SMALL SAMPLE INTERVALS FOR GENERALIZED LINEAR-REGRESSION

Small sample confidence intervals are constructed for inference in a generalized linear model. Intervals for a real parameter theta are calculated using the empirical distribution of the observed values of the influence curve for theta. Assumptions about adequacy of the experimental design lead to robust behaviour of the confidence intervals. The model considered is that of an IxJ table of counts. These can be viewed as many J-dimensional multinomial responses or as IJ poisson observations with row totals fixed. Maximum likelihood estimates are used to estimate the parameters beta for multinomial response with canonical link. The small sample intervals which are constructed for the model are not symmetric about the parameter estimate. Confidence intervals for linear combinations of components of beta are compared with some asymptotic intervals, obtained from the normal approximation to the signed root likelihood. Comparisons are also made with the simpler asymptotic intervals obtained from the asymptotic normality of the maximum likelihood estimate. For the logit model, intervals are computed for LD50 and LD80, nonlinear functions of beta. The small sample intervals are shown to be reliable for small samples and provide a method of checking the accuracy of the simple asymptotic intervals as well as giving feasible alternatives to the computationally intensive asymptotic intervals based on the signed root likelihood.