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

Marc Schwartz marc_schwartz at me.com
Thu Jul 13 21:41:12 CEST 2017


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



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