observation level random effects; estimated variance of variance component estimates

I have a hacked version of lme4 that comments out the
error you are hitting (in the C code), and gets a plausible fit (at
least the fixed effects look pretty similar to Breslow and
Clayton 1993) -- see below.

  Don't know about your second question --

============================

fit

Generalized linear mixed model fit by the Laplace approximation
Formula: update(formula1, . ~ . + (1 | id) + (1 | rand))
   Data: dat
   AIC   BIC logLik deviance
 499.7 527.4 -241.9    483.7
Random effects:
 Groups Name        Variance Std.Dev.
 rand   (Intercept) 0.12747  0.35702
 id     (Intercept) 0.21097  0.45932
Number of obs: 236, groups: rand, 236; id, 59

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)
(Intercept)   -1.41194    1.16349  -1.214   0.2249
Base           0.88034    0.12910   6.819 9.17e-12 ***
Trt           -0.94857    0.39521  -2.400   0.0164 *
I(Trt * Base)  0.34922    0.20027   1.744   0.0812 .
Age            0.49015    0.34162   1.435   0.1514
V4TRUE        -0.10312    0.08583  -1.201   0.2296
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Correlation of Fixed Effects:
            (Intr) Base   Trt    I(T*B) Age
Base        -0.163
Trt          0.047  0.595
I(Trt*Base) -0.119 -0.653 -0.930
Age         -0.976 -0.038 -0.192  0.254
V4TRUE      -0.018 -0.003  0.002  0.000  0.001

sessionInfo()

R version 2.8.1 (2008-12-22)
i486-pc-linux-gnu

locale:
LC_CTYPE=en_US.UTF-8;LC_NUMERIC=C;LC_TIME=en_US.UTF-8;LC_COLLATE=en_US.UTF-8;LC_MONETARY=C;LC_MESSAGES=en_US.UTF-8;LC_PAPER=en_US.UTF-8;LC_NAME=C;LC_ADDRESS=C;LC_TELEPHONE=C;LC_MEASUREMENT=en_US.UTF-8;LC_IDENTIFICATION=C

attached base packages:
[1] splines   stats     graphics  grDevices utils     datasets  methods
[8] base

other attached packages:
[1] glmmAK_1.2         mvtnorm_0.9-4      coda_0.13-4
smoothSurv_0.3-12
[5] survival_2.34-1    lme4_0.999375-28   Matrix_0.999375-20
lattice_0.17-20

loaded via a namespace (and not attached):
[1] grid_2.8.1    rjags_1.0.3-4 tools_2.8.1

Dear lmers,

I have two questions regarding fitting GLMM using maximum likelihood method.
The first one arises from trying repeat an analysis in the Breslow and
Clayton 1993 JASA paper. Model 3 of the epileptic dataset has two random
effects, one subject specific, and one observation specific. Thus if we
count random effects, there are more parameters than observations. When I
try to run the following code, I get an error saying: "Error in
mer_finalize(ans) : q = 295 > n = 236".

require (lme4)
require (glmmAK)
data(epilepticBC)
dat = epilepticBC
dat$rand=1:nrow(dat)
dat$V4=dat$visit==4
formula1 = Seizure ~ Base + Trt + I(Trt*Base) + Age + V4
fit=lmer (update (formula1, .~. + (1|id) + (1|rand)), family=poisson,
data=dat, nAGQ=1)

Is it true that there is no way to fit such a model in an ML analysis? In
other words, is there a way to approximate the likelihood of fixed effects
and variance components without relying on estimates of random effects?

The second question is that when it is possible to obtain MLE of a GLMM
model, how can I obtain an estimated variance of the variance component
estimates using lmer or other functions?

Thank you very much for your help!

Youyi Fong

-------------------------------------------------------------------------------------
Youyi Fong, Graduate Student, Department of Biostatistics
University of Washington, Box 357232, Seattle, WA 98195

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