Multidimensionality and Structural Coefficient Bias in Structural Equation Modeling

TLDR

The authors aim to identify indices that determine whether multidimensional data can be treated as unidimensional for measurement models, thereby preventing excessive bias in structural parameter estimates. They evaluate explained common variance, omega hierarchical, and fit indices (RMSEA, CFI, SRMR) across simulated bifactor correlation matrices varying general versus group factor loadings, number of group factors, and item counts. Bias in structural coefficients is inversely related to explained common variance and moderated by the proportion of uncontaminated correlations, which increases with more group factors; high uncontaminated proportions yield unbiased coefficients even with weak general factors, yet fit indices like CFI or SRMR often reject unidimensional models despite low bias, making them unreliable predictors of bias magnitude.

Abstract

In this study, the authors consider several indices to indicate whether multidimensional data are “unidimensional enough” to fit with a unidimensional measurement model, especially when the goal is to avoid excessive bias in structural parameter estimates. They examine two factor strength indices (the explained common variance and omega hierarchical) and several model fit indices (root mean square error of approximation, comparative fit index, and standardized root mean square residual). These statistics are compared in population correlation matrices determined by known bifactor structures that vary on the (a) relative strength of general and group factor loadings, (b) number of group factors, and (c) number of items or indicators. When fit with a unidimensional measurement model, the degree of structural coefficient bias depends strongly and inversely on explained common variance, but its effects are moderated by the percentage of correlations uncontaminated by multidimensionality, a statistic that rises combinatorially with the number of group factors. When the percentage of uncontaminated correlations is high, structural coefficients are relatively unbiased even when general factor strength is low relative to group factor strength. On the other hand, popular structural equation modeling fit indices such as comparative fit index or standardized root mean square residual routinely reject unidimensional measurement models even in contexts in which the structural coefficient bias is low. In general, such statistics cannot be used to predict the magnitude of structural coefficient bias.