Use generalized linear models or generalized partially linear models?

We propose test statistics based on the penalized spline to decide between generalized linear models and generalized partially linear models. The numerical performance of the proposed statistics is comparable to that of their kernel-based competitors, which have been shown to be asymptotically normal in the literature (Härdle et al. in J Am Stat Assoc 93:1461–1474, 1998). We also numerically explore the possibility of using the proposed statistics for goodness of fit checking for GLM. The proposed proposed procedures are illustrated to analyze two datasets.