[R-sig-ME] Response variable with zero variance

[Ben Bolker]

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?
> >
> >