Score and Pseudo-Score Confidence Intervals for Categorical Data Analysis

This article reviews methods for constructing confidence intervals for analyzing categorical data. A considerable literature indicates that the method of inverting score tests performs well for a variety of cases. When the sample size is small or the parameter is near the parameter space boundary, this method usually performs much better than inverting Wald tests and sometimes better than inverting likelihood-ratio tests. For small samples, exact methods are also available. Although these methods can be quite conservative, inverting a score test using the mid P-value provides a sensible compromise that uses the small-sample distribution while reducing the conservatism and only slightly sacrificing the lower bound for the desired confidence level. For some models, score-test-based inferences are impractical, such as when the likelihood function is not an explicit function of the model parameters. For such cases, pseudo-score inference can be based on a Pearson-type chi-squared statistic that compares fitted values for a working model with fitted values when the parameter of interest takes a fixed value. For some simple cases involving proportions and their differences, a different pseudo-score approach that adds artificial observations before forming Wald confidence intervals provides a simple way of approximating score confidence intervals.