[R-sig-ME] Residual Variance or Dispersion of Gamma GLMER
Ben Bolker
bbolker at gmail.com
Wed Oct 25 21:58:03 CEST 2017
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
>
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