Research Article Open Access

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

David Todem and KyungMann Kim

Abstract

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 univariate components formulated as 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 models is 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.

Journal of Mathematics and Statistics
Volume 3 No. 3, 2007, 134-141

DOI: https://doi.org/10.3844/jmssp.2007.134.141

Submitted On: 17 June 2006 Published On: 30 September 2007

How to Cite: Todem, D. & Kim, K. (2007). Existence and Uniqueness Conditions for the Maximum Likelihood Solution In Regression Models For Correlated Bernoulli Random Variables. Journal of Mathematics and Statistics, 3(3), 134-141. https://doi.org/10.3844/jmssp.2007.134.141

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Keywords

  • Correlated Bernoulli data
  • Existence/uniqueness conditions
  • Latent variables
  • Linear programming
  • Maximum likelihood estimate
  • Overlap/separation conditions
  • Threshold values