Analysis with latent variables is a common theme in mainstream statistics, although the term latent variable is not always used to describe such analysis. The term latent variable is more typically encountered in psychometric analyses of social and behavioral science data, where latent variables are used to represent variables without measurement error or hypothetical constructs measured by multiple indicators. This course explores more general features of latent variable analysis. Topics to be covered include factor analysis, latent class analysis, random effect growth modeling, multilevel analysis, missing data, finite mixture modeling, and general latent variable analysis with a combination of continuous and categorical latent variables. A unified framework will be presented drawing on the Mplus program. For a quick perusal of the variety of examples covered in this modeling framework, see the list of 125 examples included in the new User's Guide at http://www.statmodel.com/ugexcerpts.html.

There is no suitable textbook covering all the topics of the course, but the course content will be covered by lecture notes. The course covers a wide range of topics in order to present relevant analysis opportunities, which means that each topic is presented concisely. Given this, student attendance at all lectures is necessary with absences accepted only for strong reasons.

Parts of the categorical variable modeling material is covered in the 1990 Wiley book by Agresti (Categorical Data Analysis), parts of the latent class modeling material is covered in the 1987 Sage Quantitative Applications book (#64) by McCutcheon (Latent Class Analysis) and in the 1987 Griffin book by Bartholomew (Latent Variable Models and Factor Analysis), and parts of the structural equation modeling material is covered in the 1989 Wiley book by Bollen (Structural Equations with Latent Variables). It is up to the student to order any of these books.

Suitable background for the course is regression analysis, categorical data analysis, multivariate analysis, and matrix algebra. Good knowledge of regression analysis is the only required background, but students will clearly get more out of the course the more courses he/she has taken, including structural equation modeling and multilevel modeling.

Assignments typically involve data analyses using the new Version 3 of the Mplus program. For a free demo version of the program, see http://www.statmodel.com. A user’s guide is not necessary, but a summary of the Mplus language can be found at the same web site, in the help menu of the demo version, and in the discussion section below.