This article introduces a graphical diagnostic methodology to systematically examine the sensitivity of longitudinal results to extreme observational units and periods of time (unit-dependency and time-specificity); the methodology is illustrated in the testing of policy effects on Black and white female victimization in intimate partner homicides.
With the added sophistication of longitudinal analysis comes a complexity that makes it difficult to identify potentially misleading anomalies within the data. Unit-dependency occurs when the inclusion of a repeated outlying unit (e.g., a peculiar geographic region or person) alters the results of the analysis. Without systematic methods to clearly identify influential units in longitudinal analysis, statistical artifacts could give more credence to interventions than warranted. Time-specificity refers to unusually influential periods of time that can be obscured in the estimate of an overall effect; i.e., the effectiveness of explanatory variables may not be constant over the entire time span. This could result from unmeasured changes during this period that are jointly related to the response and explanatory variables, creating discontinuity of effect. This article introduces a systematic graphical methodology designed to test the dependency of results from longitudinal analysis on observational units and to identify unusually influential periods of time. The author shows how the methodology addresses each problem by systematically deleting subsets of rows defined by the same observational unit, range of time, or both. The resulting product is a graphical display that shows the robustness of the relationship between each explanatory variable and the response variable. This allows the identification of results that are vulnerable to atypical units of analysis and temporal changes in the pattern of effectiveness. This methodology is illustrated in testing the effectiveness of domestic-violence resources in reducing the rates of female victimization in intimate partner homicide by race in 48 large U.S. cities. 3 tables, 6 figures, and 35 references