irtc.mml: Marginal Maximum Likelihood Estimation of Fixed-Slope Item...

In IRTC: Marginal Maximum Likelihood Estimation for Item Response Models

Marginal Maximum Likelihood Estimation of Fixed-Slope Item Response Models

Description

Estimates unidimensional and multidimensional fixed-slope item response models by marginal maximum likelihood (MML). Supported models include the Rasch / 1PL model, the partial credit model ("PCM", "PCM2") and the rating scale model ("RSM"). Latent regression on covariates, multiple groups, case weights and user-specified design matrices are supported.

Usage

irtc.mml(resp, Y = NULL, group = NULL, irtmodel = "1PL",
   formulaY = NULL, dataY = NULL, ndim = 1, pid = NULL,
   xsi.fixed = NULL, xsi.inits = NULL, beta.fixed = NULL, beta.inits = NULL,
   variance.fixed = NULL, variance.inits = NULL, est.variance = TRUE,
   constraint = "cases", A = NULL, B = NULL, B.fixed = NULL, Q = NULL,
   est.slopegroups = NULL, E = NULL, pweights = NULL,
   userfct.variance = NULL, variance.Npars = NULL, item.elim = TRUE,
   verbose = TRUE, control = list())

## S3 method for class 'irtc'
summary(object, file = NULL, ...)

## S3 method for class 'irtc'
print(x, ...)

## S3 method for class 'irtc'
logLik(object, ...)

## S3 method for class 'irtc'
anova(object, ...)

Arguments

resp	A data frame or matrix of polytomous or dichotomous item responses. Missing responses are coded NA.
Y	An optional matrix of covariates for the latent regression.
group	An optional vector of integer group identifiers for multiple-group estimation.
irtmodel	The estimated item response model. One of "1PL", "PCM", "PCM2" or "RSM".
formulaY	An optional formula for the latent regression in conjunction with dataY.
dataY	An optional data frame of covariates used together with formulaY.
ndim	The number of latent dimensions (used when no Q or B is supplied).
pid	An optional vector of person identifiers.
xsi.fixed	An optional matrix with two columns for fixing item parameters: parameter index and fixed value.
xsi.inits	An optional matrix of initial item parameter values.
beta.fixed	An optional matrix for fixing regression coefficients, or FALSE to estimate all.
beta.inits	An optional matrix of initial regression coefficients.
variance.fixed	An optional matrix for fixing entries of the covariance matrix.
variance.inits	An optional initial covariance matrix.
est.variance	Logical: should the covariance matrix be estimated?
constraint	Identification constraint, either "cases" or "items".
A	An optional design array for the item intercepts.
B	An optional design array for the (fixed) item slopes / scoring.
B.fixed	An optional matrix for fixing entries of the loading array B.
Q	An optional loading (Q-) matrix mapping items to dimensions.
est.slopegroups	An optional vector grouping items with common slope design (advanced use).
E	An optional design array used together with est.slopegroups.
pweights	An optional vector of person (case) weights.
userfct.variance	An optional user function imposing constraints on the covariance matrix.
variance.Npars	The number of estimated parameters in a user-constrained covariance matrix.
item.elim	Logical: should items with no observed responses in a category be eliminated?
verbose	Logical: print progress during estimation?
control	A list of control arguments for the estimation (e.g. maxiter, conv, snodes, nodes). Performance-related elements: n_threads (threads for the parallel E-step; default and maximum = 2), fast (logical, default FALSE; opt-in approximate mode that prunes negligible-weight quadrature nodes), and fast_threshold (pruning cutoff, default 1e-6).
object, x	An object of class irtc as produced by irtc.mml.
file	An optional file name; if supplied, summary output is written there.
...	Further arguments passed to methods.

Value

An object of class irtc, a list with (among others) the components:

xsi	A data frame of estimated item parameters and standard errors.
beta	The estimated latent regression coefficients.
variance	The estimated covariance matrix of the latent dimensions.
person	A data frame of person parameter estimates (EAP) and related statistics.
EAP.rel	The EAP reliability per dimension.
deviance	The deviance (-2 \log L) at the solution.
ic	A list of information criteria (AIC, BIC, ...).
CALL	The matched call.

References

Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21(1), 1–23. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0146621697211001")}

See Also

irtc.mml.2pl for models with estimated item slopes.

Examples

#############################################################################
# EXAMPLE 1: Unidimensional Rasch model
#############################################################################

data(data.sim.rasch)
mod1 <- irtc.mml(resp = data.sim.rasch)
summary(mod1)

#############################################################################
# EXAMPLE 2: Partial credit model
#############################################################################

data(data.gpcm)
mod2 <- irtc.mml(resp = data.gpcm, irtmodel = "PCM")
summary(mod2)

IRTC documentation built on July 24, 2026, 5:07 p.m.