A Review of Score-Test-Based Inference for Categorical Data

One of C. R. Rao's many important contributions to statistical science was his introduction of the score test, based on the derivative of the log-likelihood function at the null hypothesis value of the parameter of interest. This article reviews methods for constructing score tests and score-test-based confidence intervals for analyzing parameters that arise in analyzing categorical data. A considerable literature indicates that score tests and their inversion for constructing confidence intervals perform well in a variety of settings and sometimes much better than Wald-test and likelihood-ratio test-based methods. We also discuss extensions of score-based inference and potential future research on generalizations for longitudinal data, complex sampling, and high-dimensional data.