R/fscores.R
fscores.RdComputes 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,
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,
...
)a computed model object of class SingleGroupClass,
MultipleGroupClass, or DiscreteClass
type of factor score estimation method. Can be:
"EAP" for the expected a-posteriori (default). For models fit using
mdirt this will return the posterior classification probabilities
"MAP" for the maximum a-posteriori (i.e, Bayes modal)
"ML" for maximum likelihood
"WLE" for weighted likelihood estimation
"EAPsum" for the expected a-posteriori for each sum score
"plausible" for a single plausible value imputation for each case.
This is equivalent to setting plausible.draws = 1
"classify" for the posteriori classification probabilities (only
applicable when the input model was of class MixtureClass)
if FALSE then a summary table with factor scores
for each unique pattern is displayed as a formatted matrix object.
Otherwise, a matrix of factor scores for each response pattern in the data
is returned (default)
prior rotation to be used when estimating the factor scores. See
summary-method for details. If the object is not an exploratory model
then this argument is ignored
target rotation; see summary-method for details
an optional argument used to calculate the factor scores and standard errors for a given response vector or matrix/data.frame
logical; should the inputs from response.pattern also be
appended to the factor score output?
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
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 mirt for details), but can
also be generated when no predictor variables were modelled. If plausible.draws
is greater than 0 a list of plausible values will be returned
type of plausible values to obtain. Can be either 'normal' (default)
to use a normal approximation based on the ACOV matrix, or 'MH' to obtain Metropolis-Hastings
samples from the posterior (silently passes object to mirt, therefore arguments like
technical can be supplied to increase the number of burn-in draws and discarded samples)
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
quadpts <- switch(as.character(nfact), '1'=61, '2'=31, '3'=15, '4'=9, '5'=7, 3)
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
logical; return empirical reliability (also known as marginal reliability) estimates as a numeric values?
logical; return a list containing covariance matrices instead of factors
scores? impute = TRUE not supported with this option
a vector for custom latent variable means. If NULL, the default for 'group' values from the computed mirt object will be used
a custom matrix of the latent variable covariance matrix. If NULL, the default for 'group' values from the computed mirt object will be used
when latent regression model has been fitted, and the response.pattern
input is used to score individuals, then this argument is used to include the latent regression
covariate terms for each row vector supplied to response.pattern
logical; print verbose output messages?
logical; when full.scores == TRUE, also return the
standard errors associated with each respondent? Default is FALSE
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
a number indicating how many multiple imputation draws to perform. Default is 0, indicating that no MI draws will be performed
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)
logical; use quasi-Monte Carlo integration? If quadpts is omitted the
default number of nodes is 5000
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:
function(Theta, ...)
where Theta is a matrix of latent trait values (will be a grid of values
if method == 'EAPsum' or method == 'EAP', otherwise Theta will have only 1 row).
Additional arguments may included and are caught through the fscores(...) input. The
function must return a numeric vector of density weights (one for each row in Theta)
a matrix of custom integration nodes to use instead of the default, where each column corresponds to the respective dimension in the model
when computing goodness of fit tests when method = 'EAPsum', this value is used
to collapse across the conditioned total scores until the expected values are greater than this value. Note
that this only affect the goodness of fit tests and not the returned EAP for sum scores table
the maximum/minimum value any given factor score estimate will achieve using any modal estimator method (e.g., MAP, WLE, ML)
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
full.scores = FALSE (mostly used in the mirtCAT package)
additional arguments to be passed to nlm
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).
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, 1)
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 -2.7492687 0.6293569
#> [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 -2.5437808 0.5909117
#> [6,] 2 1 2 4 -1.2478570 0.5840105
# \donttest{
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
# 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 0.6054169
# 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 0.6054169
#> [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 0.6054169
# 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 rxx_F1
#> stats 10 16.31202 0.09104204 0.6241528
#>
#> 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,] 0.3960901
#>
#> $`1`
#> [,1]
#> [1,] 0.3804013
#>
#> $`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,] 0.4282523
#>
# 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 0.6332802
#> [3,] 1 4 2 3 -1.1387624 0.6557002
#> [4,] 1 4 3 1 -0.8489387 0.7000115
#> [5,] 2 1 1 1 -4.0112458 1.1423935
#> [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,] 0.40372860
#> [2,] 0.05213443
#> [3,] -0.87326106
#> [4,] -0.87326106
#> [5,] 0.73588860
#> [6,] 0.67168522
# 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
#> 0.004113732 1.015978140 -3.141719690 2.826871142
#>
#> [[2]]
#> mean var min max
#> -0.03553089 1.07442924 -3.41117554 2.91259345
#>
#> [[3]]
#> mean var min max
#> -0.04658776 0.99236135 -3.80501935 2.77315045
#>
#> [[4]]
#> mean var min max
#> -0.007163955 1.010456675 -3.694015453 2.777961489
#>
#> [[5]]
#> mean var min max
#> 0.02381234 1.06136458 -4.22355342 2.93987861
#>
## define a custom_den function. 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,] 0.62811597
#> [2,] 0.07362511
#> [3,] -1.23497086
#> [4,] -1.23497086
#> [5,] 1.25827841
#> [6,] 1.00860231
# 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 -1.9999997 0.5955534
#> [2,] 1 3 2 1 -1.4234806 0.5680859
#> [3,] 1 4 2 3 -0.7627999 0.5920502
#> [4,] 1 4 3 1 -0.4621219 0.6529191
#> [5,] 2 1 1 1 -1.9999972 0.5706602
#> [6,] 2 1 2 4 -1.2729394 0.5680222
####################
# 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,] 0.3085525 0.3442170
#> [2,] -0.3474238 0.3408507
#> [3,] 2.0484681 0.3903336
#> [4,] -1.9418770 0.3670519
#> [5,] -0.7631629 0.3432706
#> [6,] 2.1019773 0.3922135
# score only two response patterns
rp <- dat[1:2, ]
cd <- covdata[1:2, ]
fscores(mod, response.pattern=rp, covdata=cd)
#> F1 SE_F1
#> [1,] 0.3085525 0.3442170
#> [2,] -0.3474238 0.3408507
fscores(mod, response.pattern=rp[2,], covdata=cd[2,]) # just one pattern
#> F1 SE_F1
#> [1,] -0.3474238 0.3408507
# }