Hello. I'm trying to analyze data, which is looking at the relationship between temperature and survival for fish (from fertilization to emergence). Looking at the raw data, there appears to be a bell shaped relationship. Ordinarily for survival data, I would run a generalized linear model (because the data has a binomial error structure). However, I am thinking that running a generalized additive model (which I've never used before), as its my understanding that they are better able to deal with non-linear relationships. Hopefully this is a correct assumption. 

Question 1: Unfortunately, the data I have to work with is not formatted to be as #successes or # failures, as R seems to want for other generalized models (the survival data I have is percent survival). I'm using 'The R Book' by Mick Crawley,and have searched online, but haven't had much luck finding the right code that will run with percentage data for GAM (and whether or not its appropriate to use percentage data). Is it inappropriate to run the analyses like this? With Generalized Linear Models R seems to want #successes and failures, but the GAM doesn't (it worked--output below). I'm just wondering whether it is alright to run the model as I have done (with percentage data)? 

Question 2: For this type of model (GAM), is there a simple way of constructing an equation for the model (e.g., to come up with predicted values). This is probably not the best, but I've plotted the predicted values in Excel, fitted a polynomial trend line and got the equation from there. I'm just wondering if there's a more appropriate way to get it in R? 

Not sure if it would be useful, but I've provided the code and output for the model below. Any help you can offer would be much appreciated. Thanks in advance for your help--I really appreciate it! 

Kris 




> names(data) 
[1] "Temp" "Survival" 
> str(data) 
'data.frame': 17 obs. of 2 variables: 
$ Temp : num 35.6 38.8 39 39 41 ... 
$ Survival: num 0.14 0.972 0.697 0.938 0.83 0.987 0.989 0.9 0.996 0.87 ... 
> 
> Surv<-gam(Survival~s(Temp), quasibinomial, data=na.omit(data)) 
> summary(Surv) 

Family: quasibinomial 
Link function: logit 

Formula: 
Survival ~ s(Temp) 

Parametric coefficients: 
Estimate Std. Error t value Pr(>|t|) 
(Intercept) 1.9938 0.3067 6.501 8.02e-05 *** 
--- 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Approximate significance of smooth terms: 
edf Ref.df F p-value 
s(Temp) 6.325 6.325 4.065 0.0257 * 
--- 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

R-sq.(adj) = 0.775 Deviance explained = 81.2% 
GCV score = 0.18885 Scale est. = 0.10748 n = 17 





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