pls: Partial Least Squares regression

In mdatools: Multivariate Data Analysis for Chemometrics

Partial Least Squares regression

Description

pls is used to calibrate, validate and use of partial least squares (PLS) regression model.

Usage

pls(
  x,
  y,
  ncomp = min(nrow(x) - 1, ncol(x), 20),
  center = TRUE,
  scale = FALSE,
  cv = NULL,
  exclcols = NULL,
  exclrows = NULL,
  x.test = NULL,
  y.test = NULL,
  method = "simpls",
  info = "",
  ncomp.selcrit = "min",
  lim.type = "ddmoments",
  alpha = 0.05,
  gamma = 0.01,
  cv.scope = "local"
)

Arguments

x	matrix with predictors.
y	matrix with responses.
ncomp	maximum number of components to calculate.
center	logical, center or not predictors and response values.
scale	logical, scale (standardize) or not predictors and response values.
cv	cross-validation settings (see details).
exclcols	columns of x to be excluded from calculations (numbers, names or vector with logical values)
exclrows	rows to be excluded from calculations (numbers, names or vector with logical values)
x.test	matrix with predictors for test set.
y.test	matrix with responses for test set.
method	algorithm for computing PLS model (only 'simpls' is supported so far)
info	short text with information about the model.
ncomp.selcrit	criterion for selecting optimal number of components ('min' for first local minimum of RMSECV and 'wold' for Wold's rule.)
lim.type	which method to use for calculation of critical limits for residual distances (see details)
alpha	significance level for extreme limits for T2 and Q disances.
gamma	significance level for outlier limits for T2 and Q distances.
cv.scope	scope for center/scale operations inside CV loop: 'global' — using globally computed mean and std or 'local' — recompute new for each local calibration set.

Details

So far only SIMPLS method [1] is available. Implementation works both with one and multiple response variables.

Like in pca, pls uses number of components (ncomp) as a minimum of number of objects - 1, number of x variables and the default or provided value. Regression coefficients, predictions and other results are calculated for each set of components from 1 to ncomp: 1, 1:2, 1:3, etc. The optimal number of components, (ncomp.selected), is found using first local minumum, but can be also forced to user defined value using function (selectCompNum.pls). The selected optimal number of components is used for all default operations - predictions, plots, etc.

Cross-validation settings, cv, can be a number or a list. If cv is a number, it will be used as a number of segments for random cross-validation (if cv = 1, full cross-validation will be preformed). If it is a list, the following syntax can be used: cv = list("rand", nseg, nrep) for random repeated cross-validation with nseg segments and nrep repetitions or cv = list("ven", nseg) for systematic splits to nseg segments ('venetian blinds').

Calculation of confidence intervals and p-values for regression coefficients can by done based on Jack-Knifing resampling. This is done automatically if cross-validation is used. However it is recommended to use at least 10 segments for stable JK result. See help for regcoeffs objects for more details.

Value

Returns an object of pls class with following fields:

ncomp	number of components included to the model.
ncomp.selected	selected (optimal) number of components.
xcenter	vector with values used to center the predictors (x).
ycenter	vector with values used to center the responses (y).
xscale	vector with values used to scale the predictors (x).
yscale	vector with values used to scale the responses (y).
xloadings	matrix with loading values for x decomposition.
yloadings	matrix with loading values for y decomposition.
xeigenvals	vector with eigenvalues of components (variance of x-scores).
yeigenvals	vector with eigenvalues of components (variance of y-scores).
weights	matrix with PLS weights.
coeffs	object of class regcoeffs with regression coefficients calculated for each component.
info	information about the model, provided by user when build the model.
cv	information cross-validation method used (if any).
res	a list with result objects (e.g. calibration, cv, etc.)

Author(s)

Sergey Kucheryavskiy ([e-mail])

References

1. S. de Jong, Chemometrics and Intelligent Laboratory Systems 18 (1993) 251-263. 2. Tarja Rajalahti et al. Chemometrics and Laboratory Systems, 95 (2009), 35-48. 3. Il-Gyo Chong, Chi-Hyuck Jun. Chemometrics and Laboratory Systems, 78 (2005), 103-112.

See Also

Main methods for pls objects:

print	prints information about a pls object.
summary.pls	shows performance statistics for the model.
plot.pls	shows plot overview of the model.
pls.simpls	implementation of SIMPLS algorithm.
predict.pls	applies PLS model to a new data.
selectCompNum.pls	set number of optimal components in the model.
setDistanceLimits.pls	allows to change parameters for critical limits.
categorize.pls	categorize data rows similar to categorize.pca.
selratio	computes matrix with selectivity ratio values.
vipscores	computes matrix with VIP scores values.

