On Expressing the Probabilities of Categorical Responses as Linear Functions of Covariates  

作　　者：Tejas A. Desai 

机构地区：[1]The Adani Institute of Infrastructure Management, Ahmedabad, India

出　　处：《Applied Mathematics》2013年第11期1485-1489,共5页应用数学（英文）

摘　　要：Logistic regression is usually used to model probabilities of categorical responses as functions of covariates. However, the link connecting the probabilities to the covariates is non-linear. We show in this paper that when the cross-classification of all the covariates and the dependent variable have no empty cells, then the probabilities of responses can be expressed as linear functions of the covariates. We demonstrate this for both the dichotmous and polytomous dependent variables.Logistic regression is usually used to model probabilities of categorical responses as functions of covariates. However, the link connecting the probabilities to the covariates is non-linear. We show in this paper that when the cross-classification of all the covariates and the dependent variable have no empty cells, then the probabilities of responses can be expressed as linear functions of the covariates. We demonstrate this for both the dichotmous and polytomous dependent variables.

关 键 词：Logistic Regression Linear Regression Maximum LIKELIHOOD ESTIMATION LEAST-SQUARES ESTIMATION 

分 类 号：R73[医药卫生—肿瘤]