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Function to calculate the marginal moments for items and bundles fit via IRT models

Source: R/marginal_moments.R
marginal_moments.Rd

Given an estimated model and a prior density function, compute the marginal moments for either and item or a bundle of items. Function returns the first found moments implied by the model and select density function (MEAN, VAR, SKEW, and KURT). Currently limited to unidimensional IRT models.

Usage

marginal_moments(
  mod,
  which.items = NULL,
  group = NULL,
  bundle = TRUE,
  density = NULL,
  Theta_lim = c(-6, 6),
  quadpts = 121,
  ...
)

Arguments

mod

an object of class 'SingleGroupClass' or 'MultipleGroupClass'

which.items

vector indicating which items to use in the computation of the expected values. Default (NULL) uses all available items

group

optional indicator to return only specific group information for multiple group models. Default compute moments for each group, returning a list

bundle

logical; given which.items, should the composite of the response functions be used as a collective bundle? If TRUE then expected.test will be used, otherwise expected.item will be used

density

a density function to use for integration. Default assumes the latent traits are from a normal (Gaussian) distribution. Function definition must be of the form function(quadrature, mean, sd) as the values of the mean/variance are extracted and passed from the supplied model

Theta_lim

range of integration grid to use when forming expectations

quadpts

number of discrete quadrature to use in the computations

...

additional arguments passed to the density function

References

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

See also

expected.item, expected.test

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# \donttest{

# single group
dat <- expand.table(deAyala)
mod <- mirt(dat)
TS <- rowSums(dat)

# expected moments of total scores given model
marginal_moments(mod)
#>    MEAN   VAR   SKEW  KURT
#> 1 2.917 1.297 -0.253 2.032
c(mean=mean(TS), var=var(TS))  # first two moments of data
#>     mean      var 
#> 2.911790 2.056759 

# same, however focusing on individual items
marginal_moments(mod, bundle = FALSE)
#>         MEAN   VAR   SKEW  KURT
#> Item.1 0.887 0.015 -2.121 8.454
#> Item.2 0.646 0.089 -0.597 2.053
#> Item.3 0.568 0.075 -0.260 1.874
#> Item.4 0.428 0.075  0.275 1.888
#> Item.5 0.388 0.040  0.394 2.367
cbind(mean=colMeans(dat), var=apply(dat, 2, var)) # first two moments of data
#>             mean        var
#> Item.1 0.8874547 0.09988393
#> Item.2 0.6440488 0.22926165
#> Item.3 0.5659915 0.24565765
#> Item.4 0.4269680 0.24467881
#> Item.5 0.3873272 0.23731694

############################################
## same as above, however with multiple group model

set.seed(1234)
group <- sample(c('G1', 'G2'), nrow(dat), replace=TRUE)
modMG <- multipleGroup(dat, group=group,
 invariance=c(colnames(dat), 'free_mean', 'free_var'))
coef(modMG, simplify=TRUE)
#> $G1
#> $items
#>           a1      d g u
#> Item.1 1.244  2.588 0 1
#> Item.2 2.021  1.000 0 1
#> Item.3 1.572  0.397 0 1
#> Item.4 1.566 -0.413 0 1
#> Item.5 0.995 -0.548 0 1
#> 
#> $means
#> F1 
#>  0 
#> 
#> $cov
#>    F1
#> F1  1
#> 
#> 
#> $G2
#> $items
#>           a1      d g u
#> Item.1 1.244  2.588 0 1
#> Item.2 2.021  1.000 0 1
#> Item.3 1.572  0.397 0 1
#> Item.4 1.566 -0.413 0 1
#> Item.5 0.995 -0.548 0 1
#> 
#> $means
#>     F1 
#> -0.004 
#> 
#> $cov
#>       F1
#> F1 1.003
#> 
#> 

# expected moments of total scores given model
marginal_moments(modMG)
#> $G1
#>   MEAN   VAR   SKEW  KURT
#> 1 2.92 1.295 -0.255 2.034
#> 
#> $G2
#>    MEAN   VAR   SKEW KURT
#> 1 2.915 1.299 -0.251 2.03
#> 
marginal_moments(modMG, group = 'G1') # specific group only
#>   MEAN   VAR   SKEW  KURT
#> 1 2.92 1.295 -0.255 2.034

# same, however focusing on individual items
marginal_moments(modMG, bundle = FALSE)
#> $G1
#>         MEAN   VAR   SKEW  KURT
#> Item.1 0.887 0.015 -2.124 8.476
#> Item.2 0.647 0.089 -0.600 2.058
#> Item.3 0.568 0.075 -0.262 1.876
#> Item.4 0.429 0.075  0.273 1.887
#> Item.5 0.388 0.040  0.393 2.366
#> 
#> $G2
#>         MEAN   VAR   SKEW  KURT
#> Item.1 0.887 0.015 -2.118 8.432
#> Item.2 0.645 0.089 -0.594 2.048
#> Item.3 0.567 0.075 -0.257 1.872
#> Item.4 0.428 0.075  0.277 1.889
#> Item.5 0.387 0.040  0.396 2.368
#> 


# }