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Talanta 74 (2008) 1201–1210

Application of multivariate curve resolution alternating least

squares (MCR-ALS) to the quantitative analysis of
pharmaceutical and agricultural samples
T. Azzouz, R. Tauler ∗
Department of Environmental Chemistry, IIQAB-CSIC, Jordi Girona 18, Barcelona 08034, Spain
Received 13 April 2007; received in revised form 13 August 2007; accepted 24 August 2007
Available online 30 August 2007

Abstract
Application of multivariate curve resolution alternating least squares (MCR-ALS), for the resolution and quantification of different analytes
in different type of pharmaceutical and agricultural samples is shown. In particular, MCR-ALS is applied first to the UV spectrophotometric
quantitative analysis of mixtures of commercial steroid drugs, and second to the near-infrared (NIR) spectrophotometric quantitative analysis of
humidity and protein contents in forage cereal samples. Quantitative results obtained by MCR-ALS are compared to those obtained using the well
established partial least squares regression (PLSR) multivariate calibration method.
© 2007 Published by Elsevier B.V.

Keywords: Forage analysis; NIR spectroscopy; MCR-ALS; PLSR

1. Introduction spectroscopic techniques. One of the best advantages of NIR

spectroscopy is the possibility of working in reflectance mode
In this work, direct quantitative spectrophotometric deter- and the use of fibre optical probe modules easily coupled to the
mination of mixtures of analytes in two types of samples is spectrophotometer. This allows measurements of solid and liq-
investigated. First, mixtures of pharmaceutical products in drug uid samples with little sample pretreatment, the implementation
samples are analyzed by UV–vis spectrophotometry. This tech- of continuous methodologies, the fast acquisition of spectra and
nique is a rapid and inexpensive analytical technique and as such the prediction of both physical and chemical parameters from
is highly suitable for control analyses of pharmaceutical prepa- the same sample. Near-infrared spectrophotometry (NIRS) is
rations. However, the lack of selectivity of UV–vis absorption a non-destructive technique, very fast and easy to implement,
measurements hinders its general application in the presence of without needing reagents and without wastes produced. Once
strongly overlapped absorption bands of the different sample calibrated, NIRS is simple to operate and it is well suited for
components. Pharmaceutical preparations are usually mixtures the determination of the major components in many types of
of the active principles and of various excipients absorbing samples, such as protein and water contents in food and for-
in the same spectral region. The development of multivariate age samples. Multivariate calibration methods like partial least
calibration methods based on the mathematical resolution of squares regression (PLSR) have been frequently used to extract
multivariate signals can allow their rapid resolution and quan- analytical information from UV–vis and NIR spectra.
tification. The second type of samples studied in this work are Since in general it is very difficult to have completely
forage (cereal) agricultural samples analyzed by near-infrared selective analytical signals for every analyte of interest in a
(NIR) spectroscopy. This technique has gained wider acceptance multicomponent sample, their physical separation by chromato-
in different fields, due to its advantages over other analytical graphic methods or by any other analytical separation methods,
or their mathematical resolution using chemometric methods
is a preliminary step necessary for their quantitative determi-
∗ Corresponding author. nation, especially in the analysis of complex natural samples.
E-mail address: rtaqam@iiqab.csic.es (R. Tauler). Apart from the well known multivariate calibration methods

0039-9140/$ – see front matter © 2007 Published by Elsevier B.V.

doi:10.1016/j.talanta.2007.08.024
1202 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210

