Package for GLMM with correlation matrix

Hi Ben,

I want to test the association between non-normal response y and
fixed effect predictor x with a correction for relatedness between
indivdiuals (through incorporation of an individual-level random
effect). The correlation matrix is already known or can be
directly estimated from other means. Thers is no grouping of
individuals here. There is a R package called EMMA that can fit
such correlated random effect model for normally distributed
response. However, EMMA can't handle non-normal response data.

Thanks for your help.

Alex

2010/10/22 Ben Bolker <bbolker at gmail.com>:

Reading the description of your problem more carefully: you want
a correlation structure but no random effect (or equivalently an
individual-level random effect, with no grouping)?  You may have
a hard time doing this: * gls (nlme package) fits generalized
least-squares problem (no ['G-side'] random effect, but
['R-side'] correlation models) -- but 'generalized' here means
'non-trivial correlations', not 'non-normal responses in the
exponential family' * glmer (lme4 package) allows
individual-level random effects in GLMMs, but not R-side
structures (the package author isn't sure how they would be
formulated sensibly in a GLMM context) * You could create an
individual-level random effect and use it in glmmPQL, but I would
proceed with great caution, e.g.:

library(MASS) bacteria$ind <- 1:nrow(bacteria) g1 <- glmmPQL(y ~
trt + week + offset(week), random = ~ 1 | ind, family=binomial,
data=bacteria)

Are you saying you have a fixed, known correlation matrix?  That
seems surprising, but if you want to do so you will probably have
quite a bit of work in front of you -- read the appropriate
chapter of Pinheiro and Bates 2000, then probably also read some
of their papers on defining correlation structures.

I'm sorry this isn't easier, but it's not a common task.

On 10-10-22 11:26 AM, wong wrote:

Thanks ben.

The argument correlation in glmmPQL is an optional corStruct
object describing the within-group correlation structure.
However, in my dataset, there is no grouping among individuals.
Also, each individual has only one observation for response y.
I don't know how to create a corStruct object from an existing
n*n correlation matrix (n = the number of indivdiuals = length
of y). What can I do now? The documentation for corClasses is
not quite explicit.

Alex

2010/10/22 Ben Bolker <bbolker at gmail.com>: See the
documentation for lme (nlme package), specifically ?lme and
?corClasses . Beyond that, see Pinheiro and Bates 2000
(Springer).

On 10-10-22 05:35 AM, wong wrote:

Hi,

I'm looking for a R package for fitting a generalized
linear mixed model g(E[y])=X?+Zu where g is a link
function, ? is a p vector of fixed effects, u is a vector
of random effects, X is design matrix, Z is an identity
matrix. In our data, each individual has only one
observation for response y. Because individuals may be
correlated in some way, leading to similar reponses,
random effect u is employed to correct for individual
background effect. The variance of u is assumed to be
Var[u]=G*?^2, in which G is a correlation matrix.

glmmPQL in MASS has an argument for correlation. However,
I encountered an error of invalid formula when using a
n*n dimension matrix G (n is the number of individuals,
and also the length of y) for argument 'correlation' in
glmmPQL. For example:

iteration 1 Error in formula.default(object) : invalid
formula

The R help documentation for glmmPQL is very compact. No
detailed explanation. Does anybody know how to use
correlation matrix in glmmPQL? Is it good to use glmmPQL
for fitting my model?

Thanks.

Alex