Applied Measurement Modeling

Chapter 1: Introduction & History of Factor Analysis
1.1    Introduction to Workshop & Goals for the Week
1.2    Background and History of Factor Analysis
1.3    Latent Variables

Chapter 2: Principal Components Analysis
2.1    Motivation
2.2    Eigenvalues and Eigenvectors
2.3    Factor Enumeration & Rotation
2.4    Empirical Demonstration

Chapter 3: The Common Factor Model
3.1    Motivation
3.2    Maximum Likelihood Estimation
3.3    Empirical Demonstration
3.4    Extensions and Limitations

Chapter 4: Confirmatory Factor Analysis
4.1    Moving from EFA to CFA
4.2    Identification, Estimation, and Model Fit
4.3    Model Re-Specification and Non-Normality
4.4    CFA Approach to Classical Test Theory and Reliability
4.5    Scoring, Alternative Structures, & Next Steps

Chapter 5: Factor Analysis with Discrete Items
5.1    Discrete Item Responses
5.2    The Underlying Latent Variable Approach
5.3    Full Information Maximum Likelihood Estimation
5.4    Self Study: The Generalized Linear Model

Chapter 6: Multiple Group Measurement Models
6.1    Foundations of Invariance
6.2    Implications for Measured Variables and Composites
6.3    Testing Invariance
6.4    Implications for Testing Latent Variables Directly
6.5    Other Invariance Testing Contexts and Approaches

Chapter 7: Moderated Nonlinear Factor Analysis
7.1    Moderated Nonlinear Factor Analysis: Foundations
7.2    Moderated Nonlinear Factor Analysis: Model Building
7.3    MNLFA: Demonstration with Internalizing Symptomatology
7.4    Self-Study: Advanced Applications and Other Considerations

Our workshop is designed for graduate students, post-doctoral fellows, faculty, and research scientists from the behavioral, social, educational, and health sciences and other related fields. Prior exposure to the general linear model (multiple regression and ANOVA) is recommended but not required. Software demonstrations will be provided in Mplus and R (note that R can be downloaded free-of-charge). While it is helpful to have some prior familiarity with Mplus and R, this is not necessary.

Our motivating goal is to provide an intense yet enjoyable instructional experience that focuses on a large number of topics in the theory and application of contemporary measurement models. We strive to strike an equal balance between core concepts of the underlying statistical models along with the practical application and interpretation of measurement models and scoring fitted to real empirical data. Our workshop is designed to provide participants with the materials and instruction needed to develop a real understanding of both foundational and advanced measurement models and to be able to thoughtfully and knowledgeably apply these models to their own data.

Patrick Curran and Gregory Hancock co-teach the workshop via Zoom and will alternate lecturing throughout the day. Participants will receive complete 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. Please see sample copies of the lecture notes and Mplus demonstration notes from our Structural Equation Modeling class. R versions parallel the Mplus demonstration notes.