Response variable with zero variance

Tonya Haff <tonyahaff at ...> writes:

I used the lmer package, using the following code

FL.glmm <- lmer(RESPONSE ~ fEXPN + fPBN + fEXPN*fPBN + (1|fNID), data =
FL.1, family = binomial)

  By the way, the fixed effect part of the formula can also
be written as fEXPN*fPBN alone (since A*B is equivalent to A+B+A:B;
unlike in some other stats packages, * means "crossed" rather
than "interaction")

   It may be worth double-checking this with glmmPQL:

  library(MASS)
  glmmPQL(RESPONSE~fEXPN*fPBN,random=~1|fNID,data=FL.1,
    family="binomial")

although if the data are Bernoulli (0/1) then PQL is a little
bit questionable.

Here is the summary

Generalized linear mixed model fit by the Laplace approximation
Formula: RESPONSE ~ fEXPN + fPBN + fEXPN * fPBN + (1 | fNID)
   Data: FL.1
   AIC   BIC logLik deviance
 104.1 163.0 -35.04    70.09
Random effects:
 Groups Name        Variance Std.Dev.
 fNID   (Intercept) 0.047168 0.21718
Number of obs: 236, groups: fNID, 15

Fixed effects:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)     -0.4102     0.5304  -0.774    0.439
fEXPN2           1.4329     0.7880   1.818    0.069 .
fEXPN3          21.9715 12840.4523   0.002    0.999
fEXPN4          21.9715 12409.4403   0.002    0.999
fPBN2           21.9715 12409.4408   0.002    0.999
fPBN3            0.5453     0.7390   0.738    0.461
fPBN4           -1.4788     0.9286  -1.593    0.111
fEXPN2:fPBN2    -1.4171 17619.4645  -1e-04    1.000
fEXPN3:fPBN2   -21.9715 21994.2881  -0.001    0.999
fEXPN4:fPBN2   -21.9715 21493.7828  -0.001    0.999
fEXPN2:fPBN3    20.0155 12547.8259   0.002    0.999
fEXPN3:fPBN3    -0.5390 18188.0409   0.000    1.000
fEXPN4:fPBN3    -0.5390 17577.5297   0.000    1.000
fEXPN2:fPBN4   -21.1113 12447.6988  -0.002    0.999
fEXPN3:fPBN4   -41.6658 18265.7721  -0.002    0.998
fEXPN4:fPBN4   -41.6660 17647.6445  -0.002    0.998

  This looks like a Hauck-Donner effect to me (you can look it
up -- it occurs in GLM(M)s when there are strong binomial
effects).  I'm a little worried about the exact equivalence
of some of the parameter estimates though, and apparent
overfitting ... if these are Bernoulli data, how many
positive responses are there overall?  Have you tried
nAGQ=8 ?

So here I had no F statistic at all, and the results of the fixed effects
don't make sense, when compared against the actual data (where the pattern
between PBN (playback type) and EXPN (experiment) are quite stark.

Because this didn't make sense to me, and because I am not a whiz at R, I
ran the same model in SPSS 20.0, and that is where I got the huge F
statistic. Here is that model summary:

 F = 1, 229, 656.019, df1 = 15, df2=220, P<0.0001
EXPN F = 83.83, df1=3, df2=220, P<0.0001
PBN F=2,2280.08, df1=3, df2=220, P<0.0001
EXPNxPNB F=82.96, df1=9, df2=220, P<0.0001

  But: what did you do in SPSS, which doesn't fit GLMMs (as
far as I know)?

Ideally, I would like to run a GLMM on my data, which are are binomial (so
I'm trying to run a model with a binomial distribution and a logit link).
 I have two fixed effects, fledgling age and playback type.  I have
fledging ID as a random effect.  The problem I'm running into is zero
variance in my response variable - ie fledglings always respond the same
way to some of the playback types.  I can run a model and it converges, but
it spits out an F value of over a million. So I'm wondering (1) is it
possible to use a GLMM with a zero variance response; and (2) if so, which
R package is the most appropriate?