Possible Solutions to Heywood Cases in Confirmatory Factor Analysis

Heywood cases, where parameter estimates in confirmatory factor analysis (CFA) assume impossible values, challenge the accuracy of structural equation modeling. Common causes include small sample sizes, limited indicators per factor, and reliance on maximum likelihood estimation (MLE). Existing remedies, such as simply changing negative variances to zero or applying Bayesian estimation, offer partial solutions. This study introduces innovative approaches on MLE, including logistic-constrained loadings, exponential transformations and maximum a posteriori (MAP) estimation, to reduce Heywood cases and improve parameter estimation. These methods are evaluated using Monte Carlo simulations and a case study. The findings highlight their capacity to contribute meaningfully to psychometric modeling, both when the model is correctly specified and in the presence of model misfit.