Does the choice of link function matter in response propensity modelling?

Response propensity models are currently often used in survey research when predicting the response behaviour and then adjusting for biases due to non-response. Such a model yields the propensity scores or the predicted response probabilities both for the respondents and non-respondents. The quality of scores depends on the exhaustiveness of auxiliary variables on the one hand, and on the model specification on the other. This paper pays attention to model specification that may be an intricate task including many challenging aspects. We do not consider here all of these but concentrate on the choice of a link function that has been rarely discussed in the literature. The most common solution in survey research is to exploit a logit link. We compare here this link with three other ones, that is, probit, log-log and complementary log-log. Empirical exercises are based on three types of surveys.