文档介绍：JSS Journal of Statistical Software
May 2007, Volume 20, Issue 10. /
Marginal Maximum Likelihood Estimation of Item
Response Models in R
Matthew S. Johnson
Baruch College, The City University of New York
Abstract
Item response theory (IRT) models are a class of statistical models used by researchers
to describe the response behaviors of individuals to a set of categorically scored items. The
mon IRT models can be classified as generalized linear fixed- and/or mixed-effect
models. Although IRT models appear most often in the psychological testing literature,
researchers in other fields have essfully utilized IRT-like models in a wide variety of
applications. This paper discusses the three major methods of estimation in IRT and
develops R functions utilizing the built-in capabilities of the R environment to find the
marginal maximum likelihood estimates of the generalized partial credit model. The
currently available R packages ltm is also discussed.
Keywords: item response theory, partial credit model, two-parameter logistic model, mixed
effects models, marginal maximum likelihood, Gauss-Hermite quadrature.
1. Introduction to item response theory models
Item response theory (IRT) models are a class of statistical models used by researchers to
describe the response behaviors of individuals to a set of categorically scored items. The most
common IRT models can be classified as generalized linear fixed- and/or mixed-effect models.
Although IRT models appear most often in the psychological testing literature, researchers
in other fields have essfully utilized IRT-like models in a wide variety of applications.
Fienberg, Johnson, and Junker (1999) employ an item response model for population size
estimation when the assumption of homogeneous capture probabilities fails. Sinharay and
Stern (2002) use an item response model to investigate whether the clutch, or family a baby
turtle belongs to plays any role in whether or not the turtle surviv