# [R-sig-ME] Linear mixed effect model

Ben Bolker bbolker at gmail.com
Sat Mar 19 16:54:30 CET 2011

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On 11-03-19 11:27 AM, Manuel Spínola wrote:
> Thank you very much Ben,
>
> I decided to keep "otter" as a random factor:
>
> modA = lmer(Swiftness.1 ~ Lure + Sex + Facility.Size + (1|Subject), REML
> = F, data = otter)
> summary(modA)
>
> modB = lmer(Swiftness.1 ~ (1|Subject), REML = F, data = otter)
> summary(modB)
>
> modC = lmer(Swiftness.1 ~ Lure + (1|Subject), REML = F, data = otter)
> summary(modC)
>
>> AICctab(modA, modB, modC, weights = T, delta = TRUE, base = T, sort =
> TRUE, nobs = 17)
>      AICc   df dAICc  weight
> modB 1313.1 3     0.0 1
> modC 1336.3 8    23.2 <0.001
> modA 1374.5 11   61.4 <0.001
>
> Output for best model:
>
>> summary(modB)
> Linear mixed model fit by maximum likelihood
> Formula: Swiftness.1 ~ (1 | Subject)
>    Data: otter
>   AIC  BIC logLik deviance REMLdev
>  1311 1319 -652.6     1305    1298
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  Subject  (Intercept)     0      0.00
>  Residual             21133    145.37
> Number of obs: 102, groups: Subject, 17
>
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)    99.76      14.39   6.931
>
>
> Is it fair to say that there is no effect of any of the factors?
> Did you say that the variance 0 in the random effect output is low power?
>

Yes, although technically I would say that the factors are not useful
for prediction; if you want to test for the presence of a significant
effect, then fit the full model and report the p-values and confidence
intervals from it.  Yes, I would say that the zero variance represents
noise/ low power: if you were to do the equivalent aov()-analysis it
would probably report a negative variance (i.e., among-group mean square
< within-group mean square).

Ben
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