Item Response Modeling in Mplus: A Multi-Dimensional, Multi-Level, and Multi-Timepoint Example

This chapter presents item response modeling techniques in the Mplus program (Muthén & Muthén, 2012) 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 Bayes as a complement to maximum-likelihood for this high-dimensional application are discussed. Mplus scripts for all analyses are available at www.statmodel.com.