Sensitivity Analysis of Prior Distributions for Bayesian Cross-Classified Multiple-Membership Multilevel Modeling With Nonnormal Residuals

• In Event: Advancing Complex Multilevel Modeling Techniques Through Simulation

Abstract

This simulation study examines how the selection of priors affects parameter estimates in Bayesian cross-classified multiple membership multilevel modeling when residuals were nonnormally distributed. The conditions manipulated were: priors (inverse-gamma distribution (a, b): (1, 1), (.01, .01), (.001, .001), and (1,.001) and uniform distribution), number of groups (20, 30, 50 and 100), average group size (10, 20 and 40), cross-classification rate (20% and 40%), and multiple membership rate (10% and 20%). Results showed that substantial over-estimation of the level two variance component was identified for both gamma (1,1) and uniform priors while substantial under-estimation was found for gamma (1, .001) prior. With a larger number of level two units, the degree of relative biases of parameter estimates were diminished.

Author

• Hyewon Chung, Chungnam National University