# Nippls

## Contents

### 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 byn,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.