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http://dx.doi.org/10.5351/CKSS.2008.15.1.027

A Graphical Method of Checking the Adequacy of Linear Systematic Component in Generalized Linear Models  

Kim, Ji-Hyun (Department of Statistics and Actuarial Science, Soongsil University)
Publication Information
Communications for Statistical Applications and Methods / v.15, no.1, 2008 , pp. 27-41 More about this Journal
Abstract
A graphical method of checking the adequacy of a generalized linear model is proposed. The graph helps to assess the assumption that the link function of mean can be expressed as a linear combination of explanatory variables in the generalized linear model. For the graph the boosting technique is applied to estimate nonparametrically the relationship between the link function of the mean and the explanatory variables, though any other nonparametric regression methods can be applied. Through simulation studies with normal and binary data, the effectiveness of the graph is demonstrated. And we list some limitations and technical details of the graph.
Keywords
Boosting; nonparametric regression; bootstrap confidence intervals;
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1 Landwehr, J. M., Pregibon, D. and Shoemaker, A. C. (1984). Graphical methods for assessing logistic regression models. Journal of the American Statistical Association, 79, 61-71   DOI
2 R Development Core Team (2006). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org
3 Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC, London
4 Freund, Y. and Schapire, R. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55, 119-139   DOI   ScienceOn
5 Friedman, J., Hastie, T. and Tibshirani, R. (2000). Additive logistic regression: A statistical view of boosting. The Annals of Statistics, 28, 337-374
6 Therneau, T. M. and Atkinson, B. (2006). rpart: Recursive Partitioning. R package version 3.1-33. S-PLUS 6.x original at http://mayoresearch.mayo. edu/mayo/research/biostat/splusfunctions.cfm
7 Ridgeway, G. (1999). The state of boosting. Computing Science and Statistics, 31, 172-181
8 Su, J. Q. and Wei, L. J. (1991). A lack-of-fit test for the mean function in a generalized linear model. Journal of the American Statistical Association, 86, 420-426   DOI
9 Kim, J. H. (2003). Assessing practical significance of the proportional odds assumption. Statistics & Probability Letters, 65, 233-239   DOI   ScienceOn
10 Cheng, K. F. and Wu, J. W. (1994). Testing goodness of fit for a parametric family of link functions. Journal of the American Statistical Association, 89, 657-664   DOI