On the Prior Effective Sample Size of Threshold Priors in Bayesian Item Factor Analysis

• In Event: Bayesian Estimation of Structural Equation Models

Abstract

The Dirichlet distribution is commonly used as a prior in Bayesian analyses. The hyperparameters of the Dirichlet distribution are generally interpreted as the number of pseudo-observations added as prior information. In item factor analysis, this is useful for interpreting the prior as the number of additional observations endorsing each response category when using the induced-Dirichlet prior for thresholds. This study challenges the validity of this interpretation by using a simulation-based calibration method for approximating the prior-effective sample size. These results provide evidence for the interpretation of the hyperparameters of the induced-Dirichlet prior as pseudo-observations. This study also demonstrates how the prior effective sample size can be approximated for different prior specifications even with priors generally not interpreted as pseudo-observations.

Author

• R. Noah Padgett, Harvard University