like PLSR [1,2] other chemometric methods exist that allow for levonorgestrel between 3 and 20 mg/l. Etinilestradiol and lev-
the direct mathematical analysis of the different components in onorgestrel were analyzed in commercial drugs: Microgynon,
evolving mixture systems (Evolving Factor Analysis, EFA) [3], Neogynona and Triagynon (ochre and brown color). From 30
for the detection of the more selective variables (SIMPLISMA original drug samples, 20 were used as a calibration data set,
[4–6]) or for the resolution of the components simultaneously and the remaining samples were used as external validation data
present in a particular data window (Window Factor Analysis set.
method [7]). The multivariate curve resolution alternating least The procedure used to prepare the drug samples was the
squares (MCR-ALS) method proposed in this work [8–13] has following: for each drug around 20 tablets were weighted,
been shown to provide an improved resolution compared to other grinded and homogenized. Methanol was used as dissolvent.
methods and to allow quantitative determinations in the analy- Drug samples were placed in an ultrasounds bath and then
sis of complex mixtures using spectroscopic means. MCR-ALS centrifuged. UV–vis spectra were recorded, using methanol
has been applied to the study of complex industrial evolving as a blank. Concentrations of the two analytes in these drug
processes [14], to the investigation of multiequilibria systems samples were estimated by high performance of liquid chro-
using spectroscopic titrations (fluorescence, UV–vis absorption, matography (HPLC). Chromatographic determinations were
etc.) [15], to the resolution of multiple coeluted peaks in chro- performed using diode array UV–vis, Hewlett Packard detector.
matography [10], to the resolution and quantification of mixtures The column used is a reversed phase Spherisorb ODS-2 C18 col-
in flow injection analysis [16], to the resolution of the differ- umn (15 cm long × 0.4 cm i.d., 5 ␮m particle size) with a C18
ent components in kinetic reactions and processes [17], to the precolumn. The mobile phase composition used for the chro-
resolution of spectroscopic images [18], to multidimensional matographic determinations was acetonitril/H2 O (40/60) (v/v).
spectroscopy [19], to electrophoretic studies of amino acids [20], A flow rate of 1.2 ml/min was used.
to voltammetric studies of metal complexes [21–23], to studies
of conformational changes of polynucleotide [24] and protein 2.3. Forage samples
folding processes [25], and to the resolution and apportionment
of environmental sources of contamination [26]. In this work, Different analytes in Ray-Grass forage samples were deter-
the use of MCR-ALS is proposed for the quantitative determina- mined. The experimental procedure used before analyzing the
tion of mixtures of analytes using first order spectrophotometric Ray-Grass samples by means of NIR spectrophotometry was
data (UV–vis and NIR absorption spectrophotometric data). A rather simple: samples were grinded, milled, homogenized, put
correlation constraint introduced in a previous work for the anal- in a capsule and directly measured by NIR spectrophotometry.
ysis of mixtures of metal ions analyzed by voltammetry [22] is Spectra from 125 samples were selected randomly for calibra-
extended in this work to establish alternating least squares (ALS) tion, and spectra from other 46 samples were used for validation.
multivariate calibration models for the quantitative determina- Calibration samples were selected randomly trying to cover all
tion of analyte mixtures using UV and NIR spectrophotometric the observed spectral data variance. If one of the selected vali-
data. The results obtained using MCR-ALS with this new cor- dation samples resulted to be outside of the range covered by the
relation constraint are then compared to those obtained using calibration samples, it was exchanged by a calibration sample
the nowadays well established PLSR multivariate calibration within the calibration range.
[37]. Humidity reference concentrations were estimated from the
sample weight loss after oven drying at 103 ◦ C for 4 h [27]. Some
2. Experimental volatile compounds apart from water could evaporate decreas-
ing sample total weight and causing excess errors, while other
2.1. Reagents and solutions compounds may be oxidized, increasing the sample total weight
and causing defect errors. Weight errors will depend on the
The following reagents and solutions were used: compensation of these two effects. Protein reference concen-
trations have been estimated from nitrogen content analyzed
- Acetonitril (Carlo Erba) for HPLC. using Kjeldhal method [28,29] and multiplied by a factor equals
- Methanol (Panreac) was used for the synthetic preparation of to 6.25 (which is derived from the fact that proteins of for-
standard, synthetic mixture and drug samples. ages have an average content of nitrogen equals approximately
- Etinilestradiol (Sigma), minimum 98% (HPLC). to 15%). The humidity concentration range was between 4.86
- Levonorgestrel (Sigma), minimum 98% (HPLC). and 13.33% (w/w), and for protein between 6.53 and 21.70%
(w/w).
2.2. Pharmaceutical products
2.4. Instrumentation
Concentrated stock solutions of etinilestradiol and lev-
onorgestrel were prepared in methanol. From these stock UV–vis spectrophotometric determinations were performed
solutions, 25 synthetic mixtures were prepared from which 15 by a Hewlett-Packard (Waldbronn, Germany) HP8452A diode
samples were used as a calibration data set, and the remaining array spectrophotometer. The instrument’s bundled software
samples were used as external validation data set. The concentra- HP 89530 MS-DOS UV–vis includes facilities for controlling,
tion range of etinilestradiol was between 3 and 31 mg/l, and for acquiring and processing spectra. In Fig. 1, the normalized
 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210 1203

