Factor analysis
unidimensional case
Graphic
=> In FA, indicators have an individual error term (due to measurement error and uniqueness [see next slides])
Shared / non-shared variance
graphical
Uniqueness and shared variance
Overlapping area among all variables: Variance due to the common factor
Nonoverlapping area for any variable: Variance that is unique to that particular variable: Uniqueness
Consists of (1) Specificity, a true (i.e., reliable) source of variance that is not common to any other variable (e.g., writing proficiency performance affected by different genres: argumentative vs. narrative writing); and (2) random error of measurement, i.e. unreliability (e).
Definition communality
Total amount of systematic variance of a variable, called communality (h2)
= Common factor variance + group factor variance
Variance decomposition of a unifactorial EFA at a glance
Common factor model, unifactorial case
Factor loadings
Factor Analytic Model: Multiple Factor Analysis
Choices and assumptions concerning the distributions of observed and factor variables (orthogonal factor analysis)
(6)
All of the observable random variables Zj have mean zero and variance 1, i.e., are z-standardized variables
All of the latent factors have mean zero and variance 1, i.e., are z-standardized variables
All error terms have mean zero (linearity assumption)
The factors are uncorrelated (orthogonal model)
The error terms are uncorrelated across observable variables
(i.e., assumption of random errors)
The error terms are uncorrelated with the factor variables
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