793
## [2,] 0.05866659
## [3,] -0.91936052
## [4,] -0.91936052
## [5,] 0.79013883
## [6,] 0.68302194
# calculate MAP for a given response vector
fscores(mod, method='MAP', response.pattern = c(1,2,3,4))
## F1 SE_F1
## [1,] -0.3704194 0.6054172
# or matrix
fscores(mod, method='MAP', response.pattern = rbind(c(1,2,3,4), c(2,2,1,3)))
## F1 SE_F1
## [1,] -0.3704194 0.6054172
## [2,] -1.6937559 0.5773972
# return only the scores and their SEs
fscores(mod, method='MAP', response.pattern = c(1,2,3,4))
## F1 SE_F1
## [1,] -0.3704194 0.6054172
# use custom latent variable properties (diffuse prior for MAP is very close to ML)
fscores(mod, method='MAP', cov = matrix(1000), full.scores = FALSE)
##
## Method: MAP
##
## Empirical Reliability:
##
## F1
## 0.4207
## Comfort Work Future Benefit F1 SE_F1
## [1,] 1 1 1 1 -9.340 9.636
## [2,] 1 3 2 1 -2.104 0.689
## [3,] 1 4 2 3 -1.151 0.705
## [4,] 1 4 3 1 -0.781 0.807
## [5,] 2 1 1 1 -4.394 1.179
## [6,] 2 1 2 4 -1.863 0.668
## [7,] 2 2 1 1 -3.248 0.812
## [8,] 2 2 2 2 -1.911 0.588
## [9,] 2 2 2 3 -1.606 0.608
## [10,] 2 2 3 1 -1.468 0.714
## [11,] 2 2 3 2 -1.168 0.635
## [12,] 2 2 3 3 -0.797 0.639
## [13,] 2 2 4 3 0.240 0.789
## [14,] 2 3 1 3 -2.142 0.702
## [15,] 2 3 2 2 -1.609 0.626
## [16,] 2 3 2 3 -1.254 0.630
## [17,] 2 3 3 2 -0.756 0.656
## [18,] 2 3 3 3 -0.332 0.698
## [19,] 2 3 3 4 0.083 0.761
## [20,] 2 3 4 1 0.189 0.878
## [21,] 2 3 4 3 0.763 0.681
## [22,] 2 4 2 1 -1.822 0.694
## [23,] 2 4 4 3 1.307 0.753
## [24,] 2 4 4 4 2.095 1.039
## [25,] 3 1 1 1 -3.538 1.001
## [26,] 3 1 1 3 -2.510 0.697
## [27,] 3 1 2 2 -1.926 0.615
## [28,] 3 1 2 3 -1.587 0.643
## [29,] 3 1 3 2 -1.088 0.674
## [30,] 3 1 3 3 -0.658 0.696
## [31,] 3 1 3 4 -0.281 0.807
## [32,] 3 1 4 3 0.542 0.734
## [33,] 3 1 4 4 1.038 0.736
## [34,] 3 2 1 2 -2.348 0.625
## [35,] 3 2 1 4 -1.913 0.709
## [36,] 3 2 2 1 -1.861 0.616
## [37,] 3 2 2 2 -1.577 0.594
## [38,] 3 2 2 3 -1.255 0.602
## [39,] 3 2 3 1 -1.025 0.663
## [40,] 3 2 3 2 -0.798 0.629
## [41,] 3 2 3 3 -0.409 0.668
## [42,] 3 2 3 4 -0.037 0.744
## [43,] 3 2 4 1 0.015 0.900
## [44,] 3 2 4 2 0.205 0.789
## [45,] 3 2 4 3 0.643 0.684
## [46,] 3 2 4 4 1.102 0.718
## [47,] 3 3 1 3 -1.629 0.780
## [48,] 3 3 2 1 -1.518 0.659
## [49,] 3 3 2 2 -1.239 0.617
## [50,] 3 3 2 3 -0.882 0.630
## [51,] 3 3 2 4 -0.621 