Development of a hybrid method for dimensionality identification incorporating an angle-based approach.

摘要

Correct dimensionality identification (i.e., a correct decision on the number of factors to retain) is crucial not only in educational and psychological measurement, but also in various fields such as medicine and sociology that use exploratory factor analysis (EFA) in developing theories. However, to date, no single method has been endorsed for accurate dimensionality identification. In addition, past simulation studies comparing various dimensionality identification rules have ignored the scenario where underlying dimensions are highly correlated in the range of 0.6-0.9. This range has been found to be common in educational and psychological measurement.;In this dissertation, I reviewed four commonly used dimensionality identification rules (plus one variation of one of those rules) and three uncommonly used rules developed for maximum likelihood factor analysis. In addition, I described a recently developed angle-based method and further developed this method to obviate the need for subjective graph reading. I also developed and evaluated several hybrid methods using simulation studies, which took into consideration high correlations among underlying dimensions.;The results indicated that the improved angle-based method was an indispensable component of the final hybrid method. The results also demonstrated a tendency of under-estimation of various commonly used dimensionality identification rules when the underlying dimensions were highly correlated. This calls into question the validity of previously developed theories in various fields that involved the use of EFA.