[R-sig-ME] Interpreting Estimates from GLMM following a beta-distribution (glmmTMB)

[Jan Velimsky]

Dear R project mixed models users,

I am struggling to interpret the estimates from a GLMM following a 
beta-distribution with a logit link. There is not much literature 
regarding the interpretation of this special case.

We have been estimating a GLMM model following a beta-distribution (with 
a logit link) with the glmmTMB-package. The model consists of factors 
influencing referendum turnout in German municipalities. The primary 
units of investigation are city districts nested in referendums nested 
in cities. The dependent variable (0-100) has been transformed to the 
unit interval 0-1.

Here an example model:

  glmmTMB (ref_turnout ~ unemployment + contestation+ (1| 
city/referendum), family=list(family="beta", link ='logit'), data = ml)


Results example model:

Estimate      Std. Error    zvalue     Pr(>|z|)

(Intercept) -0.583             0.131      -4.455     8.4e-06***

unemployment rate (in%) -0.067              0.002      -30.397    < 
2e-16 ***

contestation 0.008              0.003        2.398     0.0165 *

All explanatory variables are grand mean centered.

Taking into account the link function and the parameterization of beta 
regression, my interpretation for the effect of unemployment would be:  
One percent increase from the average unemployment-rate in districts of 
German municipalities (grand-mean) is associated with a  0.067 unit 
decrease from the overall mean of the participation rate in referendums 
(log odds)

1) Is this interpretation correct?

2) Are there more intuitive options for interpretation (e.g. with odd 
ratios or marginal effects )

Thanks a lot for your help!

Jan

-- 
Jan Velimsky, M.A.
Wissenschaftlicher Mitarbeiter
Lehrstuhl für Politische Systeme und Europäische Integration
Geschwister-Scholl-Institut für Politikwissenschaft
Ludwig-Maximilians-Universität München

D-80538 München
Oettingenstrasse 67
Tel. 0176 73292389