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

Li, Xiaodong

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Description

Title

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

Author(s)

Li, Xiaodong

Issue Date

2006

Doctoral Committee Chair(s)

Douglas, Jeffrey

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Statistics

Language

eng

Abstract

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.

Graduation Semester

2006

Type of Resource

text

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