MCR: Functions for Multivariate Curve Resolution
In ChemometricsWithR: Chemometrics with R - Multivariate Data Analysis in the Natural Sciences and Life Sciences

Description Usage Arguments Details Value Author(s) References Examples

Multivariate Curve Resolution, or MCR, decomposes a bilinear matrix into its pure components. A classical example is a matrix consisting of a series of spectral measurements on a mixture of chemicals for following the reaction. At every time point, a spectrum is measured that is a linear combination of the pure spectra. The goal of MCR is to resolve the pure spectra and concentration profiles over time.

mcr(x, init, what = c("row", "col"), convergence = 1e-08,
    maxit = 50)
opa(x, ncomp)
efa(x, ncomp)

`x`	Data matrix
`init`	Initial guess for pure compounds
`what`	Whether the pure compounds are rows or columns of the data matrix
`convergence`	Convergence criterion
`maxit`	Maximal number of iterations
`ncomp`	Number of pure compounds

MCR uses repeated application of least-squares regression to find pure profiles and spectra. The method is iterative; both EFA and OPA are methods to provide initial guesses.

Function mcr returns a list containing

`C`	An estimate of the pure "concentration profiles"
`S`	An estimate of the pure "spectra"
`resids`	The residuals of the final decomposition
`rms`	Root-mean-square values of the individual iterations

Function opa returns a list containing

`pure.compounds:`	A matrix containing `ncomp` pure compounds, usually spectra at specific time points
`selected:`	The wavelengths leading to the estimates of the pure concentration profiles

Function efa returns a list containing

`pure.compounds:`	A matrix containing `ncomp` pure compounds, usually concentration profiles at specific wavelengths
`forward:`	The development of the singular values of the reduced data matrix when increasing the number of columns in the forward direction
`backward:`	The development of the singular values of the reduced data matrix when increasing the number of columns in the backwarddirection

Usually, opa and efa are employed in opposite ways: if opa is used to find the "purest" row of a data matrix, one would typically employ efa to find the "purest" column, and vice versa.

Ron Wehrens

R. Wehrens. "Chemometrics with R - Multivariate Data Analysis in the Natural Sciences and Life Sciences". Springer, Heidelberg, 2011.

## Not run: 
if (require("ChemometricsWithRData")) {
  data(bdata, package = "ChemometricsWithRData")
  D1.efa <- efa(bdata$d1, 3)
  matplot(D1.efa$forward, type = "l")
  matplot(D1.efa$backward, type = "l")
  matplot(D1.efa$pure.comp, type = "l")

  D1.opa <- opa(bdata$d1, 3)
  matplot(D1.opa$pure.comp, type = "l")

  D1.mcr.efa <- mcr(bdata$d1, D1.efa$pure.comp, what = "col")
  matplot(D1.mcr.efa$C, type = "l", main = "Concentration profiles")
  matplot(t(D1.mcr.efa$S), type = "l", main = "Pure spectra")
  }

## End(Not run)

Attaching package: 'ChemometricsWithR'

The following objects are masked from 'package:stats':

    loadings, screeplot

Loading required package: ChemometricsWithRData
Warning message:
In library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE,  :
  there is no package called 'ChemometricsWithRData'