0.708
## [52,] 3 3 3 1 -0.549 0.711
## [53,] 3 3 3 2 -0.347 0.687
## [54,] 3 3 3 3 0.086 0.687
## [55,] 3 3 3 4 0.490 0.676
## [56,] 3 3 4 2 0.732 0.681
## [57,] 3 3 4 3 1.048 0.650
## [58,] 3 3 4 4 1.525 0.746
## [59,] 3 4 1 3 -1.381 0.943
## [60,] 3 4 2 3 -0.608 0.726
## [61,] 3 4 3 2 0.099 0.768
## [62,] 3 4 3 3 0.538 0.677
## [63,] 3 4 3 4 0.961 0.675
## [64,] 3 4 4 1 1.218 0.758
## [65,] 3 4 4 2 1.272 0.749
## [66,] 3 4 4 3 1.599 0.766
## [67,] 3 4 4 4 2.422 1.040
## [68,] 4 1 1 4 -2.106 0.772
## [69,] 4 1 2 2 -1.638 0.654
## [70,] 4 1 2 4 -1.014 0.724
## [71,] 4 1 3 4 0.361 0.778
## [72,] 4 2 2 1 -1.568 0.651
## [73,] 4 2 2 3 -0.935 0.628
## [74,] 4 2 3 3 0.054 0.711
## [75,] 4 2 3 4 0.492 0.710
## [76,] 4 2 4 2 0.762 0.723
## [77,] 4 2 4 4 1.760 0.931
## [78,] 4 3 2 3 -0.485 0.704
## [79,] 4 3 3 2 0.139 0.718
## [80,] 4 3 3 3 0.533 0.652
## [81,] 4 3 3 4 0.929 0.655
## [82,] 4 3 4 2 1.216 0.719
## [83,] 4 3 4 3 1.527 0.734
## [84,] 4 3 4 4 2.258 0.968
## [85,] 4 4 3 2 0.640 0.707
## [86,] 4 4 3 3 0.981 0.661
## [87,] 4 4 3 4 1.465 0.749
## [88,] 4 4 4 2 2.028 1.010
## [89,] 4 4 4 3 2.390 1.015
## [90,] 4 4 4 4 7.112 10.616
fscores(mod, method='ML', full.scores = FALSE)
##
## Method: ML
##
## Empirical Reliability:
##
## F1
## 0.716
## Comfort Work Future Benefit F1 SE_F1
## [1,] 1 1 1 1 -Inf NA
## [2,] 1 3 2 1 -2.105 0.689
## [3,] 1 4 2 3 -1.151 0.705
## [4,] 1 4 3 1 -0.781 0.807
## [5,] 2 1 1 1 -4.400 1.182
## [6,] 2 1 2 4 -1.864 0.668
## [7,] 2 2 1 1 -3.250 0.813
## [8,] 2 2 2 2 -1.912 0.588
## [9,] 2 2 2 3 -1.606 0.609
## [10,] 2 2 3 1 -1.469 0.714
## [11,] 2 2 3 2 -1.169 0.635
## [12,] 2 2 3 3 -0.797 0.639
## [13,] 2 2 4 3 0.240 0.789
## [14,] 2 3 1 3 -2.143 0.702
## [15,] 2 3 2 2 -1.609 0.626
## [16,] 2 3 2 3 -1.254 0.630
## [17,] 2 3 3 2 -0.756 0.656
## [18,] 2 3 3 3 -0.332 0.698
## [19,] 2 3 3 4 0.083 0.762
## [20,] 2 3 4 1 0.189 0.878
## [21,] 2 3 4 3 0.763 0.681
## [22,] 2 4 2 1 -1.823 0.694
## [23,] 2 4 4 3 1.308 0.754
## [24,] 2 4 4 4 2.097 1.041
## [25,] 3 1 1 1 -3.542 1.004
## [26,] 3 1 1 3 -2.511 0.698
## [27,] 3 1 2 2 -1.926 0.615
## [28,] 3 1 2 3 -1.588 0.644
## [29,] 3 1 3 2 -1.088 0.674
## [30,] 3 1 3 3 -0.658 0.696
## [31,] 3 1 3 4 -0.281 0.808
## [32,] 3 1 4 3 0.543 0.734
## [33,] 3 1 4 4 1.038 0.736
## [34,] 3 2 1 2 -2.349 0.625
