R help - Oct 2004 - manual recreation of varConstPower using new fixed effects variables in nlme

Hello, I am trying to design new variance structures
by using fixed effects variables in combination with
the VarPower function.  That is, I would like to
create and evaluate my own variance function in the
data frame and then incorporate it into the model
using varPower, with value=.5.  

As a start, I am trying to recreate the function of
VarConstPower by introducing two new variables in the
data frame, d1 and d2. I am using a self-made
function, fx, which contains a logistic equation.  It
all works just fine in combination with the built-in
varConstPower variance structure.  

I try to mimic the varConstPower structure by using
the varPower variance function:
  varPower(form= ~vartemp, fixed= .5)

and then passing the variables d1 and d2 to fx and
adding a statement in fx like:
  vartemp <- (d1+theta^d2)^2
where theta is my covariate.  
  
However, even though the built-in varConstPower
function does work with my data set, the substitute
function discussed above does not work, even with d1
and d2 set to the correct values.   After about five
passes through the fx function I get the error
message:

Error in MEEM(object, conLin, control$niterEM) :
Singularity in backsolve at level 0, block 1

All, fixed effect variables look correct at the time
the error occurs.  Can anyone tell me if there is some
reason why this kind of approach would not work?  It
seems like it should be straightforward, but I am
having no luck.

I actually pass the d1 and d2 variables to the
function as d1.1, d1.2, d1.3, and d2.1, d2.2, d2.3 to
take into account the three grouping levels I have. 
The three d1's are then condensed into a single d1
column with respect to group.  Same with the d2's. 

Thanks.  John

PS:  Can anyone tell me what the reStruct parameter
means?  In looking at the verbose output, I obtain a
reStruct parameter value of -0.8352462 (this is for my
grouping factor for the random effect).  Does anyone
know what it means?  The actual value of my single
random effect is different, as is its variance.

> PS:  Can anyone tell me what the reStruct parameter
> means?  In looking at the verbose output, I obtain a
> reStruct parameter value of -0.8352462 (this is for my
> grouping factor for the random effect).  Does anyone
> know what it means?  The actual value of my single
> random effect is different, as is its variance.
IIRC it is the logarithm of the relative precision of the random effects.

Thanks much, Dr. Bates.  That helps.  Would you have
any comment on the other part of my other question
regarding the manual recreation of varConstPower
function using new fixed effects?  Im guessing I
obtain a singularity error because the additional
fixed effects may not alter the return value of my
function, fx.  The goal of attempting new variance
equations is to obtain in the end a variance function
that is of the form:

(d1 + (covariant)^d2)^2 + U,

where U is a random effect.

Thanks again.  John




--- Douglas Bates <bates at stat.wisc.edu> wrote:
> > PS:  Can anyone tell me what the reStruct
> parameter
> > means?  In looking at the verbose output, I obtain
> a
> > reStruct parameter value of -0.8352462 (this is
> for my
> > grouping factor for the random effect).  Does
> anyone
> > know what it means?  The actual value of my single
> > random effect is different, as is its variance.
> 
> IIRC it is the logarithm of the relative precision
> of the random effects.
> 
> 
>

Ah, I think Ive found a solution.  A variance 
function of the form:

(d1 + (covariant)^d2)^2 + U,

can be made by altering the line in varWeights.varComb
to read:

apply(as.data.frame(lapply(object, varWeights)), 1,
sum)

Then the function varComb can be used as in:

varComb(varPower(form = ~cov1|g1,value=list(...)),
varConstPower(form = ~g2|g2, fixedlist(power=(c(...)))))

That seems to work just fine.  John