Detecting Outlying Cells in Two-Way Contingency Tables Via Backwards-Stepping
Jeffrey S. Simonoff · Technometrics · 1988
When fitting a model to a contingency table, a significant lack of fit can sometimes be caused by a few outlier cells, with the model fitting the remaining cells well. These cells can be identified by using deleted residuals (the residual from the expected count with the cell deleted) and tested using the drop in likelihood ratio goodness-of-fit statistic (from the model with the cell included to the model with the cell deleted), with the cells being tested from least extreme to most extreme (“backwards-stepping”). This article shows that using a Bonferroni bound for the outlier test at each step results in a conservative test with good power to detect multiple outliers; backwards-stepping and the use of deleted residuals results in the limiting of both masking and swamping effects. The procedure generalizes easily to complicated probability models.