## [35,] 3 2 1 4 -1.914 0.709
## [36,] 3 2 2 1 -1.862 0.616
## [37,] 3 2 2 2 -1.577 0.594
## [38,] 3 2 2 3 -1.255 0.602
## [39,] 3 2 3 1 -1.026 0.663
## [40,] 3 2 3 2 -0.798 0.629
## [41,] 3 2 3 3 -0.409 0.668
## [42,] 3 2 3 4 -0.037 0.744
## [43,] 3 2 4 1 0.015 0.901
## [44,] 3 2 4 2 0.206 0.789
## [45,] 3 2 4 3 0.643 0.684
## [46,] 3 2 4 4 1.102 0.719
## [47,] 3 3 1 3 -1.630 0.780
## [48,] 3 3 2 1 -1.518 0.659
## [49,] 3 3 2 2 -1.240 0.617
## [50,] 3 3 2 3 -0.883 0.630
## [51,] 3 3 2 4 -0.621 0.708
## [52,] 3 3 3 1 -0.549 0.711
## [53,] 3 3 3 2 -0.348 0.688
## [54,] 3 3 3 3 0.086 0.687
## [55,] 3 3 3 4 0.490 0.676
## [56,] 3 3 4 2 0.733 0.681
## [57,] 3 3 4 3 1.048 0.650
## [58,] 3 3 4 4 1.526 0.746
## [59,] 3 4 1 3 -1.383 0.943
## [60,] 3 4 2 3 -0.609 0.726
## [61,] 3 4 3 2 0.099 0.768
## [62,] 3 4 3 3 0.538 0.678
## [63,] 3 4 3 4 0.962 0.675
## [64,] 3 4 4 1 1.219 0.759
## [65,] 3 4 4 2 1.273 0.749
## [66,] 3 4 4 3 1.600 0.767
## [67,] 3 4 4 4 2.425 1.042
## [68,] 4 1 1 4 -2.107 0.772
## [69,] 4 1 2 2 -1.639 0.654
## [70,] 4 1 2 4 -1.015 0.724
## [71,] 4 1 3 4 0.361 0.778
## [72,] 4 2 2 1 -1.568 0.651
## [73,] 4 2 2 3 -0.936 0.628
## [74,] 4 2 3 3 0.054 0.711
## [75,] 4 2 3 4 0.492 0.710
## [76,] 4 2 4 2 0.763 0.723
## [77,] 4 2 4 4 1.761 0.932
## [78,] 4 3 2 3 -0.485 0.704
## [79,] 4 3 3 2 0.139 0.718
## [80,] 4 3 3 3 0.533 0.652
## [81,] 4 3 3 4 0.929 0.656
## [82,] 4 3 4 2 1.216 0.720
## [83,] 4 3 4 3 1.527 0.735
## [84,] 4 3 4 4 2.261 0.969
## [85,] 4 4 3 2 0.640 0.707
## [86,] 4 4 3 3 0.982 0.662
## [87,] 4 4 3 4 1.465 0.749
## [88,] 4 4 4 2 2.030 1.011
## [89,] 4 4 4 3 2.392 1.016
## [90,] 4 4 4 4 Inf NA
# EAPsum table of values based on total scores
(fs <- fscores(mod, method = 'EAPsum', full.scores = FALSE))
## df X2 p.X2 SEM.alpha rxx.alpha rxx_F1
## stats 10 16.312 0.091 1.262 0.616 0.624
## Sum.Scores F1 SE_F1 observed expected std.res
## 4 4 -2.749 0.629 2 0.124 5.324
## 5 5 -2.431 0.617 1 0.790 0.236
## 6 6 -2.081 0.610 2 2.760 0.457
## 7 7 -1.718 0.602 1 7.252 2.322
## 8 8 -1.364 0.598 11 15.893 1.227
## 9 9 -1.012 0.604 32 29.674 0.427
## 10 10 -0.649 0.610 58 48.363 1.386
## 11 11 -0.287 0.605 70 68.485 0.183
## 12 12 0.082 0.600 91 80.553 1.164
## 13 13 0.487 0.613 56 65.668 1.193
## 14 14 0.934 0.617 36 42.637 1.016
## 15 15 1.384 0.622 20 22.331 0.493
## 16 16 1.854 0.654 12 7.470 1.657
# convert expected counts back into marginal probability distribution
within(fs,
