S

I am using mixed models for variance components analysis and have encountered some problems with non-constant variance

and non-normal errors.

Here is my model (I'm using R): y = 1 + (1|A/B)

There are no predictors, just 2 nested factors A and B. Most variables are well-behaved and var(A) is always greater than var(B). The response variable y shows a skewed distribution in 3 cases and is a count variable in 1 case.

Here are some results for a skewed y. Is the variance component A > B or A < B? By how much? Transforms make big changes:

linear mixed models

gaussian sdA/sdB = 1.80

gaussian + log transform sdA/sdB = 1.11 (best fit)

generalised linear mixed models

gamma+identity link sdA/sdB = 1.15

gamma+log link sdA/sdB = 0.68

And for the count variable:

linear mixed models

gaussian sdA/sdB = 1.38

gaussian + log transform sdA/sdB = 1.88

generalised linear mixed models

poisson + identity link sdA/sdB = 1.15

poisson + log link sdA/sdB = 1.26 (best fit)

Log transforms and links mean that effects are multiplicative, not additive. Should variance components analysis (dividing each variance component by the sum of the variances) therefore not be applied when transforms are involved???

How should I proceed when the relative magnitudes of the random effects A, B and the residual are of primary interest? I guess I can present the linear mixed model results and caution that the model fits were poor for a few variables and those results could be biased?

Stephen.