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Selection of Designs in Ordinal Regression Models under Linear Predictor Misspecification
Authors: Ishapathik Das
Abstract:The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125519Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 611
 M. A. Heise and R. H. Myers, “Optimal designs for bivariate logistic regression,” Biometrics, vol. 52, pp. 613–624, 1996.
 S. S. Zocchi and A. C. Atkinson, “Optimum experimental designs for multinomial logistics models,” Biometrics, vol. 55, pp. 437–443, 1999.
 S. Mukhopadhyay and A. I. Khuri, “Comparison of designs for multivariate generalized linear models,” Journal of Statistical Planning and Inference, vol. 138, pp. 169–183, 2008.
 L. Fahrmeir and G. Tutz, Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd ed. New York: Springer, 2001.
 G. Tutz, Regression for categorical data. Cambridge University Press, 2011, vol. 34.
 A. J. Adewale and X. Xu, “Robust designs for generalized linear models with possible overdispersion and misspecified link functions,” Computational Statistics and Data Analysis, vol. 54, pp. 875–890, 2010.
 A. J. Adewale and D. P. Wiens, “Robust designs for misspecified logistic models,” Journal of Statistical Planning and Inference, vol. 139, pp. 3–15, 2009.
 S. N. Lophaven, H. B. Nielsen, and J. Sondergaard, “A matlab kriging toolbox,” Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark, Tech. Rep., 2002.
 T. J. Santner, B. J. Williams, and W. Notz, The Design And Analysis of Computer Experiments. Springer-Verlag, 2003.
 A. Wald, “Tests of statistical hypotheses concerning several parameters when the number of observations is large,” Trans. Amer. Math. Soc., vol. 54, pp. 426–482, 1943.