Fig. 1. Spectra of etinilestradiol and levonorgestrel analytes (left) and spectra of a synthetic mixture of them and of Microgynon and Neogynona drugs (right).

experimental spectra of etinilestradiol and levonorgestrel are concentration profiles of the different K analytes presents in the
presented (left), as well as spectra of the synthetic and com- samples; ST (K,J) is the spectra matrix, whose K rows contain the
mercial drug mixtures of them (right). pure spectra associate with the K species present in the samples;
E(I,J) is the matrix associated to the experimental error. The
- Ultrasounds Bath, Selecta 0.61. resolution of experimental spectral data matrix D consists of the
- Centrifuge, Arlesa model Digicen. following steps, which are summarized in Fig. 3.
- NIR spectrophotometric determinations were performed To initiate the iterative ALS procedure, an initial estimation is
using NIRSystems 6500 FOSS spectrophotometer. Each of needed for the spectral or concentration profiles for each species.
the spectra finally considered is an average of 32 diffuse Different methods are used for this purpose like evolving fac-
reflectance spectra. Sample containers were rectangular cups. tor analysis [1–3] or the determination of the purest variables
The wavelength interval was 1100–2500 nm with 2 nm resolu- [4–6]. In this work, initial estimations based on purest variables
tion. In Fig. 2, the obtained spectra of Ray-Grass samples are were preferred. If the initial estimations are the spectral profiles,
shown. Laboratory temperatures were always kept between the unconstrained least squares solution for the concentration
20 and 25 ◦ C and relative humidity was always between 45 profiles can be calculated from the expression:
and 65%. +
C = D(ST ) (2)
3. Chemometric methods where (ST )+ is the pseudoinverse matrix of the spectra matrix
ST , which is equal to S(ST S)−1 , when ST is of full rank [31]. If
3.1. Multivariate curve resolution alternating least squares the initial estimations are the concentration profiles, the uncon-
(MCR-ALS) strained least squares solution for the spectra can be calculated

The first step of this chemometric data analysis procedure is

to build up the data matrix, D. In the rows of this data matrix are
the different individual spectra measured for the different ana-
lyzed samples and in the columns the absorbance (UV–vis) or
Log 1/R (NIRS) measured values at each spectral wavelength.
First a rough estimation of the possible number of components
is obtained using different methods like principal component
analysis (PCA) [2,5,13]. A bilinear relation between the exper-
imental data, the concentrations and the pure spectra of the
components is assumed, of analogous structure to the general-
ized law of Lambert–Beer [30], where the individual responses
of each analyte or component are additive. In matrix form, this
bilinear model is expressed in the following way:

D = CST + E (1)

where D(I,J) is the matrix of experimental data, of dimensions

I samples (spectra) by J wavelengths; C(I,K) is the matrix of Fig. 2. NIR spectra of Ray-Grass calibration samples.
1204 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210

calculations, a series of constraints with the purpose of giving

solutions with physical meaning and of limiting their possible
number are applied [11,12]. Iterations continue until an optimal
solution is obtained that fulfils the constraints postulated and
the established convergence criteria. Constraints applied in this
work are only described briefly.

