[R] Quadratic function with interaction terms for the PLS fitting model?

[Bert Gunter]

David et.al.:

It's a problem with poly (or rather with how it is being misused)

> mx <- as.matrix(gasoline[1:50,"NIR"])
> str(mx)
 AsIs [1:50, 1:401] -0.0502 -0.0442 -0.0469 -0.0467 -0.0509 ...
 - attr(*, "dimnames")=List of 2
  ..$ : chr [1:50] "1" "2" "3" "4" ...
  ..$ : chr [1:401] "900 nm" "902 nm" "904 nm" "906 nm" ...

> poly(mx[,1:5],2)  ## only 5 columns
Error in poly(dots[[i]], degree, raw = raw, simple = raw) :
  'degree' must be less than number of unique points
> out <- poly(mx[,1:5], degree =2)
> dim(out)
[1] 50 20
## So this is same issue as before. But:

> out <- poly(mx[,1:30],degree = 2)

## 30 columns means 30*30 =900 2nd degree terms, but there are at most 50
## orthogonal vectors for the 50 -d space; ergo, poly() chokes rather
gracelessly, which is what you saw, with the following output:

rsession(2093,0x7fffe0c113c0) malloc: ***
mach_vm_map(size=823564528381952) failed (error code=3)
*** error: can't allocate region
*** set a breakpoint in malloc_error_break to debug
rsession(2093,0x7fffe0c113c0) malloc: ***
mach_vm_map(size=823564528381952) failed (error code=3)
*** error: can't allocate region
*** set a breakpoint in malloc_error_break to debug
Error: cannot allocate vector of size 767004.2 Gb

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Thu, Jul 13, 2017 at 4:36 PM, David Winsemius <dwinsemius at comcast.net> wrote:
>
>> On Jul 13, 2017, at 10:43 AM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
>>
>> poly(NIR, degree = 2) will work if NIR is a matrix, not a data.frame.
>> The degree argument apparently  *must* be explicitly named if NIR is
>> not a numeric vector. AFAICS, this is unclear or unstated in ?poly.
>
> I still get the same error with:
>
> library(pld)
> data(gasoline)
> gasTrain <- gasoline[1:50,]
> gas1 <- plsr(octane ~ poly(as.matrix(NIR), 2), ncomp = 10, data = gasTrain, validation = "LOO")
>
>
> Error in rep.int(rep.int(seq_len(nx), rep.int(rep.fac, nx)), orep) :
>   invalid 'times' value
>
>> gas1 <- plsr(octane ~ poly(as.matrix(gasTrain$NIR), degree=2), ncomp = 10, data = gasTrain, validation = "CV")
> Error in rep.int(rep.int(seq_len(nx), rep.int(rep.fac, nx)), orep) :
>   invalid 'times' value
>
>> str(as.matrix(gasTrain$NIR))
>  AsIs [1:50, 1:401] -0.0502 -0.0442 -0.0469 -0.0467 -0.0509 ...
>  - attr(*, "dimnames")=List of 2
>   ..$ : chr [1:50] "1" "2" "3" "4" ...
>   ..$ : chr [1:401] "900 nm" "902 nm" "904 nm" "906 nm" ...
>
> So tried to strip the RHS down to a "simple" matrix
>
>> gas1 <- plsr(octane ~ poly(matrix(gasTrain$NIR, nrow=nrow(gasTrain$NIR) ), degree=2), ncomp = 10, data = gasTrain, validation = "CV")
> Error in rep.int(rep.int(seq_len(nx), rep.int(rep.fac, nx)), orep) :
>   invalid 'times' value
>
> I guess it reflects my lack of understanding of poly (which parallels my lack of understanding of PLS.)
> --
> David.
>>
>>
>> -- Bert
>>
>> Bert Gunter
>>
>> "The trouble with having an open mind is that people keep coming along
>> and sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>
>>
>> On Thu, Jul 13, 2017 at 10:15 AM, David Winsemius
>> <dwinsemius at comcast.net> wrote:
>>>
>>>> On Jul 12, 2017, at 6:58 PM, Ng, Kelvin Sai-cheong <kscng at connect.hku.hk> wrote:
>>>>
>>>> Dear all,
>>>>
>>>> I am using the pls package of R to perform partial least square on a set of
>>>> multivariate data.  Instead of fitting a linear model, I want to fit my
>>>> data with a quadratic function with interaction terms.  But I am not sure
>>>> how.  I will use an example to illustrate my problem:
>>>>
>>>> Following the example in the PLS manual:
>>>> ## Read data
>>>> data(gasoline)
>>>> gasTrain <- gasoline[1:50,]
>>>> ## Perform PLS
>>>> gas1 <- plsr(octane ~ NIR, ncomp = 10, data = gasTrain, validation = "LOO")
>>>>
>>>> where octane ~ NIR is the model that this example is fitting with.
>>>>
>>>> NIR is a collective of variables, i.e. NIR spectra consists of 401 diffuse
>>>> reflectance measurements from 900 to 1700 nm.
>>>>
>>>> Instead of fitting with predict.octane[i] = a[0] * NIR[0,i] + a[1] *
>>>> NIR[1,i] + ...
>>>> I want to fit the data with:
>>>> predict.octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... +
>>>> b[0]*NIR[0,i]*NIR[0,i] + b[1] * NIR[0,i]*NIR[1,i] + ...
>>>>
>>>> i.e. quadratic with interaction terms.
>>>>
>>>> But I don't know how to formulate this.
>>>
>>> I did not see any terms in the model that I would have called interaction terms. I'm seeing a desire for a polynomial function in NIR. For that purpose, one might see if you get satisfactory results with:
>>>
>>> gas1 <- plsr(octane ~NIR + I(NIR^2), ncomp = 10, data = gasTrain, validation = "LOO")
>>> gas1
>>>
>>> I first tried using poly(NIR, 2) on the RHS and it threw an error, which raises concerns in my mind that this may not be a proper model. I have no experience with the use of plsr or its underlying theory, so the fact that this is not throwing an error is no guarantee of validity. Using this construction in ordinary least squares regression has dangers with inferential statistics because of the correlation of the linear and squared terms as well as likely violation of homoscedasticity.
>>>
>>> --
>>> David.
>>>
>>>
>>>>
>>>> May I have some help please?
>>>>
>>>> Thanks,
>>>>
>>>> Kelvin
>>>>
>>>>      [[alternative HTML version deleted]]
>>>>
>>>> ______________________________________________
>>>> 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.
>>>
>>> David Winsemius
>>> Alameda, CA, USA
>>>
>>> ______________________________________________
>>> 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.
>
> David Winsemius
> Alameda, CA, USA
>