I'm analysing chick survival between 3 different years using a glm with quasibinomial error structure. Hence, my response variable is a cbind of fledged chicks and dead chicks, and one of my explanatory variables is Year (2013,2014,2015). After finding out that Year has a significant effect, I wanted to know how chick survival changed between the years according to my model.
So I ran a 'glht' with Tukey:
SurvivalYear<-glht(survival.model,linfct=mcp(Year="Tukey"))
and got this:
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
2014 - 2013 == 0 0.6131290 0.2421515 2.532 0.0304 *
2015 - 2013 == 0 0.6139173 0.2450897 2.505 0.0327 *
2015 - 2014 == 0 0.0007884 0.2324065 0.003 1.0000
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported -- single-step method)
After that I transformed the logg odds to proportions:
1/(1+1/exp(coef(summary(SurvivalYear))))
and I got this:
2014 - 2013 2015 - 2013 2015 - 2014
0.6486542 0.6488339 0.5001971
Does this mean that in 2013 64% more chicks survived? According to my raw data this can't be true. You can see the mean proportions of fledged/hatched chicks for 2013, 2014 and 2015 here:
> mean((SurvivalData$Fledglings/SurvivalData$Hatchlings)[SurvivalData$Year=="2013"])
[1] 0.6028452
> mean((SurvivalData$Fledglings/SurvivalData$Hatchlings)[SurvivalData$Year=="2014"])
[1] 0.6393909
> mean((SurvivalData$Fledglings/SurvivalData$Hatchlings)[SurvivalData$Year=="2015"])
[1] 0.7186566
What did I do wrong or what did I miss?
Thanks a lot in advance!
Best Answer
Putting my comment into an answer:
The estimates from
glht
are log odds ratios because they give you differences between logits. You can see this easily, if you write down the maths:$\ln{\frac{p_{2014}}{1-p_{2014}}} - \ln{\frac{p_{2013}}{1-p_{2013}}} = \ln{\frac{p_{2014}(1-p_{2013})}{p_{2013}(1-p_{2014})}}$
The estimate of 0.6131 means that the odds (i.e., $\frac{p}{1-p}$) of a chick surviving in 2014 were almost twice as high as in 2013: $\exp(0.6131) = 1.846146$
(Assuming I understand correctly, how you specified the dependent. Possible those are the odds that they died instead.)