[R] setting constraints on gam

[Michael Dewey]

Dear Alejandra

in case you want to move on before Simon replies see inline

On 12/01/2018 22:50, Alejandra Martínez Blancas wrote:
> Thanks Simon, by cloning a smooth construct do you mean copying and
> modifying the smooth constructor code?

That is what I understand him to mean yes. (I believe it is clon in 
Spanish if that helps).

  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 Martínez 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.
> 
> ______________________________________________
> 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.
> 

-- 
Michael
http://www.dewey.myzen.co.uk/home.html