[R-sig-ME] Residual Variance or Dispersion of Gamma GLMER

[Ben Bolker]

  Depending on what exactly you mean by for "dispersion" (there are lots
of different definitions depending on context): sigma() gives you
1/sqrt(shape) (i.e. the scaled standard deviation or coefficient of
variation: mean=shape*scale, variance=shape*scale^2, so sd/mean =
sqrt(shape)*scale/(shape*scale) = 1/sqrt(shape).

In the classic GLM sense phi=sigma^2=1/shape is the dispersion
parameter, because we define variance= V(mu)/phi,  V=mu^2
((shape*scale)^2/shape = shape*scale^2 - variance).

sigma() is the same value as the one reported in the Residual Std.Dev.
column.

 For what it's worth I wouldn't call the conditional (Gamma) model
"zero-altered" in this case, as the Gamma has a zero (or infinite)
probability density for x=0 anyway.


On 17-10-25 10:31 AM, andreu blanco wrote:
> Hi,
> I am trying to fit a Hurdle model using glmer, however in order to
> calculate the variance of the Hurdle model I need to know the dispersion of
> the gamma ZAG, which I cannot find from the summary of my model:
>> summary(H1)
> Generalized linear mixed model fit by maximum likelihood (Laplace
> Approximation) ['glmerMod']
>  Family: Gamma  ( log )
> Formula: Biomass ~ Protection * Exposure + (1 | Location)
>    Data: Aarmata.pos
> 
>      AIC      BIC   logLik deviance df.resid
>    644.9    657.5   -316.4    632.9       55
> 
> Scaled residuals:
>     Min      1Q  Median      3Q     Max
> -1.2278 -0.7188 -0.1149  0.3721  3.4934
> 
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  Location (Intercept) 0.5489   0.7409
>  Residual             0.6531   0.8082
> Number of obs: 61, groups:  Location, 8
> 
> Fixed effects:
>                                         Estimate Std. Error t value
> Pr(>|z|)
> (Intercept)                               4.1195     0.4866   8.466
>  <2e-16 ***
> ProtectionProtected                       0.2202     0.6940   0.317
>  0.7510
> ExposureSemiexposed                      -0.6357     0.3319  -1.915
>  0.0555 .
> ProtectionProtected:ExposureSemiexposed  -0.7128     0.5492  -1.298
>  0.1944
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> Correlation of Fixed Effects:
>             (Intr) PrtctP ExpsrS
> PrtctnPrtct -0.701
> ExpsrSmxpsd -0.212  0.143
> PrtctnPr:ES  0.131 -0.242 -0.562
>