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Dear list,

I'm running a lmer (package lme4) with a binomial error distribution and
"bird" as the random effect (160 observations of 25 birds). The response
variable "ars1" is coded as 0, 1.
The fixed effect "sit" is numerical and "dive" is categorical (0, 1).

What puzzles me a little is that the a variance and sd of the random effect
is ZERO. Same question has been posted before and Douglas Bates answer was:

"No, an estimate of zero is not suspicious.  It is simply an indication

that the variability between individuals is not significantly larger
than what one would expect from the random variability in the
response."


While another answer suggested that the model was "wrong":


"A zero estimate of a variance possibly indicates the model is wrong."  This
wrong model seemed to be related to a negative covariation of one of the
fixed effects ?



 My simplified model is:

mod6 <- lmer(ars1 ~ sit + dive + (1|bird), data=dat, family=binomial)

> summary(mod6)
Generalized linear mixed model fit by the Laplace approximation
Formula: ars1 ~ sit + dive + (1 | bird)
   Data: dat
   AIC   BIC logLik deviance
 159.4 171.7 -75.71    151.4
Random effects:
 Groups Name        Variance Std.Dev.
 bird   (Intercept)  0        0
Number of obs: 160, groups: bird, 25

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.3615     0.4037  -0.895  0.37059
sit           0.7492     0.1448   5.175 2.28e-07 ***
dive          1.3076     0.4374   2.990  0.00279 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
     (Intr) sit
sit   0.422
dive -0.756  0.005
>


Based on the summary output (zero variance and sd) I'm inclined to believe
that in fact my random effect bird does not account for any of the variance
in the model. I.e., that there is no significant variability between birds
that I should account for. Further, if I plot

*dotplot(ranef(mod6, postVar=TRUE))*

to represent the 95% prediction intervals for each of the birds, these are
all plotted on zero.

The same for:


*qqnorm(unlist(ranef(mod6)), main="normal qq-plot, random effects")
qqline(unlist(ranef(mod6))) # qq of random effects*

All dots are on zero!


*QUESTION: Could I be overlooking something or is it justified to run a glm
without the random effect bird instead of a lmer?*

Thank you!

Best regards, Julia


dotplot(ranef(mod6, postVar=TRUE))








-- 
Julia Sommerfeld - PhD Candidate
Institute for Marine and Antarctic Studies
University of Tasmania
Private Bag 129, Hobart
TAS 7001

Phone: +61 477 289 301
Email: julia.somma@gmx.de
Julia.Sommerfeld@utas.edu.au

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