Conceptualizing correlated residuals as item-level method effects in confirmatory factor analysis.

Schweizer, Karl; Gold, Andreas; Krampen, Dorothea; Troche, Stefan (2023). Conceptualizing correlated residuals as item-level method effects in confirmatory factor analysis. Educational and psychological measurement SAGE 10.1177/00131644231218401

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Conceptualizing two-variable disturbances preventing good model fit in confirmatory factor analysis as item-level method effects instead of correlated residuals avoids violating the principle that residual variation is unique for each item. The possibility of representing such a disturbance by a method factor of a bifactor measurement model was investigated with respect to model identification. It turned out that a suitableway of realizing the method factor is its integration into a fixed-links, parallel-measurement or tau-equivalent measurement submodel that is part of the bifactor model. A simulation study comparing these submodels revealed similar degrees of efficiency in controlling the influence of two-variable disturbances on model fit. Perfect correspondence characterized the fit results of the model assuming correlated residuals and the fixed-links model, and virtually also the tau-equivalent model.

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