Skip to content

Residual Variance or Dispersion of Gamma GLMER

3 messages · Ben Bolker, andreu blanco

Original
andreu blanco
# 
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:
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
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:
andreu blanco
# 
Thank you both very much.
On 25 October 2017 at 16:31, andreu blanco <andreu.blanco at gmail.com> wrote: