### Department of Biostatistics Seminar/Workshop Series

# Good Confidence Intervals for Categorical Data Analyses

## Alan Agresti, PhD

### Distinguished Professor Emeritus, Department of Statistics, University of Florida

### Wednesday, February 22, 1:30-2:30pm, MRBIII Room 1220

This talk surveys confidence intervals that perform well for estimating parameters used in categorical data analysis. Considerable research has now shown that intervals resulting from inverting score tests perform much better than inverting Wald tests and usually better than inverting likelihood-ratio tests. For some models, ordinary score-test-based inferences are impractical, such as when the likelihood function is not an explicit function of the model parameters. For such cases, we propose pseudo-score inference based on a Pearson-type chi-squared statistic that compares fitted values for a working model with fitted values of the model when a parameter of interest takes a fixed value. For multinomial data, the pseudo-score interval simplifies to the score interval when the model is saturated but otherwise can be much simpler to construct. For small samples, `exact' methods are conservative inferentially, but inverting a score test using the mid-P value provides a sensible compromise. If time, we will briefly review a different pseudo-score approach for proportions and their differences that approximates the score intervals and is much better than the ordinary Wald intervals by adding pseudo data before forming the Wald intervals.