Bert Gunter
2017-Jul-13 17:43 UTC
[R] Quadratic function with interaction terms for the PLS fitting model?
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.
Marc Schwartz
2017-Jul-13 18:17 UTC
[R] Quadratic function with interaction terms for the PLS fitting model?
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.
Bert Gunter
2017-Jul-13 18:34 UTC
[R] 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. >
David Winsemius
2017-Jul-13 23:36 UTC
[R] Quadratic function with interaction terms for the PLS fitting model?
> 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
Bert Gunter
2017-Jul-14 01:12 UTC
[R] Quadratic function with interaction terms for the PLS fitting model?
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 columnsError 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 >
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