[R-sig-ME] Overdispersion lme4 binomial

[Jarrod Hadfield]

Dear Chris,

Over-dispersion does not occur with a binary response variable so you  
don't need to test for it.

This does not mean that between-datum heterogeneity in the probability  
of success is absent, only that it cannot be observed. For example,  
take 1000 random draws from a binomial distribution with constant  
probability (0.5):

table(rbinom(1000, 1, 0.5))

and compare the frequency of outcomes with a 1000 draws from 1000  
binomial distributions with different probabilities of success (but  
with mean = 0.5)

table(rbinom(1000, 1, runif(1000)))

The data look the same, and so the between-datum heterogeneity  
(residual variance if you like) although it may exist cannot be  
estimated from the data.

Cheers,

Jarrod


Quoting Chris Mcowen <cm744 at st-andrews.ac.uk>:

> Dear List,
>
> I am wanting to test for overdispersion in my model and am unsure   
> how for my specific case.
>
> I have 2 random factors, 7 fixed factors that have multiple levels   
> and are categorical and then i have a binary response (True or False).
>
> model1 <- lmer(threattf~1+(1|order/family) + geophyte + seasonality   
> + pollendispersal + breedingsystem*fruit + habit + lifeform +   
> woodyness, family=binomial)
>
> I would be very grateful if somebody could point me in the right   
> direction for testing for overdispersion under such scenarios?
>
> Please see part of the output below -
>
> Thanks for any help, and if more data is required feel free to ask.
>
> Chris
>
> Generalized linear mixed model fit by the Laplace approximation
> Formula: threattf ~ 1 + (1 | order/family) + geophyte + seasonality   
> +      pollendispersal + breedingsystem * fruit + habit + lifeform +  
>       woodyness
>   AIC  BIC logLik deviance
>  1562 1649 -764.2     1528
> Random effects:
>  Groups       Name        Variance Std.Dev.
>  family:order (Intercept) 0.26932  0.51896
>  order        (Intercept) 0.00000  0.00000
> Number of obs: 1242, groups: family:order, 43; order, 9
>
> Fixed effects:
>                        Estimate Std. Error z value Pr(>|z|)
> (Intercept)            -0.10413    0.98004  -0.106  0.91538
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>
>



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