A new robust parameter estimation approach for multinomial categorical response data with outliers and mismeasured covariates

Being confronted with multinomial categorical response data often occurs in the medical, health, social sciences and other fields. However, the data in practice are subject to measurement error (ME) or outliers due to some unavoidable reasons. There are few studies dealing with problems of ME and outliers in the data with unordered and multi-classified responses simultaneously. To address the effects of ME and outliers in multinomial logistic models, which are most suitable for analyzing categorical outcome variables, we propose novel approaches. Firstly, we develop the extensively weighed corrected score method to estimate parameters in multinomial logistic models with ME. Furthermore, to tackle the problem of that how to obtain parameter estimations when the ME and outliers occur simultaneously, we develop a new robust method, namely the robust extensive weighted corrected score method. Some simulation studies are conducted to evaluate the estimators' finite sample performance. It has been verified that these estimators are consistent and asymptotically normally distributed under general conditions. They are easy to compute, perform well and stably and are robust against the normality assumption for the ME. The proposed methods are also applied to two real datasets to illustrate the practicability of methods.