`P(y)` <- expected / sum(observed))
## Sum.Scores F1 SE_F1 observed expected std.res P(y)
## 4 4 -2.749 0.629 2 0.124 5.324 0.000
## 5 5 -2.431 0.617 1 0.790 0.236 0.002
## 6 6 -2.081 0.610 2 2.760 0.457 0.007
## 7 7 -1.718 0.602 1 7.252 2.322 0.018
## 8 8 -1.364 0.598 11 15.893 1.227 0.041
## 9 9 -1.012 0.604 32 29.674 0.427 0.076
## 10 10 -0.649 0.610 58 48.363 1.386 0.123
## 11 11 -0.287 0.605 70 68.485 0.183 0.175
## 12 12 0.082 0.600 91 80.553 1.164 0.205
## 13 13 0.487 0.613 56 65.668 1.193 0.168
## 14 14 0.934 0.617 36 42.637 1.016 0.109
## 15 15 1.384 0.622 20 22.331 0.493 0.057
## 16 16 1.854 0.654 12 7.470 1.657 0.019
# list of error VCOV matrices for EAPsum (works for other estimators as well)
acovs <- fscores(mod, method = 'EAPsum', full.scores = FALSE, return.acov = TRUE)
acovs
## $`0`
## [,1]
## [1,] 0.3960846
##
## $`1`
## [,1]
## [1,] 0.3804011
##
## $`2`
## [,1]
## [1,] 0.3723228
##
## $`3`
## [,1]
## [1,] 0.3623228
##
## $`4`
## [,1]
## [1,] 0.3575813
##
## $`5`
## [,1]
## [1,] 0.3646464
##
## $`6`
## [,1]
## [1,] 0.3722588
##
## $`7`
## [,1]
## [1,] 0.365832
##
## $`8`
## [,1]
## [1,] 0.3595964
##
## $`9`
## [,1]
## [1,] 0.3762024
##
## $`10`
## [,1]
## [1,] 0.3807206
##
## $`11`
## [,1]
## [1,] 0.3866677
##
## $`12`
## [,1]
## [1,] 0.4282521
# WLE estimation, run in parallel using available cores
if(interactive()) mirtCluster()
head(fscores(mod, method='WLE', full.scores = FALSE))
##
## Method: WLE
##
## Empirical Reliability:
##
## F1
## 0.7513
## Comfort Work Future Benefit F1 SE_F1
## [1,] 1 1 1 1 -5.6980733 1.5782656
## [2,] 1 3 2 1 -2.1191038 0.6332801
## [3,] 1 4 2 3 -1.1387624 0.6557003
## [4,] 1 4 3 1 -0.8489387 0.7000117
## [5,] 2 1 1 1 -4.0112458 1.1423934
## [6,] 2 1 2 4 -1.8957020 0.6698434
# multiple imputation using 30 draws for EAP scores. Requires information matrix
mod <- mirt(Science, 1, SE=TRUE)
fs <- fscores(mod, MI = 30)
head(fs)
## F1
## [1,] 0.44176153
## [2,] 0.07193746
## [3,] -0.83790601
## [4,] -0.83790601
## [5,] 0.73027479
## [6,] 0.71605941
# plausible values for future work
pv <- fscores(mod, plausible.draws = 5)
lapply(pv, function(x) c(mean=mean(x), var=var(x), min=min(x), max=max(x)))
