[R-sig-ME] Details on specifying random parameters in 3-level HLM with lme

[Ben Bolker]

Richard Asturia <richard.asturia at ...> writes:

> 
> Dears,
> 
> I am used to fit 3-level HLM with Stata or HLM software, but now I have to
> do it with lme, from package nlme. Unfortunatelly, though, I am struggling
> with basic things and I could use any tips or suggestions.
> 
> What I am trying to do is to estimate a 3-level linear model where some of
> random effects are in the 2nd level, some are in the 3rd. The specification
> equations and the R code I was thinking of are as follows:
> 
> *Y* = b0 + b1**X1* + b2**X2* + e
> 
>       b0 = a00 + a01**X3* + r0
>       b1 = a10 + a11**X4* + r1
>       b2 = a20 + r2
> 
>               a00 = c00
>               a01 = c10 + u1
>               a10 = c20 + u2
>               a11 = c30
>               a20 = c40
> 
> *Y* = a00 + a01**X3* + r0 + a10**X1* + a11**X4***X1* + r1**X1* + a20**X2* +
> r2**X2* + e
> 
> *Y* = c00 +c10**X3* + u1**X3* + r0 + c20**X1* + u2**X1* + c30**X4***X1* + r1
> **X1* + c40**X2* + r2**X2* + e
> 
> *Y* = c00 + c20**X1* + c40**X2* + c10**X3* + c30**X4***X1* + r0 + r1**X1* +
> r2**X2* + u2**X1* + u1**X3* + e
> 
> So far, I could only wonder this code:
> lme(Y ~ X1 + X2 + X3 + X1:X4, random= ~ X1 + X2 + X3 | level3 / level2,
> data=mydataset)
> 
> But I feel this is somewhat wrong, as it estimates the random parameters of
> X1, X2 and X3 both in level 2 and in level 3, while the correct would be to
> put the random compenents of X1 and x2 in level 2 and of X1 and X3 in level
> 3. Which is something I don't know how to separate in the "random"
> parameter of the lme function and I couldn't find out anywhere so far.

  I haven't actually tried this out (I would be more likely to
test it before answering if you gave a reproducible example),
but have you noticed that under the
description of the 'random' argument, ?lme says

(ii) a list of one-sided formulas of the
form ‘~x1+...+xn | g’, with possibly different random effects
models for each grouping level. The order of nesting will be
assumed the same as the order of the elements in the list;

  So I would think that something like

  random = list( ~ X1 + X2 | level2, ~ X1 + X3 | level3:level2 )

might work?
  
  Ben Bolker