A nonparametric local linear smoothing technique for testing goodness-of-fit of ordinal logistic regression models with continuous and categorical covariates is presented. This proposed test statistic is a generalization of Lin and Chen's statistic (2005 Lin , K. C. , Chen , Y. J. ( 2005 ). Testing the goodness-of-fit of logistic models based on local linear smoothing . Int. J. Infor. Mgmnt. Sci. 16 : 83 – 95 .
) to ordinal response data. The extension of logistic regression models for binary responses to ordinal responses is usually involved by modeling cumulative logits. The expectation and variance of the proposed test statistic are derived, and the sampling distribution of the test statistic, which approximates a scaled chi-square distribution is evaluated by simulation. The power comparison between the proposed test and methods of Pulkstenis and Robinson (2004 Pulkstenis , E. , Robinson , T. J. ( 2004 ). Goodness-of-fit tests for ordinal response regression models . Statist. Med. 23 : 999 – 1014 .
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) are also provided. The simulations reveal that the proposed test has greater power to detect the omitted interaction term, incorrectly functional form of continuous covariates, or misspecification of the complimentary log-log link function for various sample sizes. The proposed testing procedure is illustrated by a numerical study.
Communications in Statistics : Theory and Methods 37(6) , pp. 917-930