Spurious Multidimensionality in Psychological Measures: Disentangling Measurement-Model Misspecification From Persistent Secondary Variance

Psychological measures frequently exhibit secondary factors that may reflect substantive dimensions, systematic response processes, measurement-model misspecification, or combinations of these sources. We focus on spurious multidimensionality arising when the functional form linking a latent variable to its indicators is misspecified. Using a Height Inventory administered to 11,979 participants (51% women), we compared dimensionality based on Pearson and polychoric correlations and estimated continuous and ordinal one-factor and bifactor models. We additionally examined item-level response-function fit, nonlinear dependence between general- and specific-factor estimates, shared residual patterns, and item endorsement. Polychoric and ordinal modeling strengthened several indicators of general-factor dominance, markedly improved correspondence between model-implied and empirical item-response functions, and nearly eliminated nonlinear dependence between general- and specific-factor estimates. These findings indicate that treating ordinal responses as continuous introduced systematic construct-related variance into the specific factor. However, a strong specific factor remained under ordinal modeling, continued to substantially improve model fit, and showed a highly similar loading pattern across continuous and ordinal specifications. Its loadings were only partly accounted for by shared residual patterns and were systematically related to item endorsement. The results therefore suggest that a single secondary factor can simultaneously capture spurious variance caused by measurement-model misspecification and persistent systematic variance potentially arising from response processes. Secondary factors should consequently not be treated as necessarily substantive or wholly artifactual; their sources should be investigated by comparing alternative measurement specifications and examining item-level response functions and residual structure.