Fitting generalized linear models with unspecified link function: A P-spline approach

Generalized linear models (GLMs) outline a wide class of regression models where the effect of the explanatory variables on themean of the response variable is modelled throughout the link function. The choice of the link function is typically overlooked inapplications and the canonical link is commonly used. The estimation of GLMs with unspecified link function is discussed, wherethe linearity assumption between the link and the linear predictor is relaxed and the unspecified relationship is modelled flexiblyby means of P-splines. An estimating algorithm is presented, alternating estimation of two working GLMs up to convergence. The method is applied to the analysis of quit behavior of production workers where the logit, probit and clog–log links do not appear to be appropriate.