# Nippls

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## 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.)

- 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

= a structure containing the fields:**options**

**display**: [ 'off' |{'on'}], governs display to command window.