5
$\begingroup$

I have a real data set ($n=50$). I would like to fit some parametric models to this data set and then compare the maximum log-likelihood values with my spline model which is a nonparametric model. Could I use AIC criteria as a model selection? If not, which model selection criteria can I use?

$\endgroup$
-1
$\begingroup$

You shouldn't generally use AIC to choose between parametric and nonparametric models. Parametric and nonparametric models have different modeling assumptions. The traditional AIC is based on a function of the likelihood. Likelihoods of parametric and nonparametric models are not always comparable.

An alternative that in theory can naturally compare parametric and nonparametric is a generalized degrees of freedom based criteria. See Ye's paper or Huang and Chen's paper for geostatistical data

| cite | improve this answer | |
$\endgroup$
  • 2
    $\begingroup$ You can't generally use AIC to compare parametric and non-parametric models. But for many spline models, it is a fairly reasonable thing to do (assuming it's not a penalized spline). $\endgroup$ – Cliff AB Nov 13 '15 at 4:41
  • $\begingroup$ Yes, but in practice most spline based models are penalized to control overfitting. Also, AIC may be used to choose the appropriate spline based model to use, but that's a different problem of the one stated by shany $\endgroup$ – Roberto Rivera Nov 14 '15 at 14:12
  • 1
    $\begingroup$ If AIC can discriminate between different smoothing parameters, why can't it discriminate between a smoothing parameter of infinity and a smoothing parameter of 0? I guess this assumes an unpenalized intercept. $\endgroup$ – generic_user Feb 16 '17 at 20:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.