[R-sig-ME] Presentation of results from GLMMs

[Renwick, A. R.]

Dear All

A while back there was a question regarding plotting predicted values (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q1/002044.html). There was not much response which I take to assume there is no definitive answer. However I wonder if anyone could give me a bit of advice as to how to present results for a GLMM model with a binomial error structure.

Here is an example:

y<-cbind(both$Totalmoreonce,both$UsedOnce)#an index of aggregation in a population of voles

hier3<-lmer(y~Sex+Margin+sess+(1|Farm/Site), family=binomial, data=both, REML=FALSE)

summary(hier3)
#Generalized linear mixed model fit by the Laplace approximation
#Formula: y ~ Sex + Margin + sess + (1 | Farm/Site)
#   Data: both
#   AIC   BIC logLik deviance
# 191.0 213.5 -86.49    173.0
#Random effects:
# Groups    Name        Variance Std.Dev.
# Site:Farm (Intercept) 0.039191 0.19797
# Farm      (Intercept) 0.000000 0.00000
#Number of obs: 90, groups: Site:Farm, 14; Farm, 7
#
#Fixed effects:
#             Estimate Std. Error z value Pr(>|z|)
#(Intercept)  -2.20209    0.33088  -6.655 2.83e-11 ***
#Sexmale      -0.31110    0.12781  -2.434 0.014928 *
#Marginmedium  0.07763    0.34604   0.224 0.822483
#Marginwide    1.23916    0.30748   4.030 5.58e-05 ***
#sessAugust    0.60537    0.18324   3.304 0.000954 ***
#sessJune      0.58132    0.18511   3.140 0.001687 **
#sessOctober  -0.64398    0.24468  -2.632 0.008491 **

Now I want to show graphically that y changes with margin width, ideally using predicted values while accounting for the other variables in the model.

invlogit<-function(x){1/(1+exp(-x))}#function to backtransform the logit values in model

#predicted values bsaed on only the fixed effects for each margin width
w<-invlogit(cbind(1,0,0,1,0,0,0)%*%fixef(hier3))#wide
m<-invlogit(cbind(1,0,0,0,0,0,0)%*%fixef(hier3))#medium
n<-invlogit(cbind(1,0,1,0,0,0,0)%*%fixef(hier3))#narrow

I become stuck when trying to predict the CI of these values.

I was wondering if anyone has any ideas either how to calculate the CI OR any better ways to present the data.

Many thanks,
Anna


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