modelling saturated random effects with glmm

Thank you Greg and Ben for clearing that up. Sometimes I get so
caught up in the detail of mixed modelling that I forget some of the 
fundamentals. By the way, I can see how adding a random effect level 
per observation would account for some of the heterogeniety causing 
overdispersion, but wouldn't this be dependent on the potential 
underlying causes of the overdispersion? For example, if you have a 
high proportion of  zeros in the data, would this approach still be 
valid? Wouldn't it be better to address the causes of overdispersion 
directly by refining the fixed and random effects structure more or
by using a more appropriate distribution such as a negative binomial,
zip or zinerb?

Best Jos

2009/7/27 Greg Snow <Greg.Snow at imail.org>:

This is a basic property of the distributions.

The normal distribution has 2 parameters, the mean and the variance
which are independent of each other.  Therefore in any type of
model based on the normal distribution you need at least 1 degree
of freedom left over after estimating the mean in order to estimate
the variance.

The poisson distribution only has 1 parameter because the variance
is equal to the mean in the poisson, so you can use all the degrees
of freedom estimating the mean, and that gives you the variance,
you don't need additional information to estimate it.

All this of course is dependent on your assumptions about the
distributions being reasonable (the routines do what you tell them
too whether they make sense or not).  And any model that uses all
or even the majority of the degrees of freedom is unlikely to be
very precise or informative even if you do get an "answer".

Hope this helps,

-- Gregory (Greg) L. Snow Ph.D. Statistical Data Center 
Intermountain Healthcare greg.snow at imail.org 801.408.8111

-----Original Message----- From:
r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed- 
models-bounces at r-project.org] On Behalf Of jos matejus Sent:
Monday, July 27, 2009 8:19 AM To:
r-sig-mixed-models at r-project.org Subject: [R-sig-ME] modelling
saturated random effects with glmm

Dear all,

I was wondering whether anyone could enlighten me on the
following.

Why is it I can fit a generalized linear mixed model (family =
poisson for example) with lmer where I have as many levels of my
random effect as data points whereas with a linear mixed effects
model (gaussian distributed errors) I get an error message. I
understand that the random effect variance is completely
confounded with the residual variance in the case of a linear
mixed model, but why is this not so with a generalized linear
mixed model?

for example

data(ergoStool, package="nlme") # load data ergoStool$rantest <-
1:36 #create a pseudo random effect to illustrate

library(lme4)

stool.lmm <- lmer(effort~Type+(1|rantest),  data=ergoStool) 
#Error: length(levels(dm$flist[[1]])) < length(Y) is not TRUE

stool.glmm <- lmer(effort~Type+(1|rantest) , family=poisson, 
data=ergoStool)

summary(stool.glmm)

Generalized linear mixed model fit by the Laplace approximation 
#Formula: effort ~ Type + (1 | rantest) Data: ergoStool AIC   BIC
logLik deviance 19.47 27.39 -4.737    9.474 Random effects: 
Groups  Name        Variance Std.Dev. rantest (Intercept)  0
0 Number of obs: 36, groups: rantest, 36

Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept)
2.14658    0.11396  18.836   <2e-16 *** TypeT2       0.37469
0.14804   2.531   0.0114 * TypeT3       0.23091    0.15263
1.513   0.1303 TypeT4       0.07503    0.15823   0.474   0.6354 
--- Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' '
1

Correlation of Fixed Effects: (Intr) TypeT2 TypeT3 TypeT2 -0.770 
TypeT3 -0.747  0.575 TypeT4 -0.720  0.554  0.538

Many thanks in advance Jos