Heywood You Go Away! Examining Causes, Effects, and Treatments for Heywood Cases in Exploratory Factor Analysis

Exploratory factor analysis (EFA) is a popular method for elucidating the latent structure of data. Unfortunately, EFA models can sometimes produce improper solutions with nonsensical results. For example, improper EFA solutions can include one or more Heywood cases, where common factors account for 100% or more of an observed variable’s variance. To better understand these senseless estimates, we conducted four Monte Carlo studies that illuminate the (a) causes, (b) consequences, and (c) effective treatments for Heywood cases in EFA models. Studies 1 and 2 showed that numerous model and data characteristics are associated with Heywood cases, such as small sample sizes, poorly defined factors with low factor score determinacy values, and factor overextraction. In Study 3, we examined the consequences of Heywood cases for EFA model interpretation and found that Heywood cases increase factor loading variances and upwardly bias factor score determinacy values. Study 4 compared the model recovery of several EFA algorithms that were designed to avoid Heywood cases. Our results indicated that, among the algorithms compared, regularized common factor analysis (Jung & Takane, 2008) was the most reliable method for avoiding Heywood cases and producing EFA parameter estimates with small mean squared errors. We discuss best practices for conducting EFA with data sets that might yield Heywood cases.