I am fitting a model in which the response variable y is a function of two independent, quantitative variables x1 and x2; thus: y = f(x1, x2). For reasons I do not believe to be important for the purpose of this post, I find it desirable to find f by means of GAM; also, I require principal effects and interactions to be specified separately, so I am using using te and ti tensors. Thus, I am using the following command: f = gam(y ~ te(x1) + te(x2) + ti(x1, x2)) This results in a model that corresponds to one of the hypotheses I am testing. Nevertheless, another hypothesis requires that, when one of the independent variables (say x2) is zero, the value of y is unaffected by the other variable (in this example x1). In other words f(x1, 0) = k for every value of x1, where k is a constant to be estimated. For x2 values other than zero I would like to let GAM choose the appropriate function relating x1 and y. Is there a way to specify such model in mgcv?
There probably is a way, but it involves some programming. You would
need to clone a smooth constructor (e.g. for the "cr" class), and then
modify it to add a linear constraint matrix C to the returned smooth
object. If b are the smooth coefficients then C should? be the matrix
such that s(0) = Cb (you can get this from the Predict.matrix method for
the class). Then the constraint Cb=0 will be applied during basis setup,
and is equivalent to s(0)=0.
Now you can use your cloned class in a tensor product smooth, using the
'ti' constructor. Suppose your cloned smooth class is called
"foo", then
ti(x,z,bs="foo",mc=c(0,1))
will create a smooth for which s(x,0)=0. Your requirement that s(x,0)=k
is then taken care of by the model intercept.
If you want to try something similar with the full nested structure it's
more complicated still. Then I think you would need something like
s(x,by=as.numeric(z!=0)) + s(z) + ti(x,z,bs=c("cr","foo"))
Simon
On 11/01/18 22:33, Alejandra Mart?nez Blancas wrote:> I am fitting a model in which the response variable y is a function of
> two independent, quantitative variables x1 and x2; thus: y = f(x1,
> x2). For reasons I do not believe to be important for the purpose of
> this post, I find it desirable to find f by means of GAM; also, I
> require principal effects and interactions to be specified separately,
> so I am using using te and ti tensors. Thus, I am using the following
> command:
>
>
>
> f = gam(y ~ te(x1) + te(x2) + ti(x1, x2))
>
>
>
> This results in a model that corresponds to one of the hypotheses I am
> testing. Nevertheless, another hypothesis requires that, when one of
> the independent variables (say x2) is zero, the value of y is
> unaffected by the other variable (in this example x1). In other words
> f(x1, 0) = k for every value of x1, where k is a constant to be
> estimated. For x2 values other than zero I would like to let GAM
> choose the appropriate function relating x1 and y. Is there a way to
> specify such model in mgcv?
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
--
Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
+44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190
Thanks Simon, by cloning a smooth construct do you mean copying and modifying the smooth constructor code? Could you pleas elaborate on your answer? Which is the Predict.matrix method? 2018-01-12 3:20 GMT-06:00 Simon Wood <simon.wood at bath.edu>:> There probably is a way, but it involves some programming. You would need to > clone a smooth constructor (e.g. for the "cr" class), and then modify it to > add a linear constraint matrix C to the returned smooth object. If b are the > smooth coefficients then C should be the matrix such that s(0) = Cb (you > can get this from the Predict.matrix method for the class). Then the > constraint Cb=0 will be applied during basis setup, and is equivalent to > s(0)=0. > > Now you can use your cloned class in a tensor product smooth, using the 'ti' > constructor. Suppose your cloned smooth class is called "foo", then > > ti(x,z,bs="foo",mc=c(0,1)) > > will create a smooth for which s(x,0)=0. Your requirement that s(x,0)=k is > then taken care of by the model intercept. > > If you want to try something similar with the full nested structure it's > more complicated still. Then I think you would need something like > > s(x,by=as.numeric(z!=0)) + s(z) + ti(x,z,bs=c("cr","foo")) > > Simon > > > > On 11/01/18 22:33, Alejandra Mart?nez Blancas wrote: >> >> I am fitting a model in which the response variable y is a function of >> two independent, quantitative variables x1 and x2; thus: y = f(x1, >> x2). For reasons I do not believe to be important for the purpose of >> this post, I find it desirable to find f by means of GAM; also, I >> require principal effects and interactions to be specified separately, >> so I am using using te and ti tensors. Thus, I am using the following >> command: >> >> >> >> f = gam(y ~ te(x1) + te(x2) + ti(x1, x2)) >> >> >> >> This results in a model that corresponds to one of the hypotheses I am >> testing. Nevertheless, another hypothesis requires that, when one of >> the independent variables (say x2) is zero, the value of y is >> unaffected by the other variable (in this example x1). In other words >> f(x1, 0) = k for every value of x1, where k is a constant to be >> estimated. For x2 values other than zero I would like to let GAM >> choose the appropriate function relating x1 and y. Is there a way to >> specify such model in mgcv? >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > > > -- > Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK > +44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190 > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.