Howdy,
I have a question sort of related to Ben's "differing variances within
different random effects levels".
I have a data set consisting of 23 mice, 11 Treated and 12 controls. The
mice are bred to have
a neurodengerative disease, and their neuromuscular connections degrade over
time. So the animals were sacrificed and
a left and right leg muscle were removed and sectioned, fixed on slides and
stained appropriately. There were 12 slides
per a muscle, and 6 sections per slide. Two slides per side were chosen, and
in all sections on the slide the total number of neuro-muscular
junctions, and the number innervated was counted. Oh and within each muscle,
there were 5 compartments, so counts are by muscle compartment.
So I have a binomial response, and for fixed effects I have Sex +
Treatment*Musclecompartment
and random (1|Animal/Side/Slide/Section) So the model is

gm1 <- glmer(cbind(Innervated.count,Total.count-Innervated.count) ~ Sex +
Treatment*Muscle.Compartment+(1|animal.ID/Side/Slide/Section), data=dat,
family = binomial)

So my questions are about interpretation of the variance components in a
binomial model.
1) the variance component for slide is 0, is that because there are only 2
slides
     or is something else going on, there is an estimated variance for side,
and when I last
     counted there were only 2 of those as well :)
2) do the variances/covariances have a similar interpretation to the
Gaussian case
     for which in an lmm everything is easier to understand? Meaning that
the error term is
    binomal, glm part, but the random effects are gaussian, so i am looking
at the variances
    from a mixture model, or is that just the integrated variance over all
levels.

Thanks

Nicholas
Genentech


Generalized linear mixed model fit by the Laplace approximation
Formula: cbind(Total.count, Innervated.count) ~ Sex + Treatment *
Muscle.Compartment +      (1 | animal.ID/Side/Slide/Section)
   Data: dat[-i, ]
  AIC  BIC logLik deviance
 3598 3684  -1784     3568
Random effects:
 Groups                           Name        Variance  Std.Dev.
 Section:(Slide:(Side:animal.ID)) (Intercept) 0.1537492 0.392109
 Slide:(Side:animal.ID)           (Intercept) 0.0000000 0.000000
 Side:animal.ID                   (Intercept) 0.0020578 0.045363
 animal.ID                        (Intercept) 0.0295573 0.171922
Number of obs: 2294, groups: Section:(Slide:(Side:animal.ID)), 542;
Slide:(Side:animal.ID), 92; Side:animal.ID, 46; animal.ID, 23

Fixed effects:
                                        Estimate Std. Error z value Pr(>|z|)
(Intercept)                              0.24425    0.08512   2.869  0.00411
SexM                                    -0.04511    0.08310  -0.543  0.58721
TreatmentVehicle                         0.02514    0.09304   0.270  0.78705
Muscle.CompartmentmLGC                   0.78672    0.03759  20.932  < 2e-16
Muscle.CompartmentMGC                    0.58850    0.03560  16.532  < 2e-16
Muscle.CompartmentlLGC                   0.79096    0.03686  21.458  < 2e-16
Muscle.CompartmentiLGC                   0.55246    0.04057  13.618  < 2e-16
TreatmentVehicle:Muscle.CompartmentmLGC  0.04322    0.05248   0.824  0.41016
TreatmentVehicle:Muscle.CompartmentMGC   0.04726    0.04982   0.949  0.34286
TreatmentVehicle:Muscle.CompartmentlLGC  0.07916    0.05168   1.532  0.12559
TreatmentVehicle:Muscle.CompartmentiLGC -0.02411    0.05667  -0.425  0.67057

(Intercept)                             **
SexM
TreatmentVehicle
Muscle.CompartmentmLGC                  ***
Muscle.CompartmentMGC                   ***
Muscle.CompartmentlLGC                  ***
Muscle.CompartmentiLGC                  ***
TreatmentVehicle:Muscle.CompartmentmLGC
TreatmentVehicle:Muscle.CompartmentMGC
TreatmentVehicle:Muscle.CompartmentlLGC
TreatmentVehicle:Muscle.CompartmentiLGC
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
                             (Intr) SexM   TrtmnV Mscl.CmprtmntmLGC M.CMGC
SexM                         -0.624
TretmntVhcl                  -0.634  0.121
Mscl.CmprtmntmLGC            -0.332  0.004  0.302
Mscl.CmpMGC                  -0.342  0.004  0.311  0.781
Mscl.CmprtmntlLGC            -0.326  0.003  0.297  0.743             0.767
Muscl.CmprtmntLGC            -0.316  0.006  0.287  0.716             0.734
TrtmntVhcl:Mscl.CmprtmntmLGC  0.237 -0.002 -0.420 -0.716            -0.560
TrtV:M.CMGC                   0.244 -0.003 -0.432 -0.558            -0.715
TrtmntVhcl:Mscl.CmprtmntlLGC  0.233 -0.003 -0.413 -0.530            -0.547
TretmntVhcl:Mscl.CmprtmntLGC  0.226 -0.003 -0.397 -0.513            -0.525
                             Mscl.CmprtmntlLGC Muscl.CmprtmntLGC
SexM
TretmntVhcl
Mscl.CmprtmntmLGC
Mscl.CmpMGC
Mscl.CmprtmntlLGC
Muscl.CmprtmntLGC             0.699
TrtmntVhcl:Mscl.CmprtmntmLGC -0.533            -0.513
TrtV:M.CMGC                  -0.548            -0.524
TrtmntVhcl:Mscl.CmprtmntlLGC -0.713            -0.499
TretmntVhcl:Mscl.CmprtmntLGC -0.500            -0.716
                             TrtmntVhcl:Mscl.CmprtmntmLGC TV:M.CM
SexM
TretmntVhcl
Mscl.CmprtmntmLGC
Mscl.CmpMGC
Mscl.CmprtmntlLGC
Muscl.CmprtmntLGC
TrtmntVhcl:Mscl.CmprtmntmLGC
TrtV:M.CMGC                   0.776
TrtmntVhcl:Mscl.CmprtmntlLGC  0.740                        0.762
TretmntVhcl:Mscl.CmprtmntLGC  0.711                        0.728
                             TrtmntVhcl:Mscl.CmprtmntlLGC
SexM
TretmntVhcl
Mscl.CmprtmntmLGC
Mscl.CmpMGC
Mscl.CmprtmntlLGC
Muscl.CmprtmntLGC
TrtmntVhcl:Mscl.CmprtmntmLGC
TrtV:M.CMGC
TrtmntVhcl:Mscl.CmprtmntlLGC
TretmntVhcl:Mscl.CmprtmntLGC  0.694


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