Worse Than Measurement Error: Consequences of Inappropriate Latent Variable Measurement Models

Previous research and methodological advice has focused on the importance of accounting for measurement error in psychological data, That perspective assumes that psychological variables conform to a common factor model. We explore what happens when data that are not generated from a common factor model are nonetheless modeled as reflecting a common factor. Through a series of hypothetical examples and an empirical reanalysis, we show that when a common factor model is misused, structural parameter estimates that indicate the relations among psychological constructs can be severely biased. Moreover, this bias can arise even when model fit is perfect. In some situations, composite models perform better than common factor models. These demonstrations point to a need for models to he justified on substantive, theoretical bases in addition to statistical ones. Translational Abstract Previous research and methodological advice has focused on the importance of accounting for measurement error in psychological data. This focus on measurement error has led many researchers to believe that latent Variable or common factor models should be used whenever possible, because they remove the measurement error from observed data, resulting in more reliable analyses. We present evidence that this is not always true: In particular, depending on the way in which observed variables are related to the psychological constructs under investigation, use of a latent variable model can introduce severe bias into a model and can result in incorrect substantive interpretations. We use a combination of proof's, examples, and an empirical reanalysis to make this point.