Mixture Modeling and Latent Class Analysis

Chapter 1. Introduction
1.1 Introduction and Organization of the Workshop
1.2 Historical Context: Types and Taxonomies
1.3 Goals and Motivations: When and How Clustering can be Useful
1.4 Perspectives on Classification
1.5 Overview of General Approaches for Clustering

Chapter 2. Preliminaries: Matrix Algebra, Visualization, and Variable Selection
2.1 Brief Introduction to Matrix Algebra
2.2 Seeing Clusters: Graphical Visualization Methods
2.3 Why Variable Selection Matters
2.4 How to Decide Which Variables to Include / Exclude from Analysis

Chapter 3. Hiearchical Clustering
3.1 Motivations Behind Development and Application of Hierarchical Clustering Algorithms
3.2 Assessing (Dis)Similarity
3.3 Hierarchical Clustering Techniques: Basis and Application
3.4 Assessing Fit and Determining the Number of Clusters

Chapter 4. Non-Hierarchical Clustering
4.1 Motivations Behind Development and Application of Non-Hierarchical Clustering Algorithms
4.2 Using K-Mean Clustering to Partition Groups
4.3 Clustering with Respect to Prototypes: K-Median Clustering
4.4 Extensions

Chapter 5. Finite Normal Mixture Models with One Variable
5.1 Motivations Behind Development and Application of Finite Mixture Models
5.2 Explicating the Model
5.3 How to Specify, Estimate, and Interpret the Model
5.4 Conducting Class Enumeration: Determining the Number of Mixing Components / Latent Classes

Chapter 6. Finite Normal Mixture Models with Multiple Variables
6.1 Mixtures Based on Multiple Variables: Extending to a Multivariate Normal Mixture Model
6.2 Commonly Implemented Variations in Model Specification
6.3 Applications (Including with Repeated Measures)

Chapter 7. Finite Mixture Models with Discrete or Non-Normal Indicators
7.1 Why Assuming Normality Isn't Always Optimal
7.2 Binary and Ordinal Indicators: Latent Class Analysis
7.3 Mixtures of Non-Normal Continuous Distributions

Chapter 8. Relating Latent Classes to Predictors and Distal Outcomes
8.1 Hypothesis Testing within Finite Mixture Models
8.2 One-Step Versus Three-Step Testing Approaches
8.3 Prediction of Class Membership: Predicting Who's in Which Class
8.4 Predicting Distal Outcomes: Determining Long-Range Outcomes of Class Membership
8.5 Latent Class Moderation Analysis: Do Predictors Have Differential Importance Across Classes?

Chapter 9. Growth Mixture Models
9.1 Heterogeneity in Change Over Time: When Theory Predicts Subgroups Follow Distinct Trajectories
9.2 Latent Class Growth Analysis / Semiparametric Groups Based Trajectory Modeling
9.3 "General" Growth Mixture Models with Random Effects

Chapter 10. Advanced Topics and Concluding Remarks
10.1 Survey of Advanced Applications of Finite Mixture Models:
- Factor Mixture Models
- Structural Equation Mixture Models
- Survival Mixture Models
- Latent Transition Analysis
10.2 Approaches for deciding on Best Structure
10.3 Summary of Decision Points, Recommendations, and Guidelines for Best Practice

Our workshop is designed for graduate students, post-doctoral fellows, faculty, and research scientists from the behavioral, social, and health sciences.

Software demonstrations for cluster analytic techniques will be provided in separate R and SPSS breakout sessions. Later software demonstrations for mixture models are conducted using R and Mplus. While it is helpful to have some familiarity with R or SPSS and Mplus, this is not necessary. The lectures which constitute the majority of the workshop are software-independent.

Our motivating goal is to provide an intense yet enjoyable instructional experience that focuses on a large number of both introductory and advanced topics in cluster analysis and mixture modeling. We strive to strike an equal balance between core concepts of the analytic techniques along with their practical application and interpretation when implemented with real empirical data. Our workshop is designed to provide participants with the materials and instruction needed to both develop a real understanding of cluster analysis and mixture modeling and to be able to thoughtfully apply these procedures to their own data.

Dan Bauer and Doug Steinley co-teach the workshop and alternate lecturing throughout the day. Participants will receive approximately 35 hours of total lecture time as well as PDF copies of the course notes and the computer demonstrations as well as data and code for all examples. The PDFs are not time-limited and may be retained indefinitely but should not be distributed to others without obtaining prior permission.

For examples of our course materials see sample copies of our structural equation modeling lecture notes and associated Mplus demonstration notes, as well as our multilevel modeling lecture notes and SAS software notes.

Learn more about what makes our training unique...