Lecture 3 Notes: Structural Equation Models

Introduction

• Transition from conceptual background to applications and model fitting.
• Focus on confirmatory factor analysis (CFA).

Measurement Concepts with Latent Variables

• Two approaches: Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA).
• Importance of measurement accuracy and adequacy.
• Decomposition of measured variables into true score and error.

Exploratory Factor Analysis (EFA)

• Also known as unrestricted factor model.
• Reorders data to best account for observed correlations.
• Produces as many factors as observed variables.
• Inductive, theory-less approach.
• Involves subjective judgment in retaining factors.

Limitations of EFA

• A-theoretical approach.
• Subjective in determining model.
• Doesn't reflect the pre-existing theory.

Confirmatory Factor Analysis (CFA)

• Known as restricted factor model.
• Model specified before data examination (no peeking rule).
• Tests theories of measurement by placing restrictions on parameters.
• Examples of parameter restrictions include fixing certain paths to zero.

Parameter Constraints in CFA

• Over-identification provides more degrees of freedom.
• Assigning a metric to latent variables by fixing variance or reference item.

Latent Means

• Estimating latent means in CFA for group differences or change over time.
• Introduction of a constant (value 1) in the model.

Reflective vs. Formative Indicators

• Reflective indicators: causality flows from latent variable to indicators.
• Formative indicators: causality flows from indicators to latent variable.

Item Parceling

• Used in CFA with large numbers of indicators.
• Aggregates scores of items into subgroups as indicators.

Higher-Order Factor Models

• Latent variables measured by other latent variables.
• Useful for theories about dimensional structure of data.
• Applied in longitudinal studies.

Conclusion

• Overview of using latent variables in measuring concepts.
• Comparison between EFA and CFA.
• Special cases discussed: formative indicators, item parceling, higher-order factors.