Methods and Theory for Joint Estimation of Incidental and Structural Parameters in Latent Class Models

Marginal maximum likelihood estimation has become the standard for parameter estimation in latent variable models. However, there are instances when alternative estimators that jointly estimate incidental parameters and structural parameters might be easier to implement. A drawback to joint estimation, and joint maximum likelihood estimation in particular, is that little theory has been developed to understand their asymptotic behavior. Here we consider joint estimation of class membership and structural parameters in latent class models for binary responses. An estimator that first utilizes a K-means clustering solution on a statistic that identifies class membership and then maximizes the conditional likelihood of the structural parameters is studied. It is shown that this estimator is consistent and is asymptotically normal. In addition, it is shown that this estimator is identical to the joint maximum likelihood estimator with probability approaching 1 as the sample size and item response vector length both approach infinity, for a special case. An argument is then given that we can also expect this result in more general cases. The small sample properties of the estimator are studied by simulation.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Li, Xiaodong

Contributors dc:contributor

• Douglas, Jeffrey

• Statistics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3242917

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87406