Algorithmic jingle jungle: A comparison of implementations of principal axis factoring and promax rotation in R and SPSS

Abstract

AbstractA statistical procedure is assumed to produce comparable results across programs. Using the case of an exploratory factor analysis procedure—principal axis factoring (PAF) and promax rotation—we show that this assumption is not always justified. Procedures with equal names are sometimes implemented differently across programs: a jingle fallacy. Focusing on two popular statistical analysis programs, we indeed discovered a jingle jungle for the above procedure: Both PAF and promax rotation are implemented differently in the psych R package and in SPSS. Based on analyses with 247 real and 216,000 simulated data sets implementing 108 different data structures, we show that these differences in implementations can result in fairly different factor solutions for a variety of different data structures. Differences in the solutions for real data sets ranged from negligible to very large, with 42% displaying at least one different indicator-to-factor correspondence. A simulation study revealed systematic differences in accuracies between different implementations, and large variation between data structures, with small numbers of indicators per factor, high factor intercorrelations, and weak factors resulting in the lowest accuracies. Moreover, although there was no single combination of settings that was superior for all data structures, we identified implementations of PAF and promax that maximize performance on average. We recommend researchers to use these implementations as best way through the jungle, discuss model averaging as a potential alternative, and highlight the importance of adhering to best practices of scale construction.