Simple Computation of Maximum Likelihood Estimates in Latent Class Model with Equality and Constant Constraints

Abstract

A simple computational method for estimation of parameters via a type of EM algorithm is proposed in restricted latent class analysis, where equality and constant constraints are considered. These constraints create difficulty in estimation. In order to simply and stably estimate parameters in restricted latent class analysis, a simple computational method using only first-order differentials is proposed, where the step-halving method is adopted. A simulation study shows that in almost all cases the new method gives parameter sequences monotonously increasing the Q-function in the EM algorithm. Analysis of real data is provided.

Keywords:

• Constant constraints
• Equality constraints
• Latent class analysis
• Restricted EM algorithm

Mathematics Subject Classification:

• 62H12
• 62H17
• 62K05
• 62P25
• 49M20

Notes

†Equality constraint.

∗Constant constraint.

†Equality constraint.

∗Constant constraint.