Abstract #300115

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JSM 2003 Abstract #300115
Activity Number: 248
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #300115
Title: Heterogeneous Mean and Covariance Structure Analysis for Two-Level Latent Variable Models
Author(s): Jiajuan Liang*+ and Peter M. Bentler
Companies: University of New Haven and University of California, Los Angeles
Address: 80 Edwards St., New Haven, CT, 06511-3914,
Keywords: EM algorithm ; heterogeneity ; latent variable models ; mean and covariance structure ; two-level data
Abstract:

Heterogeneous mean and covariance structure appears in two-level data like educational measurements from students nested in different schools. In this paper, heterogeneity means that measurements from level-1 units may have different dimensions and the resulting mean and covariance structure is heterogeneous. When students in schools are assigned to different classes according to their background (e.g., GPA), and bonus tests are given to those students with a higher GPA, we will obtain two-level data with different dimensions. Existing two-level latent variable models for analysis of this kind of data usually assume equal dimension for measurements from all level-1 units. By setting up a simple formulation of two-level latent variable models, we develop an EM algorithm for analysis of heterogeneous mean and covariance structure. It turns out that the M-step of the EM algorithm is equivalent to a conventional multiple-group problem in analysis of latent variables. As a result, the M-step could be realized by employing existing statistical packages such as EQS, LISREL, HLM5, and Mplus. Monte Carlo study shows that the EM algorithm has fairly good empirical performance.

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