Detection of Outlying Cells in Contingency Tables Using Model Based Diagnostics

Detecting outliers in contingency table is an interesting statistical problem and it poses additional difficulties due to the polarization of cell counts. The fundamental definition of ’markedly deviant’ cell as an outlier is clearly exploited in this study by introducing a pivot element to capture the deviations. The present study considers a two-step confirmatory procedure to detect outliers in I × J contingency table. The procedure deals with (i) identifying the reliable set of candidate outliers using the deviation from the pivot element and then (ii) detect those set of outlying cells by examining different type of residuals of the suitable fitted model. The robustness of the procedure is investigated through a simulation study along with applications to real datasets.