[R-sig-ME] Mixed model (with interaction) for gene expression and iteration
Rolf Turner
r.turner at auckland.ac.nz
Wed Jun 3 00:54:19 CEST 2009
On 3/06/2009, at 12:53 AM, Paolo Innocenti wrote:
<snip>
> Reading a bit of this mailing list, I came up with these three models:
>
> m1 <- lmer(Y1 ~ sex + (1|line) + (1|sex:line))
>
> or
>
> m2 <- lmer(Y1 ~ sex + (sex|line))
>
> or
>
> m3 <- lmer(Y1 ~ sex + (0 + sex|line))
>
> Which should all be the same model (and indeed they have all the same
> residuals) but different parametrization (see self-contained example
> below).
<snip>
I don't think that the first two models are indeed the same model.
My understanding --- which is very limited --- is that
lmer(Y1 ~ sex + (1|line) + (1|sex:line))
gives a model in which the effect of line j on sex 1 (say X_1j) and
and the effect of line j on sex 2 (say X_2j) are uncorrelated. I.e.
X_1j and X_2j have covariance matrix of the form sigma^2 * I, where I
is the 2 x 2 identity. Thus one random effect parameter is
contributed.
In contrast,
lmer(Y1 ~ sex + (sex|line))
gives a model in which correlation between X_1j and X_2j, i.e. their
covariance matrix is a ``general'' 2 x 2 positive definite matrix.
Thus three random effect parameters are contributed.
See
http://www.nabble.com/lme-nesting-interaction-advice-
td17131600i20.html#a17213604
for the posting from Doug Bates upon which I am basing my
understanding.
Compare:
lmer(score ~ Machine + (1|Worker/Machine), Machines)
and
lmer(score ~ Machine + (Machine|Worker), Machines)
with your proposed models.
I hope that I have not misinterpreted Prof. Bates' explanation.
cheers,
Rolf Turner
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