Influence functions at work
This presentation illustrates three practical uses of influence functions (IF) in Stata. First (and most obviously), inspection of IFs helps detecting influential sample observations. I show how this can be done in practice and how similar this is to examining jackknife replicates. Second, IFs make it easy to calculate (asymptotic) standard errors and confidence intervals for a wide range of statistics. I illustrate how this can be done in Stata with the total command so as to account for complex survey design easily. Third and finally, application of ‘recentered influence function (RIF) regression’ has recently been advocated to approximate the impact of covariates on (unconditional) distribution statistics. I demonstrate this use of IFs in Stata and discuss interpretation of RIF regression model coefficients. Empirical applications are to income distribution analysis. Several user-written utilities and commands are illustrated along the way.
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