i'm analysing chick survival between 3 different years using glm quasibinomial error structure. hence, response variable cbind of fledged chicks , dead chicks, , 1 of explanatory variables year (2013,2014,2015). after finding out year has significant effect, wanted know how chick survival changed between years according model.
so ran 'glht' 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 transformed logg odds proportions:
1/(1+1/exp(coef(summary(survivalyear)))) and got this:
2014 - 2013 2015 - 2013 2015 - 2014 0.6486542 0.6488339 0.5001971 does mean in 2013 64% more chicks survived? according raw data can't true. can see mean proportions of fledged/hatched chicks 2013, 2014 , 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 wrong or did miss?
thanks lot in advance!
putting comment answer:
the estimates glht log odds ratios because give differences between logits. can see easily, if write down 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 odds (i.e., $\frac{p}{1-p}$) of chick surviving in 2014 twice high in 2013: $\exp(0.6131) = 1.846146$
(assuming understand correctly, how specified dependent. possible odds died instead.)
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