R devel - Apr 2010 - GAMs and survival data

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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Kris Jones <kjones <at> fishsciences.net> writes:

Quick answer: this question is inappropriate for the r devel*pment
list (intended for questions about code development, technical questions,
etc.).  The main r help list, or the r-sig-ecology list, would be better.

  It is true that GAMs are more flexible for nonlinear relationships,
although simple polynomial (e.g. quadratic) models in GLMS can be 
OK sometimes.

  Proportion data without denominators are not appropriate for
binomial modeling (where you have to have integer numbers surviving
out of a known integer number exposed).  You have a few choices,
none of which is quite as easy as binomial modeling -- beta regression,
transforming data (although this can mess up the shapes of your
responses to your predictors), modeling heteroscedasticity explicitly
(with family="quasi" in GLM/GAM or via weights argument in gls/gnls).

* 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).

  You probably want to use the predict() functions provided with
mgcv/GAM.  It wouldn't hurt to read Simon Wood's book, either.

  Ben Bolker