{"title":"Selection of Designs in Ordinal Regression Models under Linear Predictor Misspecification","authors":"Ishapathik Das","country":null,"institution":"","volume":108,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":770,"pagesEnd":778,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10004912","abstract":"The purpose of this article is to find a method\r\nof comparing designs for ordinal regression models using\r\nquantile dispersion graphs in the presence of linear predictor\r\nmisspecification. The true relationship between response variable\r\nand the corresponding control variables are usually unknown.\r\nExperimenter assumes certain form of the linear predictor of the\r\nordinal regression models. The assumed form of the linear predictor\r\nmay not be correct always. Thus, the maximum likelihood estimates\r\n(MLE) of the unknown parameters of the model may be biased due to\r\nmisspecification of the linear predictor. In this article, the uncertainty\r\nin the linear predictor is represented by an unknown function. An\r\nalgorithm is provided to estimate the unknown function at the\r\ndesign points where observations are available. The unknown function\r\nis estimated at all points in the design region using multivariate\r\nparametric kriging. The comparison of the designs are based on\r\na scalar valued function of the mean squared error of prediction\r\n(MSEP) matrix, which incorporates both variance and bias of the\r\nprediction caused by the misspecification in the linear predictor. The\r\ndesigns are compared using quantile dispersion graphs approach.\r\nThe graphs also visually depict the robustness of the designs on the\r\nchanges in the parameter values. Numerical examples are presented\r\nto illustrate the proposed methodology.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 108, 2015"}