Luigi Biagini

2017-Jul-13 10:07 UTC

### [R] How to formulate quadratic function with interaction terms for the PLS fitting model?

I have two ideas about it. 1- i) Entering variables in quadratic form is done with the command I (variable ^ 2) - plsr (octane ~ NIR + I (nir ^ 2), ncomp = 10, data = gasTrain, validation "LOO" You could also use a new variable NIR_sq <- (NIR) ^ 2 ii) To insert a square variable, use syntax I (x ^ 2) - it is very important to insert I before the parentheses. iii) If you want to make the interaction between x and x ^ 2 use the command ":" -> x: I(x ^ 2) iv) For multiple interactions between x and x ^ 2 use the command "*" -> x *I (x ^ 2) i) plsr (octane ~ NIR + NIR_sq, ncomp = 10, data = gasTrain, validation "LOO") I (x ^ 2) ii)p lsr (octane ~ NIR + I(NIR^2), ncomp = 10, data = gasTrain, validation = "LOO") I (x ^ 2) iii)p lsr (octane ~ NIR : I(NIR^2), ncomp = 10, data = gasTrain, validation = "LOO") I (x ^ 2) iv)p lsr (octane ~ NIR * I(NIR^2), ncomp = 10, data = gasTrain, validation = "LOO") I (x ^ 2) 2 - For your regression, did you plan to use MARS instead of PLS? 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 octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... > I want to fit the data with: > 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]]

Bert Gunter

2017-Jul-13 14:43 UTC

### [R] How to formulate quadratic function with interaction terms for the PLS fitting model?

Below. -- Bert Bert Gunter On Thu, Jul 13, 2017 at 3:07 AM, Luigi Biagini <luigi.biagini at gmail.com> wrote:> I have two ideas about it. > > 1- > i) Entering variables in quadratic form is done with the command I > (variable ^ 2) - > plsr (octane ~ NIR + I (nir ^ 2), ncomp = 10, data = gasTrain, validation > "LOO" > You could also use a new variable NIR_sq <- (NIR) ^ 2 > > ii) To insert a square variable, use syntax I (x ^ 2) - it is very > important to insert I before the parentheses.True, but better I believe: see ?poly. e.g. poly(cbind(x1,x2,x3), degree = 2, raw = TRUE) is a full quadratic polynomial in x1,x2,x3 .> > iii) If you want to make the interaction between x and x ^ 2 use the > command ":" -> x: I(x ^ 2) > > iv) For multiple interactions between x and x ^ 2 use the command "*" -> x > *I (x ^ 2) > > i) plsr (octane ~ NIR + NIR_sq, ncomp = 10, data = gasTrain, validation > "LOO") I (x ^ 2) > ii)p lsr (octane ~ NIR + I(NIR^2), ncomp = 10, data = gasTrain, validation > = "LOO") I (x ^ 2) > iii)p lsr (octane ~ NIR : I(NIR^2), ncomp = 10, data = gasTrain, validation > = "LOO") I (x ^ 2) > iv)p lsr (octane ~ NIR * I(NIR^2), ncomp = 10, data = gasTrain, validation > = "LOO") I (x ^ 2) > > 2 - For your regression, did you plan to use MARS instead of PLS? > > > > > 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 octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... >> I want to fit the data with: >> 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]] > > ______________________________________________ > 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.

