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Bayesian Posterior Estimation of Logit Parameters with Small Samples

Author

Listed:
  • Francisca Galindo-Garre

    (Department of Methodology and Statistics, Tilburg University, the Netherlands)

  • Jeroen K. Vermunt

    (Department of Methodology and Statistics, Tilburg University, the Netherlands)

  • Wicher P. Bergsma

    (EURANDOM, the Netherlands)

Abstract

When the sample size is small compared to the number of cells in a contingency table, maximum likelihood estimates of logit parameters and their associated standard errors may not exist or may be biased. This problem is usually solved by “smoothing†the estimates, assuming a certain prior distribution for the parameters. This article investigates the performance of point and interval estimates obtained by assuming various prior distributions. The authors focus on two logit parameters of a 2 × 2 × 2 table: the interaction effect of two predictors on a response variable and the main effect of one of two predictors on a response variable, under the assumption that the interaction effect is zero. The results indicate the superiority of the posterior mode to the posterior mean.

Suggested Citation

  • Francisca Galindo-Garre & Jeroen K. Vermunt & Wicher P. Bergsma, 2004. "Bayesian Posterior Estimation of Logit Parameters with Small Samples," Sociological Methods & Research, , vol. 33(1), pages 88-117, August.
    • Handle: RePEc:sae:somere:v:33:y:2004:i:1:p:88-117
    DOI: 10.1177/0049124104265997
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    References listed on IDEAS

    as
    1. Gary Koop & Dale J. Poirier, 1995. "An Empirical Investigation of Wagner's Hypothesis by Using a Model Occurrence Framework," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(1), pages 123-141, January.
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