[R-sig-ME] need help with mixed effects model

[Douglas Bates]

On Fri, Feb 22, 2008 at 11:57 AM, Mark W Kimpel <mwkimpel at gmail.com> wrote:
> This is my first foray into in mixed models and, while awaiting the
>  arrival of:

>  Extending the Linear Model with R: Generalized Linear, Mixed Effects
>  and     Nonparametric Regression Models
>  Mixed Effects Models in S and S-Plus

>  I am in need to some advice.

>  I would like to look at gene-gene correlations within a multi-factorial,
>  mixed effects experiment. Here are the factors, with levels:

>  Gene Expression: 2 different genes per Animal, continuous variable
>  Animals: 6 per Strain
>  Tissues: 3 per animal

> Strain: 2

>  I thus have 6*3*2 = 36 samples

>  I do not care, for this analysis, about differences between Tissues,
>  Strains, or Animals, in fact, I want to control for them while examining
>  the correlation of expression of the two genes. In other words, I want
>  look at something very much like the Pearson correlation coefficient
>  controlled for these other factors.

>  I guess the first question I should ask is: "is a mixed model the way to
>  go, and, if not, what would be the correct approach?"

Perhaps.  How do you plan to incorporate the two genes?

>  Assuming mixed models will work, as I see it through my newbie eyes,
>  Tissue and strain are fixed effects and animals are random effects.

If you were interested in just 1 gene than I would say that this looks
like a good approach.  I'm just not sure what to do about the multiple
genes.

>  Any suggestions for an approach and a model?

The model specification (assuming that each animal has a distinct
number) would be something like

gene1 ~ Tissue * Strain + (1|Animal)

In your earlier message to the Bioconductor list you had a
specification that looked like

gene1 ~ gene2 + ...

which makes me a little queasy because you are assuming that gene2 is
"known" relative to the variability in gene1 and most of the time that
is not a reasonable approach.