I recently received the following question via email. I’ll post an answer below, but I was interested to hear what others thought.
Would you call logistic regression a non-parametric test? My understanding is that
simply labelling a test non-parametric because its data is not
normally distributed, is insufficient. Its more to do with lack of
assumptions. logistic regression does have assumptions.
Larry Wasserman defines a parametric model as a set of distributions “that can be parameterized by a finite number of parameters.” (p.87) In contrast a nonparametric model is a set of distributions that cannot be paramterised by a finite number of parameters.
Thus, by that definition standard logistic regression is a parametric model. The logistic regression model is parametric because it has a finite set of parameters. Specifically, the parameters are the regression coefficients. These usually correspond to one for each predictor plus a constant.
Logistic regression is a particular form of the generalised linear model. Specifically it involves using a logit link function to model binomially distributed data.
Interestingly, it is possible to perform a nonparametric logistic regression (e.g., Hastie, 1983). This might involve using splines or some form of non-parametric smoothing to model the effect of the predictors.
- Wasserman, L. (2004). All of statistics: a concise course in statistical inference. Springer Verlag.
- Hastie, T. (1983). Non-parametric logistic regression. SLAC PUB-3160, June. PDF