naginterfaces.library.correg.pls_​fit

naginterfaces.library.correg.pls_fit(nfact, p, c, w, rcond, orig, xbar, ybar, iscale, xstd, ystd, vipopt, ycv)

pls_fit calculates parameter estimates for a given number of factors given the output from an orthogonal scores PLS regression (pls_svd() or pls_wold()).

For full information please refer to the NAG Library document for g02lc

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/g02/g02lcf.html

Parameters

nfactint

$l$, the number of factors to include in the calculation of parameter estimates.

pfloat, array-like, shape $(\text{ip},\text{maxfac})$

$x$-loadings as returned from pls_svd() and pls_wold().

cfloat, array-like, shape $(\text{my},\text{maxfac})$

$y$-loadings as returned from pls_svd() and pls_wold().

wfloat, array-like, shape $(\text{ip},\text{maxfac})$

$x$-weights as returned from pls_svd() and pls_wold().

rcondfloat

Singular values of $P^{T}W$ less than $rcond$ times the maximum singular value are treated as zero when calculating parameter estimates. If $rcond$ is negative, a value of $0.005$ is used.

origint

Indicates how parameter estimates are calculated.

$orig=-1$

Parameter estimates for the centred, and possibly, scaled data.

$orig=1$

Parameter estimates for the original data.

xbarfloat, array-like, shape $\left(\text{ip}\right)$

If $orig=1$, mean values of predictor variables in the model; otherwise $xbar$ is not referenced.

ybarfloat, array-like, shape $\left(\text{my}\right)$

If $orig=1$, mean value of each response variable in the model; otherwise $ybar$ is not referenced.

iscaleint

If $orig=1$, $iscale$ must take the value supplied to either pls_svd() or pls_wold(); otherwise $iscale$ is not referenced.

xstdfloat, array-like, shape $\left(\text{ip}\right)$

If $orig=1$ and $iscale\ne -1$, the scalings of predictor variables in the model as returned from either pls_svd() or pls_wold(); otherwise $xstd$ is not referenced.

ystdfloat, array-like, shape $\left(\text{my}\right)$

If $orig=1$ and $iscale\ne -1$, the scalings of response variables as returned from either pls_svd() or pls_wold(); otherwise $ystd$ is not referenced.

vipoptint

A flag that determines variable influence on projections (VIP) options.

$vipopt=0$

VIP are not calculated.

$vipopt=1$

VIP are calculated for predictor variables using the mean explained variance in responses.

$vipopt=\text{my}$

VIP are calculated for predictor variables for each response variable in the model.

Note that setting $vipopt=\text{my}$ when $\text{my}=1$ gives the same result as setting $vipopt=1$ directly.

ycvfloat, array-like, shape $(:,\text{my})$

Note: the required extent for this argument in dimension 1 is determined as follows: if $vipopt\ne 0$: $nfact$; otherwise: $0$.

If $vipopt\ne 0$, $ycv[\text{i}-1,\text{j}-1]$ is the cumulative percentage of variance of the $\text{j}$th response variable explained by the first $\text{i}$ factors, for $\text{j}=1,2,\dots ,\text{my}$, for $\text{i}=1,2,\dots ,nfact$; otherwise $ycv$ is not referenced.

Returns

bfloat, ndarray, shape $(\text{ip},\text{my})$

$b[\text{i}-1,\text{j}-1]$ contains the parameter estimate for the $\text{i}$th predictor variable in the model for the $\text{j}$th response variable, for $\text{j}=1,2,\dots ,\text{my}$, for $\text{i}=1,2,\dots ,\text{ip}$.

obfloat, ndarray, shape $(:,\text{my})$

If $orig=1$, $ob[0,\text{j}-1]$ contains the intercept value for the $\text{j}$th response variable, and $ob[\text{i},\text{j}-1]$ contains the parameter estimate on the original scale for the $\text{i}$th predictor variable in the model, for $\text{j}=1,2,\dots ,\text{my}$, for $\text{i}=1,2,\dots ,\text{ip}$. Otherwise $ob$ is not referenced.

vipfloat, ndarray, shape $(:,vipopt)$

If $vipopt=1$, $vip[\text{i}-1,0]$ contains the VIP statistic for the $\text{i}$th predictor variable in the model for all response variables, for $\text{i}=1,2,\dots ,\text{ip}$.

If $vipopt=\text{my}$, $vip[\text{i}-1,\text{j}-1]$ contains the VIP statistic for the $\text{i}$th predictor variable in the model for the $\text{j}$th response variable, for $\text{j}=1,2,\dots ,\text{my}$, for $\text{i}=1,2,\dots ,\text{ip}$.

Otherwise $vip$ is not referenced.

Raises

NagValueError

(errno $1$)

On entry, $\text{ip}=⟨value⟩$.

Constraint: $\text{ip}>1$.

(errno $1$)

On entry, $\text{my}=⟨value⟩$.

Constraint: $\text{my}\ge 1$.

(errno $1$)

On entry, $orig=⟨value⟩$.

Constraint: $orig=-1$ or $1$.

(errno $1$)

On entry, $iscale=⟨value⟩$.

Constraint: if $orig=1$, $iscale=-1$ or $1$.

(errno $1$)

On entry, $vipopt=⟨value⟩$ and $\text{my}=⟨value⟩$.

Constraint: $vipopt=0$, $1$ or $\text{my}$.

(errno $2$)

On entry, $\text{maxfac}=⟨value⟩$ and $\text{ip}=⟨value⟩$.

Constraint: $1\le \text{maxfac}\le \text{ip}$.

(errno $2$)

On entry, $nfact=⟨value⟩$ and $\text{maxfac}=⟨value⟩$.

Constraint: $1\le nfact\le \text{maxfac}$.

(errno $2$)

On entry, $\text{ldob}=⟨value⟩$ and $\text{ip}=⟨value⟩$.

Constraint: if $orig=1$, $\text{ldob}\ge \text{ip}+1$.

(errno $2$)

On entry, $\text{ldycv}=⟨value⟩$ and $nfact=⟨value⟩$.

Constraint: if $vipopt\ne 0$, $\text{ldycv}\ge nfact$.

(errno $2$)

On entry, $\text{ldvip}=⟨value⟩$ and $\text{ip}=⟨value⟩$.

Constraint: if $vipopt\ne 0$, $\text{ldvip}\ge \text{ip}$.

Notes

The parameter estimates $B$ for a $l$-factor orthogonal scores PLS model with $m$ predictor variables and $r$ response variables are given by,

$$B=W{\left(P^{T}W\right)}^{-1}{C}^T\text{,}B\in R^{m\times r}\text{,}$$

where $W$ is the $m\times k$ ($\ge l$) matrix of $x$-weights; $P$ is the $m\times k$ matrix of $x$-loadings; and $C$ is the $r\times k$ matrix of $y$-loadings for a fitted PLS model.

The parameter estimates $B$ are for centred, and possibly scaled, predictor data $X_1$ and response data $Y_1$. Parameter estimates may also be given for the predictor data $X$ and response data $Y$.

Optionally, pls_fit will calculate variable influence on projection (VIP) statistics, see Wold (1994).

References

Wold, S, 1994, PLS for multivariate linear modelling QSAR: chemometric methods in molecular design, Methods and Principles in Medicinal Chemistry, (ed van de Waterbeemd H), Verlag-Chemie

See also

naginterfaces.library.examples.correg.pls_ex.main()