A1607
Title: On the choice of parametric link for binomial-response generalized linear models
Authors: Takis Besbeas - Athens University of Economics and Business (Greece) [presenting]
Dimitrios Stroungis - Athens University of Economics and Business (Greece)
Abstract: Logistic and probit regression are the two most commonly used techniques to analyse binary and binomial response data. Although these models have desirable properties, several authors have noted their sensitivity to outliers and have recognised that the use of a larger class of link functions within a binomial generalised linear model may have advantages in practice. It is illustrated that there is considerable choice beyond the use of the logit and probit, resulting from the use of a range of cumulative distribution functions to relate the probability of success to the linear predictor. Extending work on binary outcomes, a Gosset regression model is considered based on the CDF of a t-distribution with a free degree of freedom parameter, which includes the logit, probit and Cauchit models as special cases. The framework allows the choice of link function to be addressed through the estimation of the degrees of freedom parameter. Estimation of that parameter is described by profile likelihood, and the performance of the method is evaluated using simulation, illustrating that estimation is uncertain in the case of binary outcomes but improves with the number of trials. The impact of misspecification of the link function on the parameter estimates is evaluated. Results demonstrate that it is prudent to convey a more skeptical attitude about the conventional choice of logit and probit links in practice, especially when the number of trials is large.
