# [R-sig-ME] lmer problems

Douglas Bates bates at stat.wisc.edu
Sat Apr 12 14:37:58 CEST 2008

```On Sat, Apr 12, 2008 at 4:58 AM, Alexandre Courtiol
<alexandre.courtiol at gmail.com> wrote:
> Dear Douglas Bates,

> Sorry to disturb you but I posted a question on R forum in september but
> I am using lmer with quasibinomial family since I have overdispersion in my
> data. And I wish to assess significance of fixed effects. So I built two
> models and compare them using anova(). This lead to two problems, first
> anova() does not seem to take into account of the overdispersion since
> quasibinomial family results are strictly identical than results from
> anova() performed on two binomial (and not quasibinomial) models. Second if
> I ask for an F test in anova() as suggested for assessing significance in
> quasibinomial glm, anova() on the lmer objects give me a chisq test and not
> the F test I asked. So how should I do to assess significance of fixed
> effect using quasibinomial family in lmer???

I haven't worked out the details of what the log-likelihood for a
generalized linear mixed model using the quasi-binomial family should
be.  If someone else knows what it should be and can express it in
terms of the deviance residuals and the value of the quadratic form in
the random effects, I would be happy to incorporate it.

By the way, those values are found in the deviance slot.  The "disc"
element is the discrepancy, which is the sum of the deviance residuals
at the parameter estimates (without correction for the null deviance -
incorporating that is another item on the "ToDo" list).  The "usqr"
element is the quadratic form in the random effects, given the
relative variance-covariance matrix of the random effects at the
parameter estimates.  It is called "usqr" because it is calculated as
the squared length of the vector of orthogonal random effects, u.

The elements "wrss" (weighted residual sum of squares) and "pwrss"
(penalized weighted residual sum of squares) are used in the PIRLS
(penalized iteratively reweighted least squares) algorithm to
determine the condition modes of the random effects given parameter
values and the observed data.  The ldL2 element is the logarithm of
the square of the determinant of the Cholesky factor for the random
effects at the parameter estimates.  It is used in the Laplace
approximation to the integral that defines the log-likelihood.  The
"sigmaML" element should contain the estimate of sigma, calculated as
pwrss/n (I don't know if that is the appropriate value in this case).

I have taken the liberty of cc:ing the R-SIG-Mixed-Models mailing list
on this reply.  It is more likely to be noticed on that list.

```