R help - Jul 2017 - 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]]

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.

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]]

> 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