5.1 Model Estimation Approaches

Maximum likelihood estimation

• The marginalized maximum likelihood estimation (MMLE) is most common
• MMLE is generally very efficient with moderate-sized K
• It becomes inefficient as K gets larger
• Requires some (tedious) derivations
• Implemented in many software packages
• Commercial software: Mplus, Latent Gold, FlexMIRT
• Free software: CDM, GDINA, mdltm (research licence)

Bayesian estimation via Markov chain Monte Carlo (MCMC)

• Flexible and easy to derive for complicated models
• Estimate the distribution (instead of point estimates) of parameters
• Time-consuming
• Software: JAGS, WINBUGS, OpenBUGS, STAN, nimble