marginal_moments: Function to calculate the marginal moments for items and...

In mirt: Multidimensional Item Response Theory

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

Description

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

Author(s)

Phil Chalmers [e-mail]

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v048.i06")}

See Also

expected.item, expected.test

Examples

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

# expected moments of total scores given model
marginal_moments(mod)
c(mean=mean(TS), var=var(TS))  # first two moments of data

# same, however focusing on individual items
marginal_moments(mod, bundle = FALSE)
cbind(mean=colMeans(dat), var=apply(dat, 2, var)) # first two moments of data

############################################
## 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)

# expected moments of total scores given model
marginal_moments(modMG)
marginal_moments(modMG, group = 'G1') # specific group only

# same, however focusing on individual items
marginal_moments(modMG, bundle = FALSE)

mirt documentation built on March 7, 2026, 9:06 a.m.