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Regression Diagnostics: An Expository Treatment of Outliers and Influential Cases


Bollen, Kenneth A. & Jackman, Robert W. (2013). Regression Diagnostics: An Expository Treatment of Outliers and Influential Cases.. Babones, Salvatore J. (Ed.) (pp. 11-35). London: SAGE.


This new four-volume major work presents a collection of landmark studies on the topic of regression modeling, identifying the most important, fundamental articles out of thousands of relevant contributions. The social sciences - particularly sociology and political science - have made extensive use of regression models since the 1960s, and regression modeling continues to be the staple method of the field. The collection is framed by an orienting essay which presents to a guide to regression modelling, written with applied practitioners in mind.
Abstract of original article: Gauging the robustness of regression estimates is especially important in small-sample analyses. Here, we examine recent developments in the detection and analysis of outliers and influential cases in multivariate studies. Specifically, we review five diagnostic procedures: partial regression plots, the “hat” matrix, studentized residuals, DFITSi, and DFBETASij. The main part of the article presents two empirical applications (drawn from recent cross-national studies) that show (a) how the diagnostic procedures can be incorporated into the research process, and (b) what we can learn from them. These applications serve to underscore the point that the diagnostics cannot be employed mechanically. Instead, once a case is diagnosed as influential, remedial action requires a firm substantive grounding. Although case deletion may be warranted in some circumstances, it is an extreme remedy of last resort that should not be routinely followed. The more fruitful approach is to ask why a given case is influential. As our applications indicate, the diagnostics can be helpful in isolating such problems as sample composition, specification error, and errors in measurement.


Reference Type

Book Section

Year Published


Series Title

SAGE Benchmarks in Social Research Methods


Bollen, Kenneth A.
Jackman, Robert W.