[R-sig-ME] random effect variance greater than output variable variance

[Thierry Onkelinx]

Dear Norman,

Can you show us the full code of the lme4 call and the output of
summary(model). How did you calculate the variances for Y and the random
effect?

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op di 8 nov. 2022 om 17:37 schreef Norman DAURELLE via R-sig-mixed-models <
r-sig-mixed-models using r-project.org>:

>
> Dear list members,
>
> I used a mixed-effect linear model to estimate the effect of a disease on
> the yield of a crop,
> and used a formula that was as follows :
>
> Y ~ X + R1 + R2 + (1|year) + (1|location) + (1|cultivar)
>
> where for each observation :
>
> Y is the yield of the crop ,
> X the average disease severity in the field,
> R1 and R2 the rainfall values in the 1st and 2nd part of the growing
> season respectively,
> and year, location and cultivar, the year location and cultivar of the
> observation.
>
> I have 5 years, 16 locations and a lot of cultivars, with an unbalanced
> experiment design.
>
> The variance given in the summary for the factor Location is greater than
> the variance of the yield variable taken by itself, and this surprises me.
>
> I wanted to show the relative importance of each factor over yield through
> a Venn diagram presenting the variances of each factor as part of the
> overall yield variance, with each factor's variance overlapping with the
> others', but the fact that the variance associated with a factor is greater
> than the variance of the output variable makes me doubt my understanding of
> the variances shown in a summary for a mixed-effect model.
>
> Would someone have a simple explanation of what exactly these variances
> represent ?
>
> I thought that for a factor with N levels, you had V= ( Σ (xi-μ)² ) / N,
> with i = 1,..., N, and xi the output variable's mean in the i-th level of
> the factor, and μ the overall output variable's mean.
>
> Is this not how the variance for a random effect is computed ?
>
> Thanks for any answer !
>
> Cheers,
>
> Norman
>
>
>
>
>
>
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