3.1.1. Nonnegativity concentration constraint

This is a general constraint used in curve resolution methods
[32–36]. It is applied to the concentration profiles, due to the
fact that the concentrations of the chemical species are always
positive values or zero.

3.1.2. Nonnegativity spectra constraint

The application of this constraint depends on what instru-
mental technique is used for detection. In the case of UV–vis or
Fig. 3. Scheme of step of the resolution process in MCR-ALS method. See NIR spectra, the intensity of the radiation absorbed or reflected
Section 3.1. by the sample never takes negative values.

from the expression: 3.1.3. Correlation constraint

+ This constraint has been introduced for the simultaneous
S =C D
T
(3)
quantitative analysis of mixtures of metal ions using voltammet-
where C+ is pseudoinverse of matrix C (C+ = (CT C)−1 CT , when ric analysis and it implies [22] the establishment of calibration
C is of full rank) [31]. Both steps can be implemented in an alter- models for MCR-ALS, to be used for the quantitative determi-
nating least squares cycle so that in each iteration new matrices nation of the analytes in the presence of unknown interferences.
of C and ST are then obtained. However, during these iterative In this work, this constraint is extended to quantitative analysis

Fig. 4. Detailed description of the correlation constraint. See Section 3.1.

 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210 1205

of spectral data in the simultaneous analysis of different analytes 3.3. Validation of results
in samples of increasing complexity, including forage samples.
This correlation constraint is explained in detail in Fig. 4, and In order to asses the quality of multivariate calibration models
it consists, of a series of steps performed during each iteration (from PLSR and MCR-ALS), it is convenient to do their vali-
of the ALS optimization. Concentrations of a particular analyte dation using new samples not used during the calibration step.
in calibration samples, ccal
ALS , obtained by ALS at each iteration In this work, external validation was performed using a set of
are correlated with previously known reference concentration independent samples, whose spectra were not used to build the
values of the analyte cref in these samples. A local linear model calibration model. From the whole original data set, a number of
between the values ccal ref
ALS and c , is then built up so that: representative samples were selected for the calibration set. The
remaining samples were then only used to validate the model.
cref = bccal
ALS + b0 + e
ref
(4) The following expressions were used to express the validation
results:
where, b and b0 are then the slope and offset values which better
fit ccal ref
ALS to c , obtained by least squares linear regression, and
eref is the error in the reference concentrations (not modeled) The Root mean square error of prediction (RMSEP)
corresponding concentration values of these calibration samples
calculated using this local model are: 
n
i=1 (ci − ĉi )2
cal
ĉ = bccal + b0 (5) RMSEP = (9)
ALS
n
And in order to predict the unknown concentration of the
analyte in the new prediction samples ĉunk , the equation used is: Standard error of prediction (SEP)
ĉunk = bcunk
ALS + b0 (6) 
n
i=1 (ci − ĉi − Bias)2
where b and b0 are the values obtained previously in the cal- SEP = (10)
ibration step from cref , and cunk n−1
ALS are the concentrations of the
samples predicted by ALS. Each ALS iteration is then com-
pleted after updating the obtained values of prediction (i.e., by Bias (is a meaning of systematic error)
unk
substitution of cunk
ALS by ĉ ).
n
i=1 (ci − ĉi )
3.2. Partial least squares regression (PLSR) Bias = (11)
n
PLSR method has been widely used in chemometrics to
In all these expressions, ci and ĉi are, respectively, the known
regression problems with highly correlated variables as it is often
and calculated analyte concentration in sample i, and n is the
encountered in spectroscopy [37,38]. This regression method is
total number of samples considered in the validation. Also in
based on a prediction model for the analyte concentration in the
order to evaluate the quality of the obtained results of the con-
samples using efficiently the information contained in both data
centrations predicted by the application of the MCR-ALS or
blocks, the spectroscopic data block (D matrix) and the concen-
PLS models, for a particular analyte using n samples, the rela-
trations data block (c vector). D and c were mean-centered prior
tive error in the predicted concentrations, in percentage (RE%),
to decomposition in factors. The PLSR algorithm selects succes-
was calculated as:
sive orthogonal factors that maximize the covariance between
spectra (D matrix) and analyte concentration (c vector). The 
n
i=1 (ci − ĉi )
objective of fitting a PLSR model, is to find a few number of 2
PLSR factors that explain most of the covariation between both RE (%) = 100 n 2 (12)
i=1 ci
data blocks. Briefly, PLSR decomposes D and c into factor scores
(T) and factor loadings (P and q) according to:
3.4. Chemometrics software
D = TPT + E (7)

