[R-sig-ME] Likelihood Ratio Test for non-nested mixed-effect-model comparison

[Ben Bolker]

  The Vuong test <https://en.wikipedia.org/wiki/Vuong's_closeness_test>
provides a likelihood-based framework for distinguishing between
non-nested models.  I'm not immediately aware of an implementation that
works with mixed models in R, but you could look around (library("sos");
findFn("vuong") and screen the results for applicability ...)

  As a crude alternative you could do something parametric bootstrap-y
by simulating from each fitted model, fitting each realization with both
fitted models, and comparing the goodness of fit distributions (that's
intentionally vague, I haven't thought about it very much ...)

  Ben Bolker

On 15-10-23 11:40 AM, Francesco Sigona wrote:
> Hi all,
> 
> I need to compare two mixed-effects-models that would explain a
> dependent variable by means of two completely different sets of fixed
> factors (my random intercept is the same in both models).
> 
> I understand that the anova() cannot be used to perform a comparison via
> LRTest in my case, because my models are non-nested.
> 
> Thus, I would take the model with the lowest AIC (o BIC) value, but I am
> worried about the statistical significance, so I would prefer a LRTest
> and the related p-value (as provided by anova() for nested models) to
> support my model selection.
> 
> My problem is that I don't know how to compare two non-nested
> mixed-effect-models via a LRTest.
> 
> Any suggestion?
> 
> Thank you in advance.
> 
> Francesco
>