Nippls

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.)

${\begin{bmatrix}{b_{y1,1}}\\{b_{y2,1}}\\{b_{y1,2}}\\{b_{y2,2}}\\{b_{y1,3}}\\{b_{y2,3}}\end{bmatrix}}$

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.

See Also

analysis, dspls, pls, plsnipal, simpls