A Short Note on Obtaining Point Estimates of the IRT Ability Parameter With MCMC Estimation in Mplus: How Many Plausible Values Are Needed?

Abstract

Plausible values can be used to either estimate population-level statistics or compute point estimates of latent variables. While it is well known that five plausible values are usually sufficient for accurate estimation of population-level statistics in large-scale surveys, the minimum number of plausible values needed to obtain accurate latent variable point estimates is unclear. This is especially relevant when an item response theory (IRT) model is estimated with MCMC (Markov chain Monte Carlo) methods in Mplus and point estimates of the IRT ability parameter are of interest, as Mplus only estimates the posterior distribution of each ability parameter. In order to obtain point estimates of the ability parameter, a number of plausible values can be drawn from the posterior distribution of each individual ability parameter and their mean (the posterior mean ability estimate) can be used as an individual ability point estimate. In this note, we conducted a simulation study to investigate how many plausible values were needed to obtain accurate posterior mean ability estimates. The results indicate that 20 is the minimum number of plausible values required to obtain point estimates of the IRT ability parameter that are comparable to marginal maximum likelihood estimation(MMLE)/expected a posteriori (EAP) estimates. A real dataset was used to demonstrate the comparison between MMLE/EAP point estimates and posterior mean ability estimates based on different number of plausible values.