Ng, Kelvin Sai-cheong

2017-Jul-16 06:31 UTC

### [R] How to formulate quadratic function with interaction terms for the PLS fitting model?

I see. Thank you for the help. On Thu, Jul 13, 2017 at 10:43 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:> Below. > > -- Bert > Bert Gunter > > > > On Thu, Jul 13, 2017 at 3:07 AM, Luigi Biagini <luigi.biagini at gmail.com> > wrote: > > I have two ideas about it. > > > > 1- > > i) Entering variables in quadratic form is done with the command I > > (variable ^ 2) - > > plsr (octane ~ NIR + I (nir ^ 2), ncomp = 10, data = gasTrain, > validation > > "LOO" > > You could also use a new variable NIR_sq <- (NIR) ^ 2 > > > > ii) To insert a square variable, use syntax I (x ^ 2) - it is very > > important to insert I before the parentheses. > > True, but better I believe: see ?poly. > e.g. poly(cbind(x1,x2,x3), degree = 2, raw = TRUE) is a full quadratic > polynomial in x1,x2,x3 . > > > > > > iii) If you want to make the interaction between x and x ^ 2 use the > > command ":" -> x: I(x ^ 2) > > > > iv) For multiple interactions between x and x ^ 2 use the command "*" -> > x > > *I (x ^ 2) > > > > i) plsr (octane ~ NIR + NIR_sq, ncomp = 10, data = gasTrain, validation > > "LOO") I (x ^ 2) > > ii)p lsr (octane ~ NIR + I(NIR^2), ncomp = 10, data = gasTrain, > validation > > = "LOO") I (x ^ 2) > > iii)p lsr (octane ~ NIR : I(NIR^2), ncomp = 10, data = gasTrain, > validation > > = "LOO") I (x ^ 2) > > iv)p lsr (octane ~ NIR * I(NIR^2), ncomp = 10, data = gasTrain, > validation > > = "LOO") I (x ^ 2) > > > > 2 - For your regression, did you plan to use MARS instead of PLS? > > > > > > > > > > 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 octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + > ... > >> I want to fit the data with: > >> 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]] > > > > ______________________________________________ > > 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. >[[alternative HTML version deleted]]

David Winsemius

2017-Jul-16 14:36 UTC

### [R] How to formulate quadratic function with interaction terms for the PLS fitting model?

> On Jul 13, 2017, at 7:43 AM, Bert Gunter <bgunter.4567 at gmail.com> wrote: > > Below. > > -- Bert > Bert Gunter > > > > On Thu, Jul 13, 2017 at 3:07 AM, Luigi Biagini <luigi.biagini at gmail.com> wrote: >> I have two ideas about it. >> >> 1- >> i) Entering variables in quadratic form is done with the command I >> (variable ^ 2) - >> plsr (octane ~ NIR + I (nir ^ 2), ncomp = 10, data = gasTrain, validation >> "LOO" >> You could also use a new variable NIR_sq <- (NIR) ^ 2 >> >> ii) To insert a square variable, use syntax I (x ^ 2) - it is very >> important to insert I before the parentheses. > > True, but better I believe: see ?poly. > e.g. poly(cbind(x1,x2,x3), degree = 2, raw = TRUE) is a full quadratic > polynomial in x1,x2,x3 . >Is there any real difference between octane ~ NIR * I(NIR^2) octane ~ NIR * poly(NIR, degree=2, raw=TRUE) ? (I though that adding raw = TRUE prevented the beneficial process of centering the second degree terms.) __ David> >> >> iii) If you want to make the interaction between x and x ^ 2 use the >> command ":" -> x: I(x ^ 2) >> >> iv) For multiple interactions between x and x ^ 2 use the command "*" -> x >> *I (x ^ 2) >> >> i) plsr (octane ~ NIR + NIR_sq, ncomp = 10, data = gasTrain, validation >> "LOO") I (x ^ 2) >> ii)p lsr (octane ~ NIR + I(NIR^2), ncomp = 10, data = gasTrain, validation >> = "LOO") I (x ^ 2) >> iii)p lsr (octane ~ NIR : I(NIR^2), ncomp = 10, data = gasTrain, validation >> = "LOO") I (x ^ 2) >> iv)p lsr (octane ~ NIR * I(NIR^2), ncomp = 10, data = gasTrain, validation >> = "LOO") I (x ^ 2) >> >> 2 - For your regression, did you plan to use MARS instead of PLS? >> >> >> >> >> 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 octane[i] = a[0] * NIR[0,i] + a[1] * NIR[1,i] + ... >>> I want to fit the data with: >>> 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]] >> >> ______________________________________________ >> 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 Alameda, CA, USA

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