[R-sig-ME] What is the consequence of neglecting to consider variability of a fixed effect across levels of a random effect

[Mike Lawrence]

Oops, all the lmer calls should have "REML=TRUE". Also, an astute
reader pointed out that I should of course avoid permitting fixed
effects to vary across levels of the random effect if the fixed
effects are manipulated across (rather than within) levels of the
random effect.

On Tue, Aug 2, 2011 at 2:12 PM, Mike Lawrence <Mike.Lawrence at dal.ca> 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. ~
>