BOOTSTRAPPING PSEUDOLIKELIHOOD MODELS FOR CLUSTERED BINARY DATA

MARC AERTS AND GERDA CLAESKENS

Center for Statistics, Limburgs Universitair Centrum, Universitaire Campus, B3590 Diepenbeek, Belgium

(Received June 3, 1997; revised March 10, 1998)

Abstract. Asymptotic properties of the parametric bootstrap procedure for maximum pseudolikelihood estimators and hypothesis tests are studied in the general framework of associated populations. The technique is applied to the analysis of toxicological experiments which, based on pseudolikelihood inference for clustered binary data, fits into this framework. It is shown that the bootstrap approximation can be used as an interesting alternative to the classical asymptotic distribution of estimators and test statistics. Finite sample simulations for clustered binary data models confirm the asymptotic theory and indicate some substantial improvements.

Key words and phrases: Clustered binary data, developmental toxicity, exponential family, parametric bootstrap, pseudolikelihood.