[R-sig-eco] low predicted vales in GAMs

[Nicholas Lewin-Koh]

Hi Anna,
A couple of thoughts:
Did you try fitting a straight Poisson model? The quasi Poisson model is
assuming
the variance is not a strict function of the mean, and that may be
interacting with your
weighting function. Also how exactly are the weights defined? is it (#
squares counted)/(total possible squares) ?
Or can weights be greater than 1?
Did you try fitting without weights and offset? 
And lastly are your bird counts highly clustered? ie lots of 0's and
then some high counts?
because the model will probably over smooth the high counts. 
Since this is a spatial model you might want to look at geoRglm. Or try
cozigam
and try to model zero-inflation (if that is the case)

Hope this helps
Nicholas

> Message: 1
> Date: Fri, 11 Dec 2009 11:43:40 -0000
> From: "Anna Renwick" <anna.renwick at bto.org>
> Subject: [R-sig-eco] low predicted vales in GAMs
> To: <r-sig-ecology at r-project.org>
> Message-ID: <BFD6DF2C5CA142C58C272652FA017856 at btodomain.bto.org>
> Content-Type: text/plain
> 
> Dear All
> 
>  
> 
> I have come across a problem with the GAM models I am running. Basically
> the
> predicted values are consistently only about 0.4 of the actual values. 
> 
>  
> 
> A bit more detail:
> 
> MODEL:
> 
> m4<-gam(count~s(east,north,k=10)+ez+cv01+cv03+cv04+cv05+cv07+mtemp+mtotalrai
> n+ez:mtemp+ez:mtotalrain+
> 
>             offset(log(fit.vec)),
> 
>             weights=wt,
> 
>             data=spat6,
> 
>             family=quasipoisson,
> 
>             start=rep(0,26)
> 
> )
> 
> MODEL SUMMARY:
> 
>  
> 
> Family: quasipoisson 
> 
> Link function: log 
> 
>  
> 
> Formula:
> 
> count ~ s(east, north, k = 10) + ez + cv01 + cv03 + cv04 + cv05 + 
> 
>     cv07 + mtemp + mtotalrain + ez:mtemp + ez:mtotalrain +
> offset(log(fit.vec))
> 
>  
> 
> Parametric coefficients:
> 
>                  Estimate Std. Error   t value Pr(>|t|)    
> 
> (Intercept)    -5.296e+00  1.846e+00    -2.869 0.004166 ** 
> 
> ezM             1.651e+00  2.102e+00     0.785 0.432397    
> 
> ezP             7.358e+00  2.047e+00     3.595 0.000332 ***
> 
> ezU            -1.061e+02  1.064e+07 -9.97e-06 0.999992    
> 
> cv01            7.405e-02  5.437e-03    13.620  < 2e-16 ***
> 
> cv03            2.258e-02  5.145e-03     4.389 1.20e-05 ***
> 
> cv04            2.878e-02  4.839e-03     5.949 3.18e-09 ***
> 
> cv05            3.634e-02  5.326e-03     6.823 1.17e-11 ***
> 
> cv07            2.370e-02  5.712e-03     4.149 3.48e-05 ***
> 
> mtemp          -1.838e-01  1.750e-01    -1.050 0.293900    
> 
> mtotalrain      1.872e-02  5.072e-03     3.692 0.000229 ***
> 
> ezM:mtemp       6.181e-02  2.204e-01     0.280 0.779197    
> 
> ezP:mtemp      -7.028e-01  2.050e-01    -3.429 0.000619 ***
> 
> ezU:mtemp       8.697e-01  1.371e+06  6.34e-07 0.999999    
> 
> ezM:mtotalrain -3.393e-02  5.799e-03    -5.851 5.68e-09 ***
> 
> ezP:mtotalrain -1.901e-02  5.379e-03    -3.535 0.000417 ***
> 
> ezU:mtotalrain  3.510e-02  4.074e+04  8.62e-07 0.999999    
> 
> ---
> 
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
>  
> 
> Approximate significance of smooth terms:
> 
>                 edf Ref.df     F p-value    
> 
> s(east,north) 8.736  8.736 28.88  <2e-16 ***
> 
> ---
> 
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
>  
> 
> R-sq.(adj) =  0.324   Deviance explained = -5.12e+03%
> 
> GCV score = 39.556  Scale est. = 39.056    n = 2038
> 
>  
> 
>  
> 
> Count = bird counts/square
> 
> ez=environmental zone
> 
> cv = habitat types
> 
> mtemp = mean annual temperature
> 
> mtotalrain= mean total rain/year
> 
>  
> 
> Sample size is approximately 2000.
> 
>  
> 
> The offset fit.vec is bird detectability and the weighting is based on
> the
> number of squares in each area surveyed. I belief that the strange
> deviance
> explained is due to the weighting we have added into the model.
> 
>  
> 
> I would have assumed that the predicted values divided by the real counts
> should be around 1, however they are much lower and hence the model is
> consistently predicting lower counts than were observed. I was wondering
> if
> there is anything obvious which I am missing when carrying out these
> models.
> 
>  
> 
> Many thanks,
> 
> Anna
> 
>  
> 
> Dr Anna R. Renwick
> Research Ecologist
> British Trust for Ornithology, 
> The Nunnery, 
> Thetford, 
> Norfolk, 
> IP24 2PU, 
> UK
> Tel: +44 (0)1842 750050; Fax: +44 (0)1842 750030 
> 
>  
> 
> 
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> 
> 
> 
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