Nippls
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Purpose
NIPALS Partial Least Squares computational engine.
Synopsis
- [reg,ssq,xlds,ylds,wts,xscrs,yscrs,bin,nipwts] = nippls(x,y,ncomp,options)
Description
Performs PLS regression using NIPALS algorithm.
Inputs
- x = X-block (M by Nx).
- y = Y-block (M by Ny).
Optional Inputs
- ncomp = number of components {default = rank of X-block}.
- options = discussed below.
The default options can be retrieved using: options = nippls('options');.
Outputs
- reg = matrix of regression vectors where each row corresponds to a regression vector for a given number of latent variables. If the Y-block contains multiple columns, the rows of reg will be in groups of latent variables (so that the regression vectors for all columns of Y at 1 latent variable will come first, followed by the regression vectors for all columns of Y at 2 latent variables, etc.)
- where b_{yn,k} is the regression vector for column "n" of the Y-block calculated from "k" latent variables.
- ssq = the sum of squares captured (ncomp by 5) with the columns defined as follows:
- Column 1 = Number of latent variables (LVs),
- Column 2 = Variance captured (%) in the X-block by this LV,
- Column 3 = Total variance captured (%) by all LVs up to this row,
- Column 4 = Variance captured (%) in the X-block by this LV, and
- Column 5 = Total variance captured (%) by all LVs up to this row.
- xlds = X-block loadings (Nx by ncomp).
- ylds = Y-block loadings (Ny by ncomp).
- wts = X-block weights (Nx by ncomp).
- xscrs = X-block scores (M by ncomp).
- yscrs = Y-block scores (M by ncomp).
- bin = the inner relation coefficients (1 by ncomp).
- nipwts = X-block weights in the original deflated X format.
Options
- options = a structure containing the fields:
- display: [ 'off' |{'on'}], governs display to command window.