Simulating the Effects of Common and Specific Abilities on Test Performance: An Evaluation of Factor Analysis

Abstract

Factor analysis is a useful technique to aid in organizing multivariate data characterizing speech, language, and auditory abilities. However, knowledge of the limitations of factor analysis is essential for proper interpretation of results. The present study used simulated test scores to illustrate some characteristics of factor analysis. Linear models were used to simulate test scores that were determined by multiple latent variables. These simulated test scores were evaluated with principal components analysis and, in certain cases, structural equation modeling. In addition, a subset of simulated individuals characterized by poor test performance was examined. The number of factors recovered and their identity do not necessarily correspond to the structure of the latent variables that generated the test scores. The first principal component may represent variance from multiple uncorrelated sources. Practices such as correction or control for general cognitive ability may produce misleading results. Inferences from the results of factor analysis should be primarily about the structure of test batteries rather than the structure of human mental abilities. Researchers and clinicians should consider multiple sources of evidence to evaluate hypotheses about the processes generating test results.