How Many Factors in Factor Analysis?New Insights about Parallel Analysis with Confidence Intervals

Abstract

Factor analysis is an extremely popular model forscale development prior to other modeling in much research in business and the social sciences. A central question in factor analysis remainsthe determination of the number of factors to extract and retain to explain as much of the data as possible, and do so parsimoniously. Parallel analysis can be helpful, but there issome confusion surrounding this technique, which may lead to incorrectconclusions. This research seeks first to clarify and correct these confusions. Second, we offer R, SAS, and SPSS programs to conduct parallel analysis in factor analysis. Third, we incorporate inferential statistics, enabling hypothesis testing and confidence intervals. Finally, we discuss how parallel analysis can help scholars in ongoing debates about individual differences scales, construct and measure dimensionality, and the utility of multi-item scales. Hopefully, the recurrent question, “How many factors?” can be answered more definitively.