The robustness of the logistic risk function

Abstract

A Monte-Carlo simulation study is performed to compare the robustness to the assumption of normality of the discriminant function (DF) and conditional maximum likelihood (ML) methods of estimating the logistic regression coefficient (beta) for the simplified case of one independent variable. The unconditional probability of an event occurring, sample size, and beta are varied for each of four distributions - the normal, exponential, Bemouilli, and Poisson. A study of the bias of the estimate of beta, the standard deviation of the regression coefficient estimates and the significance level of the test of the coefficients suggests that, as expected, for very nonnormal distributions and moderate to large sample size, the ML estimates which do not require the normality assumption are preferred; however, for small sample sizes and highly significant beta, alternate methods to both procedures should be sought.

Keywords:

• discriminant function
• maximum likelihood
• logistic regression coefficients
• Monte-Carlo simulation