Prediction of Latent Variables in a Mixture of Structural Equation Models, with an Application to the Discrepancy between Survey and Register Data

44 Pages Posted: 16 Jun 2008

See all articles by Erik Meijer

Erik Meijer

University of Southern California; RAND Corporation

Susann Rohwedder

RAND Corporation

Tom Wansbeek

University of Groningen - Faculty of Economics and Business

Date Written: June 2008

Abstract

The authors study the prediction of latent variables in a finite mixture of linear structural equation models. The latent variables can be viewed as well-defined variables measured with error or as theoretical constructs that cannot be measured objectively, but for which proxies are observed. The finite mixture component may serve different purposes: it can denote an unobserved segmentation in subpopulations such as market segments, or it can be used as a nonparametric way to estimate an unknown distribution. In the first interpretation, it forms an additional discrete latent variable in an otherwise continuous latent variable model. Different criteria can be employed to derive 'optimal' predictors of the latent variables, leading to a taxonomy of possible predictors. The authors derive the theoretical properties of these predictors. Special attention is given to a mixture that includes components with degenerate distributions. They then apply the theory to the optimal estimation of individual earnings when two independent observations are available: one from survey data and one from register data. The discrete components of the model represent observations with or without measurement error, and with either a correct match or a mismatch between the two data sources.

Keywords: factor scores, measurement error, finite mixture, validation study

JEL Classification: J39, C39, C81

Suggested Citation

Meijer, Erik and Rohwedder, Susann and Wansbeek, Tom, Prediction of Latent Variables in a Mixture of Structural Equation Models, with an Application to the Discrepancy between Survey and Register Data (June 2008). RAND Working Paper Series No. WR-584, Available at SSRN: https://ssrn.com/abstract=1144963 or http://dx.doi.org/10.2139/ssrn.1144963

Erik Meijer (Contact Author)

University of Southern California ( email )

635 Downey Way
Los Angeles, CA 90089-3332
United States

RAND Corporation ( email )

1776 Main Street
P.O. Box 2138
Santa Monica, CA 90407-2138
United States

Susann Rohwedder

RAND Corporation ( email )

P.O. Box 2138
1776 Main Street
Santa Monica, CA 90407-2138
United States

Tom Wansbeek

University of Groningen - Faculty of Economics and Business ( email )

Postbus 72
9700 AB Groningen
Netherlands

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