In the application of regression analysis, often the data set consist of unusual observations which are either outliers (noise) or influential observations. These observations may have large residuals and affect the parameters of the regression co-efficient and the whole regression analysis and become the source of misleading results and interpretations. Therefore it is very important to consider these suspected observations very carefully and made a decision that either these observations should be included or removed from the analysis.
In regression analysis, the basic step is to determine whether one or more observations can influence the results and interpretations of the analysis. If the regression analysis have one independent variable, then it is easy to detect observations in dependent and independent variables by using scatter plot, box plot and residual plot etc. But graphical method to identify outlier and/or influential observation is a subjective approach. It is also well known that in the presence of multiple outliers there can be a masking or swamping effect. Masking (false negative) occurs when an outlying subset remains undetected due the presence of another, usually adjacent subset. Swamping (false positive) occurs when usual observation is incorrectly identified as outlier in the presence of another usually remote subset of observations.
In the present study, some well known diagnostics are compared to identify multiple influential observations. For this purpose, first, robust regression methods are used to identify influential observation in Poisson regression, then to conform that the observations identified by robust regression method are genuine influential observations, some diagnostic measures based on single case deletion approach like Pearson chi-square, deviance residual, hat matrix, likelihood residual test, cook’s distance, difference of fits, squared difference in beta are considered but in the presence of masking and swamping diagnostics based on single case deletion fail to identify outlier and influential observations. Therefore to remove or minimize the masking and swamping phenomena some group deletion approaches; generalized standardized Pearson residual, generalized difference of fits, generalized squared difference in beta are taken.