When Are Multidimensional Data Unidimensional Enough for Structural Equation Modeling? An Evaluation of the DETECT Multidimensionality Index

In structural equation modeling (SEM), researchers need to evaluate whether item response data, which are often multidimensional, can be modeled with a unidimensional measurement model without seriously biasing the parameter estimates. This issue is commonly addressed through testing the fit of a unidimensional model specification, a strategy previously determined to be problematic. As an alternative to the use of fit indexes, we considered the utility of a statistical tool that was expressly designed to assess the degree of departure from unidimensionality in a data set. Specifically, we evaluated the ability of the DETECT “essential unidimensionality” index to predict the bias in parameter estimates that results from misspecifying a unidimensional model when the data are multidimensional. We generated multidimensional data from bifactor structures that varied in general factor strength, number of group factors, and items per group factor; a unidimensional measurement model was then fit and parameter bia...