×

zbMATH — the first resource for mathematics

Latent residual analysis in binary regression with skewed link. (English) Zbl 1319.62151
Summary: Model diagnostics is an integral part of model determination and an important part of the model diagnostics is residual analysis. We adapt and implement residuals considered in the literature for the probit, logistic and skew-probit links under binary regression. New latent residuals for the skew-probit link are proposed here. We have detected the presence of outliers using the residuals proposed here for different models in a simulated dataset and a real medical dataset.
MSC:
62J20 Diagnostics, and linear inference and regression
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDF BibTeX XML Cite
Full Text: DOI Euclid
References:
[1] Albert, J. H. and Chib, S. (1995). Bayesian residual analysis for binary response regression models. Biometrika 82 , 747-956. · Zbl 0861.62022
[2] Azzalini, A. and Capitanio (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-\(t\) distribution. Journal of the Royal Statistical Society, Series B 65 , 367-389. · Zbl 1065.62094
[3] Chen, M.-H. and Dey, D. K. (1998). Bayesian modelling of correlated binary responses via scale mixture of multivariate normal link functions. Sankhyã, Ser. A 60 , 322-343. · Zbl 0976.62019
[4] Chen, M.-H., Dey, D. K. and Shao, Q.-M. (1999). A new skewed link model for dichotomous quantal response data. Journal of the American Statistical Association 94 , 1172-1186. · Zbl 1072.62655
[5] Chen, M.-H. (2004). The skewed link models for categorical response data. In Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality (M. G. Genton, ed.). Boca Raton: Chapman & Hall/CRC.
[6] Christensen, R. (1997). Log-Linear Models and Logistic Regression , 2nd ed. New York: Springer-Verlag. · Zbl 0880.62073
[7] Devroye, L. (1986). Non-Uniform Random Variate Generation . New York: Springer-Verlag. · Zbl 0593.65005
[8] Farias, R. B. A. and Branco, M. D. (2011). Efficient algorithms for Bayesian binary regression model with skew-probit link. In Recent Advances in Biostatistics (M. Bhattacharjee, S. K. Dhar and S. Subramanian, eds.) 143-168. Newark, NJ: World Scientific.
[9] Geisser, S. and Eddy, W. (1979). A predictive approach to model selection. Journal of the American Statistical Association 74 , 153-160. · Zbl 0401.62036
[10] Kass, R. E. and Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association 90 , 773-795. · Zbl 0846.62028
[11] McCullagh, P. and Nelder, J. (1989). Generalized Linear Models , 2nd ed. London: Chapman & Hall. · Zbl 0744.62098
[12] Sahu, S. K., Dey, D. K. and Branco, M. D. (2003). A new class of multivariate skew distributions with applications to Bayesian regression models. The Canadian Journal of Statistics 31 , 129-150. · Zbl 1039.62047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.