An Evaluation of the Effects of Variable Sampling On Component, Image, and Factor Analysis

An attribution of a latent variable procedure, such as factor analysis, that is sometimes cited is superior generalization from the variables sampled to the population of variables. Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Three other independent variables were manipulated: (a) the size of the loadings or saturation, (b) the average number of variables per factor, and (c) the number of variables sampled. Five different correlation matrices were generated for each condition. Ten different variable samples were randomly selected. The sample pattern was then compared to the appropriate population pattern. The effects of method of analysis were relatively minor and very complex. The results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.