ABSTRACT
Item response modeling in the general latent variable framework of the Mplus program (Muthén and Muthén, 2012) offers many unique features including multidimensional analysis (Asparouhov and Muthén, 2012a); two-level, three-level, and cross-classified analysis (Asparouhov and Muthén, 2012b); mixture modeling (Muthén, 2008; Muthén and Asparouhov, 2009); and multilevel mixture modeling (Asparouhov and Muthén, 2008; Henry and Muthén, 2010). This chapter presents a subset of the Mplus item response modeling technique through the analysis of an example with three features common in behavioral science applications: multiple latent variable dimensions, multilevel data, and multiple timepoints. The dimensionality of a measurement instrument with categorical items is investigated using exploratory factor analysis with bi-factor rotation. Variation across students and classrooms is investigated using two-level exploratory and confirmatory bi-factor models. Change over grades is investigated using a longitudinal two-level model. The analyses are carried out using weighted least-squares, maximum-likelihood, and Bayesian analysis. The strengths of weighted least-squares and Bayesian estimation
CONTENTS
31.1 Introduction ........................................................................................................................ 527 31.2 Modeling ............................................................................................................................. 528
31.2.1 Single-Level Modeling .......................................................................................... 528 31.2.2 Two-Level Modeling .............................................................................................. 529
31.3 Estimation ...........................................................................................................................530 31.3.1 Weighted Least-Squares (WLSMV) .....................................................................530 31.3.2 Bayesian Estimation .............................................................................................. 531
31.4 Empirical Examples ........................................................................................................... 531 31.4.1 Item Bi-Factor Exploratory Factor Analysis ....................................................... 532 31.4.2 Two-Level Item Bi-Factor Exploratory Factor Analysis ....................................533 31.4.3 Two-Level Item Bi-Factor Confirmatory Factor Analysis.................................533 31.4.4 Two-Level Item Bi-Factor Confirmatory Factor Analysis with Random
Factor Loadings ......................................................................................................534 31.4.5 Longitudinal Two-Level Item Bi-Factor Confirmatory Factor Analysis ........535
31.5 Conclusions ......................................................................................................................... 537 References ..................................................................................................................................... 538
