Influence analysis with panel data using Stata

The presence of anomalous cases in a dataset (for example, vertical outliers, good and bad leverage points) can severely affect least-squares estimates (coefficients or standard errors) that are sensitive to extreme cases by construction. Cook (1979)’s distance is usually used to detect such anomalies in cross-sectional data. This metric may fail to flag multiple atypical cases (Atkinson 1985; Chatterjee and Hadi 1988; Rousseeuw and Van Zomeren 1990), while a local approach overcomes this limit (Lawrance 1995). I formalize statistical measures to quantify the degree of leverage and outlyingness of units in a panel-data framework. I hence develop a unitwise method to visually detect the type of anomaly, quantify its joint and conditional influence, and quantify the direction of the enhancing and masking effects. I conduct the proposed influence analysis using two community-contributed commands. First, xtinfluence calculates the joint and conditional influence of unit i on unit j and the relative enhancing and masking effects. A two-way scatter plot or the SSC heatplot can be used to visualize the influence exerted by each unit in the sample. Second, xtlvr2plot (a panel-data version for lvr2plot) produces unitwise plots displaying the average individual influence and the average normalized squared residual of unit i.