Multiple Replication of Factor Structure: A Logical Solution for a Number of Factors Problem

Abstract

A factor replication procedure which provides a solution for the numbers of factors problem for multiple scale questionnaire responses, is described and demonstrated. In the procedure a series of factor analyses are conducted in which a reduced number of factors is used for each successive rotation until a structure is found which is replicated across subject groups. The factor matching s index, which relates loadings as they fall about a series of prescribed levels, is used to compare factors in order to show the level of similarity achieved. The procedure is illustrated using the responses of three groups of subjects to the Hopkins Symptom Checklist. Results show that the five factor structure claimed by the authors of the measure is not supported by the data but that there is clear evidence of three replicable factors. It is suggested that the procedure provides the basis for a significant improvement in decisions related to the number of factors problem.