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I'm using SPSS to try and find a mixed model that adequate explains the data that I have. Two of the explanatory variables are closely related ('Sample group' and 'individual'), as an individual is only ever part of one sample group, so I've been nesting them if they are in the same model.

I've been using the models AIC score to rank the models in order of explanatory power. Some of the models use the nested variables, and some of the models only use either 'Sample group' or 'individual'.

My question is: Is it valid to use the AIC to compare between models that use nested variables and those that don't?

To clarify by nested variables, I mean that some of the potential variables used in a model are: 1) sample site(individual) 2) sample site 3) individual

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  • $\begingroup$ The same question was asked here. You should perhaps ask for your accounts to be merged. $\endgroup$ – Scortchi - Reinstate Monica Sep 13 '13 at 10:45
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According to an informal document by Burnham, who I regard as one of the leading experts on the AIC, the notion that models need to be nested to use the AIC for model comparison is a myth. Here is the pdf. See item number 2.

While we're on the topic, I might suggest using the AICc instead of the AIC, as Burnham and Anderson (2004) recommend it as a better default model selection strategy due to its bias correction for finite samples.

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  • $\begingroup$ On second thought, I hesitate about this response. You seem to be talking about nested variables. I'm not sure what you mean by nested variables. There could be a difference between this and nested models. $\endgroup$ – zkurtz Sep 13 '13 at 1:29
  • $\begingroup$ You may want to lookup the paper "Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica: Journal of the Econometric Society, 307-333." $\endgroup$ – Alecos Papadopoulos Sep 13 '13 at 2:00
  • $\begingroup$ Clarified by what is meant by nested variable in main question $\endgroup$ – Dale Sep 13 '13 at 2:06
  • $\begingroup$ @Dale, I'm still a little vague about your use of "nesting". It sounds like variable (1) is effectively the interaction between (2) and (3). In any case, AIC/AICc are extremely general, and it's hard for me to imagine why they would not be appropriate here. If you could communicate some intuition about why the "nesting" makes you suspicious, that could be helpful. $\endgroup$ – zkurtz Sep 13 '13 at 2:25
  • $\begingroup$ From SPSS documentation: Nested terms are useful for modeling the effect of a factor or covariate whose values do not interact with the levels of another factor. For example, a grocery store chain may follow the spending of their customers at several store locations. Since each customer frequents only one of those locations, the Customer effect can be said to be nested within the Store location effect. $\endgroup$ – Dale Sep 13 '13 at 4:05
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If by nesting, you mean random effects, then yes, you can use the AIC to compare between models with/without random effects, as long as you are using the same data to create the models. You can also use the AIC to compare covariance matrices that are used to define the random effects.

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