Sorry if this is an obvious question...
I'm estimating a simple binomial generalized additive model using the
gam function in the package mgcv. The model makes sense given my data,
and the predicted values also make sense given what I know about the
data.
However, I'm having trouble interpreting the y-axis of the plot of the
gam object. The y-axis is labeled "s(x,2.52)" which I understand to
basically mean a smoothing estimator with approximately 2.52 degrees of
freedom. The y-axis in my case ranges from -2 to 6 and I thought that
it would be possible to convert the Y axis estimate to a probability via
exp(Y)/(1+exp(Y)). So for instance, my lowest y-axis estimate is -2 for
a probability of:
> exp(-2)/(1+exp(-2))
[1] 0.1192029
However, if I use the predict function my lowest estimate is -3.53862893
for a probability of 2.8%. The 2.8% estimate is a much better estimate
than 11.9% given my specific data, so I'm clearly not interpreting the
plot correctly.
The help files say plot.gam provides "the component smooth functions
that make it up, on the scale of the
linear predictor."
I'm just not sure what that description means. Does someone have
another description that might help me grasp the plot?
Similar plots are on page 286 of Venables and Ripley (3rd Edition)...
Thanks,
Paul
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