# Quadratic function with interaction terms for the PLS fitting model?

9 messages
Open this post in threaded view
|

## Quadratic function with interaction terms for the PLS fitting model?

 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. May I have some help please? Thanks, Kelvin         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|

## Re: Quadratic function with interaction terms for the PLS fitting model?

 > On Jul 12, 2017, at 6:58 PM, Ng, Kelvin Sai-cheong <[hidden email]> 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]] > > ______________________________________________ > [hidden email] 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|

## Re: Quadratic function with interaction terms for the PLS fitting model?

Open this post in threaded view
|

## Re: Quadratic function with interaction terms for the PLS fitting model?

Open this post in threaded view
|

## Re: Quadratic function with interaction terms for the PLS fitting model?

Open this post in threaded view
|

## Re: Quadratic function with interaction terms for the PLS fitting model?

 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 <[hidden email]> 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 <[hidden email]> 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 <[hidden email]> 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 >>> <[hidden email]> wrote: >>>> >>>>> On Jul 12, 2017, at 6:58 PM, Ng, Kelvin Sai-cheong <[hidden email]> 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|

## Re: Quadratic function with interaction terms for the PLS fitting model?

 > 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.