Pseudo-score confidence intervals for parameters in discrete statistical models

We propose pseudo-score confidence intervals for parameters in models for discrete data. The confidence interval is obtained by inverting a test that uses a Pearson chi-squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values. For multinomial models, the pseudo-score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test-based inferences. For cases in which ordinary score methods are impractical, such as when the likelihood function is not an explicit function of model parameters, the pseudo-score method is feasible. We illustrate the method for four such examples. Generalizations of the method are also presented for future research, including inference for complex sampling designs using a quasilikelihood Pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model.