Factor Analysis Measuring latent variables Factor Analysis Discussion

Factor Analysis Measuring latent variables

Factor Analysis - Discussion Definition l Vocabulary l Simple Procedure l SPSS example l ICPSR and hands on l

Definition l Factor analysis is a process by which we take a large number of variables (read that measurements) and reduce them into a smaller number of “factors”, by “extracting” the shared variation among variables. The result is a factor “loading” for each variable on each factor

Vocabulary and Procedure Exploratory Factor Analysis uses all of the variance of each variable to establish factors. Such technique is called “Principal Component Analysis”. It establishes the number of factors by several techniques, the two most often used are: 1) recognizing only those whose eigenvalue is > one (the Kaiser method); or 2) only those whose plot shows a vertical line (Scree method)

Vocabulary and Procedure (cont. ) l In examining the number of factors or components, we would need to “rotate” their loadings, either Orthogonally (resulting in a loading matrix), which is the correlation between variables and the factors; l Alternatively, we can rotate them Obliquely (which results in the factors being correlated with each other). This is referred to as a factor correlation matrix. Used only when we believe the factors themselves, are correlated.

Orthogonal Rotation +1. 0 X 2 X 4 X 1 -1. 0 +1. 0 X 3 -1. 0

Vocabulary and Procedure (cont. ) Interpreting loadings is quite subjective, but can be looked at largely by size. Components #1 #2 Variable X 1 . 879 . 296 Variable X 2 . 846 . 450 Variable X 3 . 763 . 509 Variable X 4 . 279 . 719 Variable X 5 . 480 . 678

Steps in the Analysis l l l Input the data Analyze, Dimension Reduction, Factor Choose the extraction and rotation method Generate the Output Interpret the results

Input the data

Generate the Procedure

Produce the Output

Produce the Output (cont. )

Produce the Output (cont. )