Existence and Uniqueness Conditions for the Maximum Likelihood Solution In Regression Models For Correlated Bernoulli Random Variables | Science Publications

Journal of Mathematics and Statistics

David Todem¹  KyungMann Kim¹ 

关键词: Correlated Bernoulli data;    Existence/uniqueness conditions;    Latent variables;    Linear programming;    Maximum likelihood estimate;    Overlap/separation conditions;    Threshold values;   

DOI  :  10.3844/jmssp.2007.134.141

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

We give sufficient and necessary conditions for the existence of the maximum likelihood estimate in a class of multivariate regression models for correlated Bernoulli random variables. The models use the concept of threshold crossing technique of an underlying multivariate latent variable with univariatecomponents formulatedas a linear regression model. However, in place of their Gaussian assumptions, any specified distribution with a strictly increasing cumulative distribution function is allowed for error terms. A well known member of this class of modelsis the multivariate probit model. We show that our results are a generalization of the concepts of separation and overlap of Albert and Anderson for the study of the existence of maximum likelihood estimate in generalized linear models. Implications of our findings are illustrated through some hypothetical examples.

【 授权许可】

Unknown