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.
Abstract: Martingale model diagnostic for assessing the fit of logistic regression model to recurrent events data are studied. One way of assessing the fit is by plotting the empirical standard deviation of the standardized martingale residual processes. Here we used another diagnostic plot based on martingale residual covariance. We investigated the plot performance under several types of model misspecification. Clearly the method has correctly picked up the wrong model. Also we present a test statistic that supplement the inspection of the two diagnostic. The test statistic power agrees with what we have seen in the plots of the estimated martingale covariance.