Mixed model (with interaction) for gene expression and iteration

<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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