## [[1]]
## mean var min max
## 0.05330257 0.93163419 -2.96163814 2.86795322
##
## [[2]]
## mean var min max
## 0.006379846 0.892739272 -2.406650845 2.754533140
##
## [[3]]
## mean var min max
## -0.03334085 1.02687639 -4.56299130 2.55592762
##
## [[4]]
## mean var min max
## 0.02008484 1.10372303 -3.36649943 2.72546297
##
## [[5]]
## mean var min max
## 0.0003896072 1.0142018274 -3.6737915702 2.8973793503
## define a custom_den function (*must* return a numeric vector).
# EAP with a uniform prior between -3 and 3
fun <- function(Theta, ...) as.numeric(dunif(Theta, min = -3, max = 3))
head(fscores(mod, custom_den = fun))
## F1
## [1,] 0.62740797
## [2,] 0.07362014
## [3,] -1.23412036
## [4,] -1.23412036
## [5,] 1.25196942
## [6,] 1.00691502
# compare EAP estimators with same modified prior
fun <- function(Theta, ...) as.numeric(dnorm(Theta, mean=.5))
head(fscores(mod, custom_den = fun))
## F1
## [1,] 0.5801169
## [2,] 0.2057691
## [3,] -0.7411082
## [4,] -0.7411082
## [5,] 0.9677165
## [6,] 0.8355336
head(fscores(mod, method = 'EAP', mean=.5))
## F1
## [1,] 0.5801169
## [2,] 0.2057691
## [3,] -0.7411082
## [4,] -0.7411082
## [5,] 0.9677165
## [6,] 0.8355336
# custom MAP prior: standard truncated normal between 5 and -2
library(msm)
# need the :: scope for parallel to see the function (not require if no mirtCluster() defined)
fun <- function(Theta, ...) msm::dtnorm(Theta, mean = 0, sd = 1, lower = -2, upper = 5)
head(fscores(mod, custom_den = fun, method = 'MAP', full.scores = FALSE))
##
## Method: MAP
##
## Empirical Reliability:
##
## F1
## 0.6637
## Comfort Work Future Benefit F1 SE_F1
## [1,] 1 1 1 1 -1.9999989 0.5955535
## [2,] 1 3 2 1 -1.4234789 0.5680859
## [3,] 1 4 2 3 -0.7627999 0.5920501
## [4,] 1 4 3 1 -0.4621220 0.6529196
## [5,] 2 1 1 1 -1.9999996 0.5706600
## [6,] 2 1 2 4 -1.2729399 0.5680221
####################
# scoring via response.pattern input (with latent regression structure)
# simulate data
set.seed(1234)
N <- 1000
# covariates
X1 <- rnorm(N); X2 <- rnorm(N)
covdata <- data.frame(X1, X2)
Theta <- matrix(0.5 * X1 + -1 * X2 + rnorm(N, sd = 0.5))
# items and response data
a <- matrix(1, 20); d <- matrix(rnorm(20))
dat <- simdata(a, d, 1000, itemtype = '2PL', Theta=Theta)
# conditional model using X1 and X2 as predictors of Theta
mod <- mirt(dat, 1, 'Rasch', covdata=covdata, formula = ~ X1 + X2)
coef(mod, simplify=TRUE)
## $items
## a1 d g u
## Item_1 1 -0.409 0 1
## Item_2 1 0.491 0 1
## Item_3 1 0.313 0 1
## Item_4 1 1.965 0 1
## Item_5 1 1.753 0 1
## Item_6 1 -0.246 0 1
## Item_7 1 -1.077 0 1
## Item_8 1 0.533 0 1
## Item_9 1 -1.232 0 1
## Item_10 1 0.603 0 1
## Item_11 1 -0.404 0 1
## Item_12 1 1.238 0 1
## Item_13 1 1.033 0 1
## Item_14 1 1.524 0 1
## Item_15 1 -0.548 0 1
## Item_16 1 2.075 0 1
## Item_17 1 -0.695 0 1
## Item_18 1 -1.200 0 1
## Item_19 1 0.121 0 1
## Item_20 1 0.523 0 1
##
## $means
## F1
## 0
##
## $cov
## F1
## F1 0.215
##
## $lr.betas
## F1
## (Intercept) 0.000
## X1 0.527
## X2 -1.036
# all EAP estimates that include latent regression information
fs <- fscores(mod, full.scores.SE=TRUE)
head(fs)
## F1 SE_F1
## [1,] 0.3085528 0.3442171
## [2,] -0.3474225 0.3408508
## [3,] 2.0484669 0.3903338
## [4,] -1.9418737 0.3670521
## [5,] -0.7631612 0.3432707
## [6,] 2.1019760 0.3922137
# score only two response patterns
rp <- dat[1:2, ]
cd <- covdata[1:2, ]
fscores(mod, response.pattern=rp, covdata=cd)
## F1 SE_F1
## [1,] 0.3085528 0.3442171
## [2,] -0.3474225 0.3408508
fscores(mod, response.pattern=rp[2,], covdata=cd[2,]) # just one pattern
## F1 SE_F1
## [1,] -0.3474225 0.3408508
## End(No test)