# [R-sig-ME] confusion about lmer output

John Maindonald john.maindonald at anu.edu.au
Sun Mar 13 11:58:37 CET 2011

```glm with a non-quasi error quotes, for binomial and poisson errors,
a dispersion parameter equal to 1.  This is a theoretical value.

To get an estimated value, specify a quasi error.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On 13/03/2011, at 2:21 PM, Paul Johnson wrote:

> On Tue, Mar 8, 2011 at 3:06 PM, Sacha Viquerat <tweedie-d at web.de> wrote:
>> hello dear mixed effects modeller! i'm a little confused about the output of
>> lmer in R. in michael j. crawleys excellent book on R and in various
>> examples in the internet, lmer outputs of poisson family models include a
>> dispersion factor (as I gather, the scale of the model). well, mine does not
>> show this factor:
>
> I've got R-2.12.2 and lme4 version and I don't see a scale estimate
> printed (see below).  But I don't exactly understand why you want one.
>
> You don't mention which Kennedy book you are looking at, but I don't
> know of one that would be current with lme4 development.  You might
> instead be reading his use of glm.  glm does give the estimated
> dispersion parameter, but it is not useful. The dispersion parameter
> is fixed at 1 (recall, it is NOT estimated in that procedure, it is
> fixed, assumed, because Poisson mean= Poisson variance.  I think to
> diagnose overdispersion, there is no certain diagnostic cue, escape
> the general idea that the model's deviance estimate should be
> somewhere in the vicinity of the degrees of freedom.
>
> If you are wanting to fit Poisson with overdispersion, there are
> easier and more conventional methods than lmer.  Most people I work
> with would expect you'd take the multiplicative log-Gamma error
> approach, which ends up with Negative Binomial model.  There are now
> many R packages that will help with that, such as "pscl" or "ZIGP" or
> "VGAM" or "MASS".
>
> pj
>
>> summary(m1)
> Generalized linear mixed model fit by the Laplace approximation
> Formula: y ~ inp + (1 | gf)
>  AIC  BIC logLik deviance
> 1066 1080 -529.8     1060
> Random effects:
> Groups Name        Variance  Std.Dev.
> gf     (Intercept) 0.0053324 0.073023
> Number of obs: 1000, groups: gf, 2
>
> Fixed effects:
>             Estimate Std. Error z value Pr(>|z|)
> (Intercept) 3.2962418  0.0556996   59.18   <2e-16 ***
> inp         0.0159236  0.0003963   40.18   <2e-16 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
>    (Intr)
> inp -0.368
>
> ====================
>
> On the other hand,
>
>
> --
> Paul E. Johnson
> Professor, Political Science
> 1541 Lilac Lane, Room 504
> University of Kansas
>
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