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

[Norman DAURELLE]

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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