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Original Article

Improving Bi-Factor Exploratory Modeling

Empirical Target Rotation Based on Loading Differences

Published Online:May 27, 2019https://doi.org/10.1027/1614-2241/a000163

Abstract

Abstract. Bi-factor exploratory modeling has recently emerged as a promising approach to multidimensional psychological measurement. However, state-of-the-art methods relying on target rotation require researchers to select an arbitrary cut-off for defining the target matrix. Unfortunately, the consequences of such choice on factor recovery remain uninvestigated under realistic conditions (e.g., factors differing in their average loadings). Built upon the iterative target rotation based on Schmid-Leiman algorithm (SLi), a novel method is here introduced (SLiD). SLiD settles an empirical, factor-specific cut-off based on the first prominent one-lagged difference of sorted squared normalized factor loadings. SLiD and SLi with arbitrary cut-off (ranging from .05 to .20) performance were evaluated via Monte Carlo simulation manipulating sample size, number of specific factors, number of indicators, and cross-loading magnitude. Results indicate that SLiD performed the best for all conditions. For SLi, and due to the presence of minor factors, smaller cut-offs (i.e., .05) outperformed higher ones (i.e., .20).

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