[R-sig-ME] Variance component models using lmer

[Douglas Bates]

On Mon, Jan 3, 2011 at 1:40 PM, Luciano La Sala
<lucianolasala at yahoo.com.ar> wrote:
> Dear everyone,
>
> I have a dataset consisting of 144 measurements of egg volume from 48 nests
> (3 eggs/nest). I am interested in answering the question of how much of the
> variation in the response variable (egg volume) can be attributed to
> within-nest variation and how much to among-nests variation. My model was
> specified as follows:
>
>> model <- lmer(EggLength ~ NestID + (1|NestID), data = Data)
>> summary(model)
>
> Linear mixed model fit by REML
> Formula: EggLength ~ NestID + (1 | NestID)
>   Data: Data
>   AIC   BIC logLik deviance REMLdev
>  712.4 724.3 -352.2    697.9   704.4
>
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  NestID   (Intercept) 5.5917   2.3647
>  Residual             4.5025   2.1219
>
> Number of obs: 144, groups: NestID, 48
>
> Fixed effects:
>            Estimate Std. Error t value
> (Intercept) 68.02159    1.26104   53.94
> NestID       0.02753    0.01540    1.79
>
> Correlation of Fixed Effects:
>       (Intr)
> NestID -0.952

The formula doesn't make sense.  You have the covariate NestID as both
a fixed-effect (treated, incorrectly, as a numeric value) and a random
effect grouping factor.  You should specify the model formula as

EggLength ~ 1 + (1|NestID)

> >From the above output I extracted the variance components by squaring the
> standard deviations, then expressing them as percentages:
>
>> vars <- c(5.5917, 4.5025)
>> 100*vars/sum(vars)
> [1] 55.39518 44.60482
>
> At this point, I would conclude that egg volume varied 55.4% among clutches
> and 44.6% within clutches.
>
> I'd appreciate suggestions/corrections to my model specification and results
> interpretation.
>
> Thank you in advance.
>
> Luciano
>
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