Abstract
Bi-factor confirmatory factor models have been influential in research on cognitive abilities because they often better fit the data than correlated factors and higher-order models. They also instantiate a perspective that differs from that offered by other models. Motivated by previous work that hypothesized an inherent statistical bias of fit indices favoring the bi-factor model, we compared the fit of correlated factors, higher-order, and bi-factor models via Monte Carlo methods. When data were sampled from a true bi-factor structure, each of the approximate fit indices was more likely than not to identify the bi-factor solution as the best fitting. When samples were selected from a true multiple correlated factors structure, approximate fit indices were more likely overall to identify the correlated factors solution as the best fitting. In contrast, when samples were generated from a true higher-order structure, approximate fit indices tended to identify the bi-factor solution as best fitting. There was extensive overlap of fit values across the models regardless of true structure. Although one model may fit a given dataset best relative to the other models, each of the models tended to fit the data well in absolute terms. Given this variability, models must also be judged on substantive and conceptual grounds.
Highlights
The bi-factor method of exploratory factor analysis (EFA) that was introduced by Holzinger and Swineford [1] allows for identification of a general factor through all measured variables and several orthogonal group factors through sets of two or more measured variables
Limitations of EFA methods and advances in theory and computer technology led to the ascendency of confirmatory factor analytic (CFA) methods that allow for testing hypotheses about the number of factors and the pattern of loadings [13,14]
Sample size might be related to non-convergence of bi-factor models
Summary
The bi-factor method of exploratory factor analysis (EFA) that was introduced by Holzinger and Swineford [1] allows for identification of a general factor through all measured variables and several orthogonal group factors through sets of two or more measured variables. Bi-factor methods received less attention than multiple factor and higher-order factor models over the subsequent decades [2,3,4,5] and were not broadly applied in influential investigations of individual differences [6,7,8,9,10,11,12]. Many CFA analyses have specified multiple correlated factors or higher-order models [15,16,17,18,19,20,21,22,23]. The bi-factor model has been recommended by Reise [25] for CFA and successfully employed in the measurement of a variety of constructs, such as cognitive ability [22], health outcomes [26], quality of life [27], psychiatric distress [28], early academic skills [29], personality [30], psychopathology [31], and emotional risk [32]
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