Handbook of Item Response Theory, Statistical Tools, Volume 2,

Abstract

and cross-classified analysis, mixture modeling, and multilevel mixture modeling. Weighted least-square (called WLSMV) and Bayesian estimation is described, and a motivating example with two-level bi-factor exploratory and confirmatory FA, with possible random FA loadings, and for the longitudinal FA version are presented. Chapter 32 of “Mixed-Coefficients Multinomial Logit Models” by Adams et al., focuses on the unified approach to specifying the models and then consequentially estimating the parameters. A generalized framework for specifying a family of logistic and multinomial-logit item response models through the specification of design matrices is given, together with estimation of parameter, latent ability, prediction, and functionals of population distributions. Model fit can be done by generalized and customized tests, and tests of relative fit. Examples include bundles of the items obtained by several models. Chapter 33 of “Explanatory Response Models” by De Boeck and Wilson, observes that the regression approach can be applied in the explanatory item response modeling where item responses are the dependent variables and the predictors’ role can be played by the properties of persons, items, and the pairs of persons and items. Person properties include demographics, socioeconomic status, treatment status, or location on another test variable. Item properties can depend on the domain of testing, for example, in a mathematical test those can be presented by the number and numerical operations. GLMM presents an adequate kind of regressions for the categorical data, with the predictors aggregate containing both fixed and random effects. More complicated data can be modeled in strata covariates and multilevel designs. Parameter estimation is performed by MCMC and Bayesian techniques, and an example of data on verbal aggression is used and described in detail. Volume 1 of this three-volume set is concluded by the comprehensive Index. Each chapter is organized by the same pattern: introduction, model presentation, parameter estimation, model fit, empirical example, discussion, and a list of references where dozens and hundreds of classical and the most recent references are given in each chapter. It makes the whole handbook to be convenient in a quick finding of the needed tool. This handbook presents a huge compendium of models which could be innovative even for specialists in IRT and related applied research. It can definitely be useful for lecturers and graduate students, researchers and practitioners in applied psycho-sociological projects. Actually, it can be useful in much wider than just IRT related area of research, because it describes a large variety of statistical ideas and methods valuable in estimations for many other problems as well.