Logistic Regression and Bayesian Model Selection in Estimation of Probability of Success

Logistic regression and linear discriminant analysis are used to estimate probability of success for binary data based on a training sample and a certain amount of prior information. Posterior probabilities of success are calculated for different choices of the model for the training sample distribution. An approach to model selection is suggested for certain classes of distributions based on the exponential family. As an illustration, we consider two examples. One is an artificially simulated dataset from a mixture of Poisson distributions. Another deals with the history of communication between a sales agent and a customer used to estimate the probability of successful sale. The dataset was obtained from a Midwestern company that uses telesales in a business-tobusiness environment. The number of decision-maker contacts X is analyzed as an explanatory variable. A comparison is made between logistic regression technique and discriminant analysis based on negative binomial or zero-modified Poisson distribution of the number of contacts. There seems to be a good agreement between the results obtained by both methods. Discriminant analysis as demonstrated by Efron (1975) can be more efficient if some model assumptions are made regarding the distribution of X . However, logistic regression may be used in order to validate the choice for a certain class of models. A. Introduction and Methods A