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

[David Duffy]

On Wed, 5 Mar 2008, Nick Isaac wrote:

> You can do SEM-type models using the smatr package. Only drawback is that
> you'd have to treat Rat as a fixed effect. This is a general class of
> problem that afflicts several of my current projects, and I'm having a tough
> time choosing between mixed effect and structural equation models. The
> former is most appropriate for partitioning the variance, but the latter is
> most appropriate for modelling error variance in the observations. I don't
> see an obvious solution with the available tools and would appreciate any
> general insights.
>
> Cheers, Nick
>

I don't know if smatr supports multiple groups (so you can have unbalanced 
type data).  We generally use the Mx SEM package, which allows both 
multiple groups as well as "irregular" data, and our main interest is always
in partitioning the variance.  Every mixed model (indeed 
every linear model) is expressible as a SEM (it just runs slower ;)).

Generally, if you want to include a random effect you set up a latent 
variable with appropriate path(s) to the observed value(s).  Your
relationships will be between the latent variables.  Often, you'll fix
the path coefficient to unity.  Have a look at Mx book/manual (Mike Neale and
Hermine Maes) and you'll get some ideas.

For the expression example, one model would be something like
                              +--------------------------+
                 Strain1-Rg1  |                          |
              --------------------------    Rat16        |
              |               |        |                 |
                    r1        |                 r1       |
Latent    Gene111 <-->  Gene112       Gene161 <-->  Gene162
          /b1   | \b3   b4/ | \       /b1    | \ 
Manif  Tissue1 T2 T3               Tissue1 T2 T3

With appropriate equality constraints (r1=r1..=r1, b1=b1..) or 
random regressions on the path coefficientsi and covariance matrix of latent
variables.  So this model states (and
can test) that tissue expressions are imperfect measures of
overall gene expression in the ith animal.

But after saying that, for this particular example, I would use a
program such as ASREML or Wombat or MENDEL that easily fit multivariate
mixed models.  Our group has used ASREML to fit mixture models to
deal with error in DNA pooling experiments for 50000 SNPs.

Hope that's clear (and even right), David Duffy.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v