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

[Ng, Kelvin Sai-cheong]

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

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