Part2

Factor Analysis

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Factor Analysis

Factor analysis is a statistical method used to study the dimensionality of a set of variables. In factor analysis, latent variables represent unobserved constructs and are referred to as factors or dimensions. • Exploratory Factor Analysis (EFA) Used to explore the dimensionality of a measurement instrument by finding the smallest number of interpretable factors needed to explain the correlations among a set of variables – exploratory in the sense that it places no structure on the linear relationships between the observed variables and on the linear relationships between the observed variables and the factors but only specifies the number of latent variables

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Factor Analysis (Continued)

• Confirmatory Factor Analysis (CFA) Used to study how well a hypothesized factor model fits a new sample from the same population or a sample from a different population – characterized by allowing restrictions on the parameters of the model Applications Of Factor Analysis • Personality and cognition in psychology • Child Behavior Checklist (CBCL) • MMPI • Attitudes in sociology, political science, etc. • Achievement in education • Diagnostic criteria in mental health

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The Factor Analysis Model

The factor analysis model expresses the variation and covariation in a set of observed continuous variables y (j = 1 to p) as a function of factors η (k = 1 to m) and residuals ε (j = 1 to p). For person i, yi1 = ν1 + λ11 ηi1 + λ12 ηi2 + … + λ1k ηik + … + λ1m ηim + εi1 . . . yij = νj + λj1 ηi1 + λj2 ηi2 + … + λjk ηik + … + λjm ηim + εij . . . yip = νp + λp1 ηi1 + λp2 ηi2 + … + λpk ηik + … + λpm ηim + εip

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The Factor Analysis Model (Continued)

where νj are intercepts λjk are factor loadings ηik are factor values εij are residuals with zero means and correlations of zero with the factors

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The Factor Analysis Model (Continued)

In matrix form, yi = ν + Λ ηi + εi , where ν Λ Ψ Θ is the vector of intercepts νj,...