Detection of Outliers in Categorical Data using Model Based Diagnostics

Detection of outliers is an important and interesting problem in data analysis. However,
detecting outliers in categorical data poses additional diculties due to polarization of cell counts.
The structure and nature of cell counts in a contingency table play an important role in the
data analysis with the cell counts ranging from zero to very high frequencies. Thus the nature
and location of frequency in cells could create polarization posing an additional challenge in the
detection of outliers. The present study considers model based approach to detect outliers in
an I x J contingency table. The procedure deals with tting a Poisson Log-Linear Model for the
count data and examine dierent types of residuals supplemented by boxplot in identifying the
outlying cells. The robustness of the model is investigated through a simulation study along
with applications to real datasets.