Bootstrap tests for misspecified models , with application to clustered binary data

When the data do not come from the assumed parametric model, the usual asymptotic chisquared distribution under the null hypothesis, remains valid for “robustified” Wald and score test statistics. In this paper we compare the performance of this chi-squared approximation to that of a semiparametric bootstrap method. The bootstrap approximation is based on a onestep bootstrap estimator reflecting the null hypothesis. One of the advantages of this one-step approach is that no bootstrap data have to be generated and no additional model fitting is required. Simulations on clustered binary data indicate that the robust score test is superior and that, in cases where the chi-squared type tests fail in reaching the prescribed significance level, the proposed bootstrap test succeeds in correcting this towards the nominal level. The different methods are also compared on real developmental toxicity data.