5.1 Model Estimation Approaches

Maximum likelihood estimation

Maximum Likelihood Estimation (MLE) is a statistical approach to estimate the parameter of a statistical model. In this approach, we find the parameter values that make the observed data most probable.

Marginalized Maximum Likelihood Estimation (Marginalized MLE) is a technique used in statistical modeling when dealing with latent (hidden) variables or unobserved components. Marginalized MLE can handle this challenge by marginalizing over the latent variable. In case of CDM, over the latent classes.

• 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