Detection of outliers in survey–weighted linear regression

Regression diagnostics help identify influential data points in a model. Detecting outliers in complex survey design data involving stratification, clustering, and unequal probability sampling is difficult due to the presence of masking, where one outlier makes it hard to detect others. The masking factor for survey–weighted linear regression is developed and applied to analyzing the Household Consumer Expenditure dataset of 68th round of the National Sample Survey Organization survey of India. Regression parameters are calculated before and after detection and removal of outliers. The standard error of regression parameters for survey-weighted least squares models is reduced by 2% for the intercept, 5% for variable “meat” (X5), 4% for “served processed food” (X9), and 4% for “packaged processed food” (X10). Inference alters the significance of regression coefficients of the variable “served processed food” (X9) leading to the emergence of significance. There is no change in inference for other variables.