[R-sig-ME] gls() vs. lmer() random effects estimation

[Maarten Jung]

Dear list,

Let x be a factor with k levels.
Why can m1 be estimated with only one data point per level of x for each
subject?
I know that the random slope variance is confounded with the residual
variance in m2 and thus m2 cannot be estimated in this case.
But how can m1 overcome this limitation whereas m3 (which I think is
equivalent to m4) is the maximal linear mixed model that can be estimated
with lmer? And is there a way to achieve the same with lmer?

m1 <- gls(y ~ x, correlation = corSymm(form = ~1|subject), data = d)
m2 <- lmer(y ~ x + (x|subject), data = d)
m3 <- lmer(y ~ x + (1|subject), data = d)
m4 <- gls(y ~ x, correlation = corCompSymm(form = ~1|subject), data = d)

Best,
Maarten

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