# [R-sig-ME] Problem with binomial-normal model in lmer

Douglas Bates bates at stat.wisc.edu
Sun Feb 24 20:04:41 CET 2008

On 22 Feb 2008 01:04:08 -0600,  <nasi0009 at umn.edu> wrote:
> I have a question about the possibility of fitting a binomial-normal model
>  with lmer. I explain my problem using notation used in "Linear mixed model
>  implementation in lme4" by Prof. Bates
>  (http://stat.ethz.ch/CRAN/doc/vignettes/lme4/Implementation.pdf).
>
>  By binomial-normal, I mean a model that another term is added to Equation
>  (29) (on page 28) of the paper, i.e. \eta=X\beta+Zb+\epsilon where \epsilon
>  is N(0,\sigma_e). I thought that by modifying Z, \epsilon can be absorbed
>  into Z. However, when I tried to test this on a simple simulated data set I
>  received an error "Error in mer_finalize(ans, verbose) : q = > n = ".

Did it really give that error message?  The way I had intended the
message to display is including the values of q and n.  Looking at the
code I think it should give the values.

>  Basically, it seems that the basic assumption in lmer for GLMM models is
>  that Z should be a thin matrix (more rows than columns). Naturally, this
>  data-level normal error term can not be absorbed as another random effect
>  since the total number of random effects exceeds the number of
>  observations. Is there any other way around this problem? Am I doing
>  something nonsense?

The reason for checking if the dimension of the random effects vector
exceed the number of observations is because the conditional modes of
the random effects are determined via iteratively reweighted least
squares.  It happens that the least squares problem is a penalized
least squares problem and a solution may exist even when q > n.  You
may want to try suppressing the check (near the beginning of the C
function called "update_u" in the file lme4/src/lmer.c) and seeing if
things still work for your example.

If you aren't comfortable modifying the source code and rebuilding the
package then please supply an example.

>  I appreciate if Prof. Bates or anyone who used lmer for GLMM comments on
>  this.
>
>  Thanks,
>  Ali
>
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