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A Latent Markov Model to Correct for Measurement Error

Author

Listed:
  • FRANK VAN DE POL

    (Netherlands Central Bureau of Statistics)

  • JAN DE LEEUW

    (University of Leyden)

Abstract

In classical test theory the reliability of a test can be estimated by test-retest correlation models. These models do not apply to data of the lowest or nominal measurement level. Instead, models for latent Markov chains may be used to correct for measurement error in panel data from three or more waves. In this article it is shown how to use the E-M algorithm for estimating the parameters of a latent Markov chain. Where previous algorithms performed badly on variables with more than two categories this algorithm performs better, although convergence is often slow. The method is applied to two trichotomous questions from the Dutch civil servants panel survey. Generally the assumptions of the model that is, a latent stationary Markov chain, are reasonably well met by the data. The probability of a correct answer, which can be interpreted as the reliability of a latent response category, is high in most cases (about. 8). Also transition tables are presented that are corrected for measurement error according to the model. Standard errors of model parameters are approximated by a finite difference method.

Suggested Citation

  • Frank Van De Pol & Jan De Leeuw, 1986. "A Latent Markov Model to Correct for Measurement Error," Sociological Methods & Research, , vol. 15(1-2), pages 118-141, November.
    • Handle: RePEc:sae:somere:v:15:y:1986:i:1-2:p:118-141
    DOI: 10.1177/0049124186015001009
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    References listed on IDEAS

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    1. Jacques Hagenaars, 1978. "Latent probability models with direct effects between indicators," Quality & Quantity: International Journal of Methodology, Springer, vol. 12(3), pages 205-222, September.
    2. Glenn Carroll, 1983. "Dynamic analysis of discrete dependent variables: A didactic essay," Quality & Quantity: International Journal of Methodology, Springer, vol. 17(6), pages 425-460, October.
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    Cited by:

    1. Breen, Richard & Moisio, Pasi, 2003. "Poverty dynamics corrected for measurement error," ISER Working Paper Series 2003-17, Institute for Social and Economic Research.
    2. Montfort, Kees van & Bijleveld, Catrien, 1997. "Dynamic analysis of multivariate panel data with nonlinear transformations," Serie Research Memoranda 0054, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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