R help - Jul 2017 - Quadratic function with interaction terms for the PLS fitting model?

Marc:

1. I am aware of the need to explicitly name arguments after ... --
see the R Language definition where this can be inferred from the
argument matching rules.

2. I am aware of the stated exception for poly(). However:
> x1 <- runif(20)
> x2 <- runif(20)
> mx <- cbind(x1,x2)
> poly(mx,2)
Error in poly(dots[[i]], degree, raw = raw, simple = raw) :
  'degree' must be less than number of unique points
> poly(mx, degree = 2)
             1.0           2.0         0.1          1.1         0.2
 [1,] -0.2984843  0.0402593349 -0.07095761  0.021179734 -0.22909595
 [2,]  0.2512177  0.2172530896  0.29620999  0.074413206  0.14508422
 [3,]  0.2775652  0.3085750335 -0.13955410 -0.038735366 -0.13729529
 [4,] -0.4090782  0.4032189266 -0.14737858  0.060289370 -0.12358925
 [5,] -0.1631886 -0.2221937915 -0.26690975  0.043556631  0.16814432
 [6,]  0.1770952  0.0009863446  0.25380650  0.044947925  0.02737265
 [7,] -0.2108146 -0.1525957018  0.34023304 -0.071726094  0.28787441
 [8,]  0.2693983  0.2794576400  0.04697126  0.012653979 -0.26792015
 [9,]  0.2014353  0.0653896008 -0.37013148 -0.074557536  0.54445808
[10,] -0.1002967 -0.2761638672 -0.29389518  0.029476714  0.25539539
[11,]  0.1132090 -0.1372916959  0.21619808  0.024475573 -0.06074932
[12,] -0.1116108 -0.2696398425 -0.14592886  0.016287234 -0.12617869
[13,]  0.1792535  0.0064357827 -0.04948750 -0.008870809 -0.24736773
[14,] -0.1167216 -0.2662346206 -0.20209364  0.023588696 -0.00923419
[15,] -0.4258838  0.4700591049  0.08836730 -0.037634205 -0.24586894
[16,]  0.1047271 -0.1523001267 -0.21491954 -0.022507896  0.02225837
[17,] -0.1985753 -0.1728455549  0.32036901 -0.063617358  0.22084868
[18,]  0.1844006  0.0196368680  0.32321195  0.059600465  0.23017961
[19,]  0.1009775 -0.1586846110 -0.08282554 -0.008363512 -0.21685556
[20,]  0.1753745 -0.0033219134  0.09871464  0.017312033 -0.23746062
attr(,"degree")
[1] 1 2 1 2 2
attr(,"coefs")
attr(,"coefs")[[1]]
attr(,"coefs")[[1]]$alpha
[1] 0.5477073 0.4154115

attr(,"coefs")[[1]]$norm2
[1]  1.00000000 20.00000000  1.55009761  0.08065872

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 11:17 AM, Marc Schwartz <marc_schwartz at me.com>
wrote:
> Bert,
>
> The 'degree' argument follows the "..." argument in the
function declaration:
>
>   poly(x, ..., degree = 1, coefs = NULL, raw = FALSE, simple = FALSE)
>
> Generally, any arguments after the "..." must be explicitly
named, but as per the Details section of ?poly:
>
> "Although formally degree should be named (as it follows ...), an
unnamed second argument of length 1 will be interpreted as the degree, such that
poly(x, 3) can be used in formulas."
>
> The issue of having to explicitly name arguments that follow the three dots
has come up over the years, but I cannot recall where that is documented in the
manuals.
>
> Regards,
>
> Marc
>
>
>
>> On Jul 13, 2017, at 12:43 PM, 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.
>>
>>
>> -- 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.
>>
>> ______________________________________________
>> 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.
>

Hi Bert,

Ok, to your initial point, the key nuance is that if 'x' is a vector,
you can leave the 'degree' argument unnamed, however, if 'x' is
a matrix, you cannot. That aspect of the behavior does not seem to change if
poly() is called stand alone or, as suggested in ?poly, within a formula to be
parsed.

Working on tracing through the code using debug(), the error is triggered with
'mx', when the following code is called within poly(), where 'x'
within the function call is 'mx'. Note that my 'mx' was
generated using new calls to rnorm():

if (is.matrix(x)) {
    m <- unclass(as.data.frame(cbind(x, ...)))
    return(do.call(polym, c(m, degree = degree, raw = raw, list(coefs =
coefs))))
}

'm' ends up being:

Browse[2]> m
$x1
 [1] 0.11551124 0.36245863 0.44844573 0.89193967 0.91431981 0.16244275
 [7] 0.28070518 0.34013156 0.26561721 0.52915461 0.88164507 0.42485427
[13] 0.48844831 0.60092526 0.01493797 0.41814162 0.31549893 0.19483697
[19] 0.16003496 0.52635862

$x2
 [1] 0.89119433 0.02665353 0.03954367 0.37604374 0.05604632 0.86123698
 [7] 0.11106261 0.15707524 0.32433273 0.62476982 0.70646979 0.78843108
[13] 0.63674970 0.17091172 0.65220425 0.64087676 0.56903083 0.21398002
[19] 0.02820857 0.47113431

