Inference about Measure of Agreement in the General Mixture Model via Parameter Orthogonalization

Collecting data through experiment, the observers are an import source of measurement error and the inference on the measure of agreement, say kappa, is necessary. The models commonly used are complicated general mixture model, which have many nuisance parameters. Orthogonalization of parameters reduce the effect of nuisance parameter. Orthogonalization of estimating function gives the same effect as the parameter orthogonalization. In this study, the method for orthogonalization of estimating equation is studied and applied to the Beta-binomial model to examine the properties of the estimate of kappa. As a result, the likelihood function is insensitive to the change of the nuisance parameter and bias is smaller than the result of m.1.e. when kappa has extreme values