Bivariate Response Logistic Regression for Categorical Data

Abstract

The bivariate logistic regression model can be used to obtain the probability of joint events as well as individual events where there are two response variables and several explanatory variables. The existing bivariate logistic model approach appears intractable. This paper provides a modeling procedure that addresses this problem. This approach compares favourably with the existing procedure. The new approach is used to model the probability of malaria and typhoid infections, using age, sex and location of the patients as associated factors. The marginal probabilities showed a decrease in malaria infection with age. Sex and location showed a significant impact on the probability of malaria infection. Typhoid fever infection on the other hand indicates an increase with age. Sex has no significant impact on the probability of typhoid infection. The joint model shows that all variables are statistically significant with odds value greater than 1 indicating higher likelihood of joint infection and odds value that are less than one indicating lower likelihood of joint infections, χ2:12.02828 (0.00729)