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 as a complement to maximum-likelihood for this high-dimensional application are discussed. Mplus scripts for all analyses are available at https://www.statmodel.com" xmlns:xlink="https://www.w3.org/1999/xlink">www.statmodel.com.
