Threshold priors in item factor analysis under DELTA and THETA parameterizations

Bayesian estimation approaches for item factor analyses (IFA) can provide a valuable tool to overcome difficulty in parameter estimation in frequentist approaches when the marginal response distribution is highly skewed. Highly skewed marginal response distributions are problematic in Bayesian IFA models with binary factor indicators depending on how the latent response distribution is parameterized. We provide an alternative implementation of Bayesian IFA under a DELTA, or a unit total variance, parameterization of the latent response distribution. We show that parameterizing the latent response distribution using fixed total variances improves coverage rates of credible intervals for threshold parameters. We apply our implementation of Bayesian IFA to data on psychopathology to illustrate the consistency in threshold recovery under relatively small sample sizes (n=200 sampled from the full population of N=9,282) when some indicators are highly skewed in the population (e.g., <3% of the population are positive on a factor indicator).