$V3
 [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

attr(,"row.names")
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20


On the third 'loop' over the list elements in 'm' via do.call(),
m$V3 is passed to polym() as its 'x' argument:

Browse[3]> x
 [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Browse[3]> degree
[1] 2
Browse[3]> length(unique(x))
[1] 1


The following check is triggered and, of course, fails with the error message:

if (degree >= length(unique(x))) stop("'degree' must be less
than number of unique points")

Thus, in effect, the following is being called:
> polym(rep(2, 20), degree = 2)
Error in poly(dots[[1L]], degree, raw = raw, simple = raw && nd > 1)
:
  'degree' must be less than number of unique points


It would seem reasonable that the help for poly() could make it explicitly clear
that if 'x' is not a vector, but is a matrix, that 'degree' must
be explicitly named.

Regards,

Marc

> On Jul 13, 2017, at 1:34 PM, Bert Gunter <bgunter.4567 at gmail.com>
wrote:
> 
> Marc:
> 
> 1. I am aware of the need to explicitly name arguments after ... --
> see the R Language definition where this can be inferred from the
> argument matching rules.
> 
> 2. I am aware of the stated exception for poly(). However:
> 
>> x1 <- runif(20)
>> x2 <- runif(20)
>> mx <- cbind(x1,x2)
>> poly(mx,2)
> Error in poly(dots[[i]], degree, raw = raw, simple = raw) :
>  'degree' must be less than number of unique points
> 
>> poly(mx, degree = 2)
>             1.0           2.0         0.1          1.1         0.2
> [1,] -0.2984843  0.0402593349 -0.07095761  0.021179734 -0.22909595
> [2,]  0.2512177  0.2172530896  0.29620999  0.074413206  0.14508422
> [3,]  0.2775652  0.3085750335 -0.13955410 -0.038735366 -0.13729529
> [4,] -0.4090782  0.4032189266 -0.14737858  0.060289370 -0.12358925
> [5,] -0.1631886 -0.2221937915 -0.26690975  0.043556631  0.16814432
> [6,]  0.1770952  0.0009863446  0.25380650  0.044947925  0.02737265
> [7,] -0.2108146 -0.1525957018  0.34023304 -0.071726094  0.28787441
> [8,]  0.2693983  0.2794576400  0.04697126  0.012653979 -0.26792015
> [9,]  0.2014353  0.0653896008 -0.37013148 -0.074557536  0.54445808
> [10,] -0.1002967 -0.2761638672 -0.29389518  0.029476714  0.25539539
> [11,]  0.1132090 -0.1372916959  0.21619808  0.024475573 -0.06074932
> [12,] -0.1116108 -0.2696398425 -0.14592886  0.016287234 -0.12617869
> [13,]  0.1792535  0.0064357827 -0.04948750 -0.008870809 -0.24736773
> [14,] -0.1167216 -0.2662346206 -0.20209364  0.023588696 -0.00923419
> [15,] -0.4258838  0.4700591049  0.08836730 -0.037634205 -0.24586894
> [16,]  0.1047271 -0.1523001267 -0.21491954 -0.022507896  0.02225837
> [17,] -0.1985753 -0.1728455549  0.32036901 -0.063617358  0.22084868
> [18,]  0.1844006  0.0196368680  0.32321195  0.059600465  0.23017961
> [19,]  0.1009775 -0.1586846110 -0.08282554 -0.008363512 -0.21685556
> [20,]  0.1753745 -0.0033219134  0.09871464  0.017312033 -0.23746062
> attr(,"degree")
> [1] 1 2 1 2 2
> attr(,"coefs")
> attr(,"coefs")[[1]]
> attr(,"coefs")[[1]]$alpha
> [1] 0.5477073 0.4154115
> 
> attr(,"coefs")[[1]]$norm2
> [1]  1.00000000 20.00000000  1.55009761  0.08065872
> 
> 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 11:17 AM, Marc Schwartz <marc_schwartz at
me.com> wrote:
>> Bert,
>> 
>> The 'degree' argument follows the "..." argument in
the function declaration:
>> 
>>  poly(x, ..., degree = 1, coefs = NULL, raw = FALSE, simple = FALSE)
>> 
>> Generally, any arguments after the "..." must be explicitly
named, but as per the Details section of ?poly:
>> 
>> "Although formally degree should be named (as it follows ...), an
unnamed second argument of length 1 will be interpreted as the degree, such that
poly(x, 3) can be used in formulas."
>> 
>> The issue of having to explicitly name arguments that follow the three
dots has come up over the years, but I cannot recall where that is documented in
the manuals.
>> 
>> Regards,
>> 
>> Marc
>> 
>> 
>> 
>>> On Jul 13, 2017, at 12:43 PM, 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.
>>> 
>>> 
>>> -- 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

> It would seem reasonable that the help for poly() could make it explicitly
clear that if 'x' is not a vector, but is a matrix, that
'degree' must be explicitly named.
>
> Regards,
>
> Marc
>
Exactly.  As written, there is no reason to believe that the stated
exception to the ... argument matching rule does not also apply to x a
matrix.

-- Bert