ABSTRACT
Consider the following two common classes of research situations:
Exploratory regression analysis: An experimenter has gathered a moderate to large number of predictors (say 15 to 40) to predict some dependent variable.
Scale development: An investigator has assembled a set of items (say 20 to 50) designed to measure some construct(s) (e.g., attitude toward education, anxiety, sociability). Here we think of the items as the variables.
In both of these situations the number of simple correlations among the variables is very large, and it is quite difficult to summarize by inspection precisely what the pattern of correlations represents. For example, with 30 items, there are 435 simple correlations. Some way is needed to determine if there is a small number of underlying constructs that might account for the main sources of variation in such a complex set of correlations.