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A robust diagnostic plot for explanatory variables under model mis-specification

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  • Li-Chu Chien

Abstract

A typical added variable plot is a commonly used plot in assessing the accuracy of a normal linear model. This plot is often used to evaluate the effect of adding an explanatory variable into the model and to detect possibly high leverage points or influential observations on the added variable. However, this type of plot is generally in doubt, once the normal distributional assumptions are violated. In this article, we extend the robust likelihood technique introduced by Royall and Tsou [11] to propose a robust added variable plot. The validity of this diagnostic plot requires no knowledge of the true underlying distributions so long as their second moments exist. The usefulness of the robust graphical approach is demonstrated through a few illustrations and simulations.

Suggested Citation

  • Li-Chu Chien, 2011. "A robust diagnostic plot for explanatory variables under model mis-specification," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 113-126.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:1:p:113-126
    DOI: 10.1080/02664760903271940
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    References listed on IDEAS

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    1. Richard Royall & Tsung‐Shan Tsou, 2003. "Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 391-404, May.
    2. A. H. M. Rahmatullah Imon, 2003. "Residuals from deletion in added variable plots," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(7), pages 827-841.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    1. Duarte Nubia E. & Giolo Suely R. & Pereira Alexandre C. & de Andrade Mariza & Soler Júlia P., 2014. "Using the theory of added-variable plot for linear mixed models to decompose genetic effects in family data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 1-20, June.

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