  Model selection criteria are rules used to select the best statistical model
among a set of candidate models, striking a trade-off between goodness of fit
and model complexity. Most popular model selection criteria measure the
goodness of fit trough the model log-likelihood function, yielding to
non-robust criteria. This paper presents a new family of robust model selection
criteria for independent but not identically distributed observations
(i.n.i.d.o.) based on the R\'enyi's pseudodistance (RP). The RP-based model
selection criterion is indexed with a tuning parameter $\alpha$ controlling the
trade-off between efficiency and robustness. Some theoretical results about the
RP criterion are derived and the theory is applied to the multiple linear
regression model, obtaining explicit expressions of the model selection
criterion. Moreover, restricted models are considered and explicit expressions
under the multiple linear regression model with nested models are accordingly
derived. Finally, a simulation study empirically illustrates the robustness
advantage of the method.
