[R] physical constraint with gam
simon.wood at bath.edu
Sat May 14 09:24:36 CEST 2016
On 12/05/16 02:29, Dominik Schneider wrote:
> Hi again,
> I'm looking for some clarification on 2 things.
> 1. On that last note, I realize that s(x1,x2) would be the other
> obvious interaction to compare with - and I see that you recommend
> te(x1,x2) if they are not on the same scale.
- yes that's right, s(x1,x2) gives an isotropic smooth, which is usually
only appropriate if x1 and x2 are naturally on the same scale.
> 2. If s(x1,by=x1) gives you a "parameter" value similar to a GLM when
> you plot s(x1):x1, why does my function above return the same yhat as
> predict(mdl,type='response') ? Shouldn't each of the terms need to be
> multiplied by the variable value before applying
> rowSums()+attr(sterms,'constant') ??
predict returns s(x1)*x1 (plot.gam just plots s(x1), because in general
s(x1,by=x2) is not smooth). If you want to get s(x1) on its own you need
to do something like this:
x2 <- x1 ## copy x1
m <- gam(y~s(x1,by=x2)) ## model implementing s(x1,by=x1) using copy of x1
predict(m,data.frame(x1=x1,x2=rep(1,length(x2))),type="terms") ## now
predicted s(x1)*x2 = s(x1)
> Thanks again
> On Wed, May 11, 2016 at 10:11 AM, Dominik Schneider
> <Dominik.Schneider at colorado.edu
> <mailto:Dominik.Schneider at colorado.edu>> wrote:
> Hi Simon, Thanks for this explanation.
> To make sure I understand, another way of explaining the y axis in
> my original example is that it is the contribution to snowdepth
> relative to the other variables (the example only had fsca, but my
> actual case has a couple others). i.e. a negative s(fsca) of -0.5
> simply means snowdepth 0.5 units below the intercept+s(x_i), where
> s(x_i) could also be negative in the case where total snowdepth is
> less than the intercept value.
> The use of by=fsca is really useful for interpreting the marginal
> impact of the different variables. With my actual data, the term
> s(fsca):fsca is never negative, which is much more intuitive. Is
> it appropriate to compare magnitudes of e.g. s(x2):x2 / mean(x2)
> and s(x2):x2 / mean(x2) where mean(x_i) are the mean of the
> actual data?
> Lastly, how would these two differ: s(x1,by=x2); or
> s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and
> i'm not sure if a linear combination is enough.
> On Wed, May 11, 2016 at 3:11 AM, Simon Wood <simon.wood at bath.edu
> <mailto:simon.wood at bath.edu>> wrote:
> The spline having a positive value is not the same as a glm
> coefficient having a positive value. When you plot a smooth,
> say s(x), that is equivalent to plotting the line 'beta * x'
> in a GLM. It is not equivalent to plotting 'beta'. The smooths
> in a gam are (usually) subject to `sum-to-zero'
> identifiability constraints to avoid confounding via the
> intercept, so they are bound to be negative over some part of
> the covariate range. For example, if I have a model y ~ s(x) +
> s(z), I can't estimate the mean level for s(x) and the mean
> level for s(z) as they are completely confounded, and
> confounded with the model intercept term.
> I suppose that if you want to interpret the smooths as glm
> parameters varying with the covariate they relate to then you
> can do, by setting the model up as a varying coefficient
> model, using the `by' argument to 's'...
> this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' .
> s(fsca,by=fsca) is not confounded with the intercept, so no
> constraint is needed or applied, and you can now interpret the
> smooth like a local GLM coefficient.
> On 11/05/16 01:30, Dominik Schneider wrote:
> Just getting into using GAM using the mgcv package. I've
> generated some
> models and extracted the splines for each of the variables
> and started
> visualizing them. I'm noticing that one of my variables is
> In the example below, my interpretation of the following
> plot is that the
> y-axis is basically the equivalent of a "parameter" value
> of a GLM; in GAM
> this value can change as the functional relationship
> changes between x and
> y. In my case, I am predicting snowdepth based on the
> fractional snow
> covered area. In no case will snowdepth realistically
> decrease for a unit
> increase in fsca so my question is: *Is there a way to
> constrain the spline
> to positive values? *
> datplot=cbind(sterms,mdl$model) %>% tbl_df
> dat=data_frame(snowdepth=runif(100,min =
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> Simon Wood, School of Mathematics, University of Bristol BS8
> 1TW UK
> +44 (0)117 33 18273 <tel:%2B44%20%280%29117%2033%2018273>
Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
+44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190
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