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Bayesian Posterior Estimation of Logit Parameters with Small Samples

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

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 x 2 x 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.

Key Words: small samples • logit models • Bayesian estimation • prior distributions

Sociological Methods & Research, Vol. 33, No. 1, 88-117 (2004)
DOI: 10.1177/0049124104265997


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