This paper is concerned with the analysis of proportions affected when an increasing dose of a compound is applied to a group of laboratory animals. Several sets of data, including a set from a teratological experiment at the Shell Toxicology Laboratory, Sittingbourne, are analysed and some simulations are performed. Among the distributional models, the beta-binomial model is, in general, found to be the most sensitive to departures from the binomial. For testing the equality of two proportions, a comparison is made between the pseudo-t test, based on the jackknife method, and the likelihood ratio test, based on the beta-binomial model. From the limited comparison, no definite advantage of one approach over the other has been found; at the 5% level of significance both approaches lead to similar conclusions.

The authors develop score tests of goodness-of-fit for discrete generalized linear models against zero-inflation. The binomial and Poisson models are treated as examples and in the latter case, the proposed test reduces to that of Broek (1995). Some simulation results and an illustrative example are presented. RÉSUMÉ Les auteurs développent des procédures scores permettant de tester l'adéquation de modèles linéaires généralisés discrets lorsque la valeur zéro est en surnombre dans l'échantillon. Les modèles binomial et de Poisson font l'objet d'une attention particulière et, dans ce dernier cas, le test obtenu se ramèneà celui de Broek (1995). Des simulations et un exemple sontégalement présentés.

We derive a first-order bias-corrected maximum likelihood estimator for the negative binomial dispersion parameter. This estimator is compared, in terms of bias and efficiency, with the maximum likelihood estimator investigated by Piegorsch (1990, Biometrics46, 863-867), the moment and the maximum extended quasi-likelihood estimators investigated by Clark and Perry (1989, Biometrics45, 309-316), and a double-extended quasi-likelihood estimator. The bias-corrected maximum likelihood estimator has superior bias and efficiency properties in most instances. For ease of comparison we give results for the two-parameter negative binomial model. However, an example involving negative binomial regression is given.

Longitudinal (clustered) response data arise in many bio-statistical applications which, in general, cannot be assumed to be independent. Generalized estimating equation (GEE) is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified, although their small sample properties are not known. In this paper, two bias adjusted GEE estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small. One is based on a bias correction, and the other is based on a bias reduction. Simulations show that the performances of both the bias-corrected methods are similar in terms of bias, efficiency, coverage probability, average coverage length, impact of misspecification of correlation structure, and impact of cluster size on bias correction. Both these methods show superior properties over the GEE estimates for small samples. Further, analysis of data involving a small number of subjects also shows improvement in bias, MSE, standard error, and length of the confidence interval of the estimates by the two bias adjusted methods over the GEE estimates. For small to moderate sample sizes (N ≤50), either of the bias-corrected methods GEEBc and GEEBr can be used. However, the method GEEBc should be preferred over GEEBr, as the former is computationally easier. For large sample sizes, the GEE method can be used.

This paper is concerned with testing the multinomial (binomial) assumption against the Dirichlet-multinomial (beta-binomial) alternatives. In particular, we discuss the distribution of the asymptotic likelihood ratio (LR) test and obtain the C(alpha) goodness-of-fit test statistic. The inadequacy of the regular chi-square approximation to the LR test is supported by some Monte Carlo experiments. The C(alpha) test is recommended based on empirical significance level and power and also computational simplicity. Two examples are given.