Influence Analysis with Panel Data using Stata

The presence of units that possess extreme values in the dependent variable and/or independent variables (i.e., vertical outliers, good and bad leverage points) has the potential to severely bias least squares (LS) estimates – i.e., regression coefficients and/or standard errors. Diagnostic plots (such as leverage-versus-squared residual plots) and measures of overall influence (e.g., Cook (1979)’s distance) are usually used to detect such anomalies, but there are two different problems arising from their use. First, available commands for diagnostic plots are built for cross-sectional data, and some data manipulation is necessary for panel data. Second, Cook-like distances may fail to flag multiple anomalous cases in the data because they not account for pair-wise influence of observations (Atkinson, 1993; Chatterjee and Hadi, 1988, Rousseeuw, 1991; Rousseeuw and Van Zomeren, 1990, Lawrance, 1995). I overcome these limits as follows. First, I formalise statistical measures to quantify the degree of leverage and outlyingness of units in a panel data framework to produce diagnostic plots suitable for panel data. Second, I build on Lawrance (1995)'s pair-wise approach by proposing measures for joint and conditional influence suitable for panel data models with fixed effects. I develop a method to: (i) visually detect anomalous units in a panel data set and identify their type; (ii) investigate the effect of these units on LS estimates, and on other units’ influence. I propose two user-written commands in Stata to implement this method. xtlvr2plot produces a leverage-versus-residual plot suitable for panel data, and a summary table with the list of detected anomalous units and their type. xtinfluence calculates the joint and conditional influence and effects of pairs of units, and generates network-style plots (an option between scatter plot or heat plot is allowed by the command).