Plotting methods for pls objects:

plotXScores.pls	shows scores plot for x decomposition.
plotXYScores.pls	shows scores plot for x and y decomposition.
plotXLoadings.pls	shows loadings plot for x decomposition.
plotXYLoadings.pls	shows loadings plot for x and y decomposition.
plotXVariance.pls	shows explained variance plot for x decomposition.
plotYVariance.pls	shows explained variance plot for y decomposition.
plotXCumVariance.pls	shows cumulative explained variance plot for y decomposition.
plotYCumVariance.pls	shows cumulative explained variance plot for y decomposition.
plotXResiduals.pls	shows distance/residuals plot for x decomposition.
plotXYResiduals.pls	shows joint distance plot for x and y decomposition.
plotWeights.pls	shows plot with weights.
plotSelectivityRatio.pls	shows plot with selectivity ratio values.
plotVIPScores.pls	shows plot with VIP scores values.

Methods inherited from regmodel object (parent class for pls):

plotPredictions.regmodel	shows predicted vs. measured plot.
plotRMSE.regmodel	shows RMSE plot.
plotRMSERatio.regmodel	shows plot for ratio RMSECV/RMSEC values.
plotYResiduals.regmodel	shows residuals plot for y values.
getRegcoeffs.regmodel	returns matrix with regression coefficients.

Most of the methods for plotting data (except loadings and regression coefficients) are also available for PLS results (plsres) objects. There is also a randomization test for PLS-regression (randtest) and implementation of interval PLS algorithm for variable selection (ipls)

Examples

### Examples of using PLS model class
library(mdatools)

## 1. Make a PLS model for concentration of first component
## using full-cross validation and automatic detection of
## optimal number of components and show an overview

data(simdata)
x = simdata$spectra.c
y = simdata$conc.c[, 1]

model = pls(x, y, ncomp = 8, cv = 1)
summary(model)
plot(model)

## 2. Make a PLS model for concentration of first component
## using test set and 10 segment cross-validation and show overview

data(simdata)
x = simdata$spectra.c
y = simdata$conc.c[, 1]
x.t = simdata$spectra.t
y.t = simdata$conc.t[, 1]

model = pls(x, y, ncomp = 8, cv = 10, x.test = x.t, y.test = y.t)
model = selectCompNum(model, 2)
summary(model)
plot(model)

## 3. Make a PLS model for concentration of first component
## using only test set validation and show overview

data(simdata)
x = simdata$spectra.c
y = simdata$conc.c[, 1]
x.t = simdata$spectra.t
y.t = simdata$conc.t[, 1]

model = pls(x, y, ncomp = 6, x.test = x.t, y.test = y.t)
model = selectCompNum(model, 2)
summary(model)
plot(model)

## 4. Show variance and error plots for a PLS model
par(mfrow = c(2, 2))
plotXCumVariance(model, type = 'h')
plotYCumVariance(model, type = 'b', show.labels = TRUE, legend.position = 'bottomright')
plotRMSE(model)
plotRMSE(model, type = 'h', show.labels = TRUE)
par(mfrow = c(1, 1))

## 5. Show scores plots for a PLS model
par(mfrow = c(2, 2))
plotXScores(model)
plotXScores(model, comp = c(1, 3), show.labels = TRUE)
plotXYScores(model)
plotXYScores(model, comp = 2, show.labels = TRUE)
par(mfrow = c(1, 1))

## 6. Show loadings and coefficients plots for a PLS model
par(mfrow = c(2, 2))
plotXLoadings(model)
plotXLoadings(model, comp = c(1, 2), type = 'l')
plotXYLoadings(model, comp = c(1, 2), legend.position = 'topleft')
plotRegcoeffs(model)
par(mfrow = c(1, 1))

## 7. Show predictions and residuals plots for a PLS model
par(mfrow = c(2, 2))
plotXResiduals(model, show.label = TRUE)
plotYResiduals(model, show.label = TRUE)
plotPredictions(model)
plotPredictions(model, ncomp = 4, xlab = 'C, reference', ylab = 'C, predictions')
par(mfrow = c(1, 1))

## 8. Selectivity ratio and VIP scores plots
par(mfrow = c(2, 2))
plotSelectivityRatio(model)
plotSelectivityRatio(model, ncomp = 1)
par(mfrow = c(1, 1))

## 9. Variable selection with selectivity ratio
selratio = getSelectivityRatio(model)
selvar = !(selratio < 8)

xsel = x[, selvar]
modelsel = pls(xsel, y, ncomp = 6, cv = 1)
modelsel = selectCompNum(modelsel, 3)

summary(model)
summary(modelsel)

## 10. Calculate average spectrum and show the selected variables
i = 1:ncol(x)
ms = apply(x, 2, mean)

par(mfrow = c(2, 2))

plot(i, ms, type = 'p', pch = 16, col = 'red', main = 'Original variables')
plotPredictions(model)

plot(i, ms, type = 'p', pch = 16, col = 'lightgray', main = 'Selected variables')
points(i[selvar], ms[selvar], col = 'red', pch = 16)
plotPredictions(modelsel)

par(mfrow = c(1, 1))

mdatools documentation built on Sept. 11, 2024, 7:59 p.m.