## Latent Class Models for Panel Data

**Latent Class Models for Panel Data**

Lecturer:

Prof. Allan McCutcheon, Ph.D.

Emeritus Distinguished Professor

Statistics & Survey Research and Methodology

University of Nebraska-Lincoln, USA

**Course description:**

As survey panel data are becoming increasingly available, our ability to measure and analyze change in groups and populations is becoming increasingly possible. This is true of the change in latent variables as well as change in manifest variables. The study of change in latent variables, however, necessarily includes the added complexity of the consideration of possible temporal changes in the measurement properties of the latent variable, as well as the possibility of temporal change in the latent variable; for example, we may wish to examine the degree to which a latent variable (e.g., religiosity, political engagement) is changing in a group or population over time.

In this course, we will explore how panel data provide opportunities for the study of change in latent variables, as well as in the measurement properties associated with such latent variables. This seminar sequence will focus on the analysis of change in the measurement and distribution of latent variables in panel data. The primary focus of the seminar will be on the estimation and characterization of latent Markov, mixed latent Markov, and related latent class models.

In this course, we will explore several topics related to the analysis of temporal change in latent class variables using survey panel data. Among the topics to be discussed are:

- The parameterizations of the basic latent class model
- Some basic latent class models (LCMs) for analyzing turnover (i.e., 2 time point) tables
- Markov latent class models – LCMs for analyzing multi-time point panels
- Mixed Markov latent class models – LCMs for cases in which multiple patterns (Markov chains) of latent change exist

The morning sessions are devoted to an explanation of the techniques illustrated with empirical examples drawn from survey data. The afternoon sessions will be computer lab assignments for analyzing survey data using the techniques discussed in the morning sessions.

**Target group:**

This course is intended for PhD and MSc students and researchers who want to explore the application of latent class models to their data. Participants can come from the social sciences (e.g., sociology, psychology, political science, economics) and other disciplines with an interest in analyzing empirical data.

**Learning objectives:**

- Understanding the equivalences of the latent class model (LCA) in its alternative parameterizations
- Being able to apply the alternative parameterizations to interpret temporal change in measurement properties and latent variables
- Being able to impose restrictions on model parameters to test specific substantive hypotheses regarding the nature of temporal change and stability
- Being able to model temporal change (and stability) at the latent level

Participants can bring their own data sets and use them to explore the techniques discussed during the course.

**Prerequisites:**

It is expected that participants have an understanding of basic statistical methods such as linear regression and factor analysis. In addition, some matrix algebra and probability theory will be used to explain the analytic methods. Most of the practical sessions will use LatentGold, though Mplus and LEM (freeware) will also. A basic understanding of a data preparation program (e.g., SPSS, SAS, Stata) will also be necessary.

**Recommended Readings:**

- Clarke, H. D., and A. L. McCutcheon (2009) “The Dynamics of Party Identification Reconsidered.”
*Public Opinion Quarterly*73: 704-728. - Langeheine, R., and F. van de Pol (2002) “Latent Markov Chains,” in J. A. Hagenaars and A. L. McCutcheon (eds.)
*Applied Latent Class Analysis.*304-341. Cambridge: Cambridge University Press. - Magidson, J., J.K. Vermunt, and B. Tran (2009) “Using Mixture Latent Markov Models to Analyze Longitudinal Data Involving Measurement Error,” in K. Shigemasu, A. Okada, T. Imaizumi, and T. Hoshino (eds.)
*New Trends in Psychometrics*. 235-242. Universal Academy Press. - McCutcheon, A.L. (2002) “Basic Concepts and Procedures in Single- and Multiple-Group Latent Class Analysis,” in J.A. Hagenaars and A.L. McCutcheon (eds.)
*Applied Latent Class Analysis*. 56-85. Cambridge: Cambridge University Press. - Neundorf, A., D. Stegmueller, and T.J. Scotto (2011) “The Individual-Level Dynamics of Bounded Partisanship.”
*Public Opinion Quarterly*75: 458-482.

**About the Instructor:**

Allan McCutcheon is an Emeritus Distinguished Professor of Statistics and Survey Research and Methodology at the University of Nebraska-Lincoln (USA). His work focuses on a range of issues related to modeling measurement and change in online panel survey data. He is author of *Latent Class Analysis* (1987) and co-editor (along with Jacques A. Hagenaars) of *Applied Latent Class Analysis* (2002), as well as author and co-author of a number of scientific articles and book chapters.

**Program outline:**

__Day 1__

Basics of Latent Class Models (LCM)

*Lab session*: Introduction to LEM and Mplus for latent class analysis.

__Day 2__

Hypothesis testing with restricted and unrestricted latent class models.

*Lab session:* Imposing parameter restrictions with various software.

__Day 3__

Some models for exploring change in measurement and latent classes.

*Lab session:* Introduction to LatentGold. Estimation of LCMs at two points in time.

__Day 4__

Markov latent class models – characterizing temporal changes in measurement and latent variables at multiple points in time.

*Lab session:* Estimation and interpretation of Markov models in the presence of temporal change in the measurement characteristics of the latent classes.

__Day 5__

Mixed Markov latent class models – characterizing temporal changes in the latent classes when there is a mixture of latent Markov chains. The mover/stayer model.

*Lab session:* estimating Mixed Markov Latent Class Models (MMLCMs).

__Day 6__

Extensions of the MMLCMs, including time-varying and time-invariant external factors.

*Lab session:* Estimating MMLCMs with external factors.