In a glm, if I fit a variable with dummy variables for every value of the variable, can I say I'm fitting the variable non parametrically? I am fitting a generalized linea model to psychometric data, there's one variable, lets call is X, that I'm fitting with individual predictor variables because X has only three values i.e. 3 dummy variables, and a simple predictor variable does not fit the data well. I'm wondering whether I can call my approach non parametric, and if not whether there is a name for this.
I've read about non parametric fitting, and it seems to be different from this, involving smooth functions, but from my understanding it also seems to make sense to call this non parametric because I'm not specifying a form for the relationship, so I'm not sure.
 A: This is not a nonparametric method because you're still using a fully parametric model. Each dummy variable will get a coefficient, which is a parameter. Your generalized linear model is fully characterized by these coefficients along with its other parameters (if any).
One way to describe this approach is that you've discretized $X$.
A: I do not think your approach can be described as non-parametric. I would refer to it as fitting a "saturated model" or a saturated effect of X. This means that the mean-model and, hence, the predictions are going to be accurate. However, the GLM introduces further assumptions about the underlying distribution to obtain correct inference and CIs. For that reason, I would not bother with the designation(s) non-parametric/semi-parametric/fully-parametric; most likely the approach is not non-parametric. "Smooth functions" like splines are not necessarily non-parametric either, since the validity of inference and error estimates may depend on the moments of the underlying distribution of values. Using robust or flexible error fitting procedures can extend these methods into non-parametric analogues.
