**Bengt Muthén, UCLA and Mplus**

The use of latent variables is a common theme in many statistical analyses. Continuous latent variables appear not only as factors measured with errors in factor analysis, item response theory, and structural equation modeling, but also appear in the form of random effects in growth modeling, components of variation in complex survey data analysis and multilevel modeling, frailties and liabilities in survival and genetic analyses, latent response variables with missing data, priors in Bayesian analysis, and as counterfactuals and potential outcomes in causal analysis. In addition, categorical latent variables appear as latent classes in finite mixture analysis and latent transition analysis (Hidden Markov modeling), latent trajectory classes in growth mixture modeling, and latent response variables with missing data on categorical variables. All these features are covered by the general latent variable modeling framework of Mplus.

Understanding the unifying theme of latent variable modeling provides a way to break down barriers between seemingly disparate types of analyses. Researchers need to be able to move freely between analysis types to more easily answer their research questions. To provide answers to the often complex substantive questions, it is also fruitful to use latent variable techniques to combine different analysis types. This half-day workshop discusses examples that use combinations of multilevel, latent class, and longitudinal modeling features in the new Mplus Version 7.

A topic of special interest to the ESRA conference is multiple-group analysis of measurement invariance and latent variable comparisons across many groups such as in cross-cultural studies. Four novel approaches are covered: Multiple-group analysis using an exploratory factor analysis model, Bayesian analysis with approximate measurement invariance, two-level analysis with random intercepts/slopes, and exploratory measurement invariance analysis.

**About the instructor**

**Bengt Muthén** obtained his Ph.D. in Statistics at the University of Uppsala, Sweden and is Professor Emeritus at UCLA. He was the 1988-89 President of the Psychometric Society and the 2011 recipient of the Psychometric Society's Lifetime Achievement Award. He has published extensively on latent variable modeling and is one of the developers of the Mplus computer program, which implements many of his statistical procedures.