Anomalous Results in : Explanations and AlternativesG: Explanations and Alternatives-Factor Models: Explanations and Alternatives

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G-factor models such as the bifactor model and the hierarchical G-factor model are increasingly applied in psychology. Many applications of these models have produced anomalous and unexpected results that are often not in line with the theoretical assumptions on which these applications are based. Examples of such anomalous results are vanishing specific factors and irregular loading patterns. In this article, the authors show that from the perspective of stochastic measurement theory anomalous results have to be expected when G-factor models are applied to a single-level (rather than a 2-level) sampling process. The authors argue that the application of the bifactor model and related models require a 2-level sampling process that is usually not present in empirical studies. We demonstrate how alternative models with a G-factor and specific factors can be derived that are more well-defined for the actual single-level sampling design that underlies most empirical studies. It is shown in detail how 2 alternative models, the bifactor-(S − 1) model and the bifactor-(S·I − 1) model, can be defined. The properties of these models are described and illustrated with an empirical example. Finally, further alternatives for analyzing multidimensional models are discussed.

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