Factor Analysis
Factor analysis is a method for describing the variability of correlated measures.
Contents
Description
Given a series of measurements, there are three influential components:
common factors that represent interpersonal differences across all measurements
specific factors, as above but for a singular measurement
measurement error
When decomposing influences on factors into these components, the first is sometimes called communality and the latter two are sometimes called uniqueness.
The relations are modeled and diagrammed like:
Importantly, note that boxes represent measurements, also called indicators or manifest variables. Unobserved components (i.e., error terms) and factors are both represented by circles. The correlations are called factor loadings.
Because latent variables are detached from any real metric, they are not directly interpretable. One strategy is to constrain the variances of latent variables to 1, so that estimates operate like standardized scores. Another strategy is to constrain one latent variable to 1, so that all other latent variables can be measured in relation to this reference variable.
Exploratory factor analysis (EFA) considers the relationship between every indicator and every factor. Confirmatory factor analysis (CFA) strictly partitions the indicators, such that every variable measures only one factor.
SEM is very closely related to CFA. The difference between CFA and the first component of SEM, the measurement model, is simply that a causal direction is assumed.