The Penalized Regression With Ordinal Multinomial Covariates

In medical and biostatistical studies,a large number of researches for regression analysis with the ordinal multinomial variables as a response have been established.But few works se-riously study them as covariates in regression,especially in high-dimensional situations.One problem in such settings is that an over-fitting model may be built due to the possible existence of pseudo categories in those categorical variables,thus providing a reasonable and practical approach to detect such pseudo categories becomes important.Based on a transformation of dummy variables,this paper proposes a consistent model selection method combined with BIC to explore pseudo categories of ordinal multinomial covariates for generalized linear models.And some regularity conditions are modified under such settings.Some representative simu-lation studies have been conducted to show the consistency of the method.For the detection of pseudo categories of the ordinal multinomial covariates in regression models with the number of covariates p_ngrows with sample size n(p_n?n,p_n=O(n~?),0<??1),this paper proposes an-norm penalized estimation procedure to detect pseudo cate-gories of OM covariates.The estimation approaches are based on the combination of a trans-formation method of dummy variables and the penalized partial likelihood.A detailed algo-rithm is also provided.Theoretical properties,such as model selection consistency,the rate of convergence of the estimators are rigorously established under some regularity conditions.The performance of the proposed method is illustrated by analyses of both simulated data and real data.Both simulation studies and real data analysis(Diabetes dataset and Breast-Cancer-Wisconsin dataset)present good performance of this method,showing its wide applicability in relevant regression analysis.