[R-sig-ME] Specifying Multiple Random Effects in NLME

[Dan]

Hi all:

I am curating an off-list thread about specifying multiple random effects
in NLME.

1.  If it's (1|Object) + (1|Object:Coating) that you want then
you should be able to use a nested specification (which nlme *can*
handle relatively easily), i.e. something like

random=a+b+c~1|Object/Coating


Although (Coating|Object) and (1|Object:Coating) both in some sense
represent "interactions" the latter is *much* simpler/more parsimonious.

If you're OK with 1|Object:Coating rather than Coating|Object it
should be *much* faster.  If you don't understand the distinction (which
would be absolutely fine and understandable) can we resume the
discussion on r-sig-mixed-models ... ?
-----------

So:
random=a+b+c~Coating|Object
does not fit.

But:
random=a+b+c~Object/Coating
fits.

Can you better explain the distinction here? I have sometimes used the
1|Object:Coating + 1|Object syntax and sometimes the Coating|Object syntax
in other models. My experience/understanding is that the former syntax with
multiple "within subject" variables produces exactly matching output to the
standard "repeated measures ANOVA" with the lmer assumption of compound
symmetry.

Are there cases where one vs. the other formulation should absolutely be
used? My understanding that for continuous variables, e.g., multiple
measurements across multiple days, Days|Object would be the correct syntax.
But here we're talking about a factor variable.


2.   I'm trying to read the "random" section for nlme right now but it's
kind of making my head explode (and I think there's a typo: " the same
as the order of the order of the elements in the list").  It *sounds*
like (1) explicitly creating an interaction
ObjCoating=interaction(Object,Coating) and (2) using something like

  list(ObjCoating=a~1,Object=b~1,Object=c~1)

should work (grouping factors as names, then [right-hand-side variable
name]~[random effects model], but I'm worried about the phrase "The
order of nesting will be assumed the same as the order of the elements
in the list": what nesting?
-----------

I think that formulation is explicitly in order. I replaced your first
ObjCoating with simply Object, just to test what would happen:

Random effects:
 Formula: a ~ 1 | Object
        a.(Intercept)
StdDev:      1.305816

 Formula: b ~ 1 | Object %in% Object
        b.(Intercept)
StdDev:    0.01576521

 Formula: c ~ 1 | Object %in% Object %in% Object
        c.(Intercept) Residual
StdDev:      2.677883 2.219676

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