Solved – Interpretation of quasibinomial glht (Tukey) results

generalized linear modelinterpretationr

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.)

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