If "fixed" really does vary over the levels of "rand", I think the first comparison will exaggerate the evidence, potentially by a lot.

- Pete

On Aug 2, 2011, at 11:12 AM, Mike Lawrence wrote:

> In the scenario where I have one random effect and one fixed effect, I
> typically attempt to evaluate the evidence for an effect of the fixed
> effect variable by:
> 
>    restricted_model = lmer(
>        formula = dv ~ (1|rand) + 1
>    )
>    unrestricted_model = lmer(
>        formula = dv ~ (1|rand) + fixed
>    )
>    bits = (AIC(restricted_model)-AIC(unrestricted_model))*log2(exp(1))
>    #"bits" of evidence: sign signifies whether the effect (+) or null (-) is
>    #    supported, absolute magnitude signifies strength of evidence.
>    print(bits)
> 
> However, this comparison ignores the possibility that the fixed effect
> may vary across levels of the random effect and that these deviations
> may correlate with the random effects' intercept deviations. I'm not
> explicitly interested in the existence of either form of deviation,
> but I wonder if anyone knows whether ignoring their possibility has
> consequences for the evaluation of the general effect of the fixed
> effect. Specifically, compared to the above, how would the following
> be expected to affect the evidence evaluation?
> 
>    restricted_model = lmer(
>        formula = dv ~ (fixed|rand) + 1
>    )
>    unrestricted_model = lmer(
>        formula = dv ~ (fixed|rand) + fixed
>    )
>    bits = (AIC(restricted_model)-AIC(unrestricted_model))*log2(exp(1))
>    print(bits)
> 
> 
> 
> Cheers,
> 
> Mike
> 
> --
> Mike Lawrence
> Graduate Student
> Department of Psychology
> Dalhousie University
> 
> Looking to arrange a meeting? Check my public calendar:
> http://tr.im/mikes_public_calendar
> 
> ~ Certainty is folly... I think. ~
> 
> _______________________________________________
> R-sig-mixed-models@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> 
> 



---
Peter Dixon
peter.dixon@ualberta.ca




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