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Factor Analysis - Harvard University

Factor Analysis Qian-Li Xue Biostatistics Program Harvard Catalyst | The Harvard Clinical & Translational Science Center Short course, October 27, 2016. 1. Well-used latent variable models Latent Observed variable scale variable scale Continuous Discrete Continuous Factor Discrete FA. Analysis IRT (item response). LISREL. Discrete Latent profile Latent class Growth mixture Analysis , regression General software: MPlus, Latent Gold, WinBugs (Bayesian), NLMIXED (SAS). Objectives What is Factor Analysis ? What do we need Factor Analysis for? What are the modeling assumptions? How to specify, fit, and interpret Factor models? What is the difference between exploratory and confirmatory Factor Analysis ? What is and how to assess model identifiability? 3. What is Factor Analysis Factor Analysis is a theory driven statistical data reduction technique used to explain covariance among observed random variables in terms of fewer unobserved random variables named factors 4. An Example: General Intelligence (Charles Spearman, 1904).

Factor loadings: λ ij λ ij = corr(Y i,F j) ! Communality of Y i: h i 2 h i 2 = λ i1 2 + λ i2 2=% variance of Y i explained by F 1 AND F 2 ! Uniqueness of Y i: 1-h i 2! Degree of factorial determination: =Σ λ ij 2/n, n=# observed variables Y 15

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