c = Tq + f (8) Data processing and PLS calibration calculations were car-

ried out using commercial software packages: PLS Toolbox
where T is the scores matrix, PT and q are the matrix and vector software version 2.1 (Eigenvector research, WA, USA) in
loadings describing the variance in D and c, respectively, and E MATLAB computer and visualization environment (The Math-
and f are the residuals in D and c, respectively. This decompo- works, MA, USA), and UNSCRAMBLER software version 6.11
sition is performed simultaneously and in such a way that the (CAMO A/S, Trondheim, Norway, 1986–1997). Multivariate
first few factors should explain most of the covariation between curve resolution (MCR-ALS) has been implemented in MAT-
D and c. The remaining factors resemble noise and can thus be LAB and it is available in Internet. See Ref. [13] for further
ignored, hence the addition of residuals E and f. details.
1206 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210

4. Results and discussion Table 1

Figures of merit in the quantitative analysis of etinilestradiol and levonorgestrel
analytes in synthetic mixtures using UV spectrophotometry (at different wave-
4.1. MCR-ALS resolution and quantification of length ranges) and PLS and MCR-ALS multivariate calibration methods
etinilestradiol and levonorgestrel steroids on commercial
drugs analyzed by UV spectrophotometry RMSEP SEP Bias RE (%) r2

Etinilestradiol
MCR-ALS has been applied first to synthetic experimental 220–300 nm
mixture samples for the resolution and quantification of steroids. ALS 0.738 0.486 0.581 3.316 0.9996
PLS 0.721 0.480 0.564 3.242 0.9996
Results were compared to those obtained by application of
PLSR. Different wavelength intervals were investigated. 230–300 nm
ALS 0.616 0.395 0.493 2.769 0.9997
In Fig. 1, spectral profiles obtained by MCR-ALS are given.
PLS 0.610 0.399 0.483 2.742 0.9997
They are in agreement with the spectra of etinilestradiol and
levonorgestrel pure standards. In contrast to MCR-ALS, PLS 250–300 nm
ALS 0.591 0.371 0.478 2.655 0.9994
regression does not provide direct estimation of the pure spec- PLS 0.645 0.383 0.536 2.897 0.9994
tra of the components of the mixture, although PLS loadings
Levonorgestrel
and weights may be interpreted in relation to the more rele-
220–300 nm
vant spectral features of the components present in the analyzed ALS 0.098 0.073 0.070 0.784 0.9999
mixtures, specially for those for which the quantitative analytic PLS 0.093 0.072 0.065 0.749 0.9999
information is available during the calibration step.
RMSEP is root mean square error of prediction (Eq. (9)); SEP is standard error
Quantitative results obtained by ALS and PLS methods for of prediction (Eq. (10)); Bias is a systematic error (Eq. (11)); r2 is coefficient
the different wavelength intervals are compared in Table 1. of correlation between calculated and actual concentration values of the ana-
Errors in Table 1 are obtained for external validation samples lyzed compounds; RE% is the relative error in the predicted concentrations, in
of synthetic mixtures. Number of components used in the cal- percentage (Eq. (12)). See text.
ibration model was two in both cases, either for etinilestradiol
or levonorgestrel. Constraints used in ALS optimization were In Table 2 (upper part), results of the quantification of
non-negativity (for concentration and spectra profiles) and the etinilestradiol and levonorgestrel steroids in Microgynon, com-
new correlation constraint proposed in this work. Quantifica- mercial drug are given. Quantification of etinilestradiol in
tion errors obtained by MCR-ALS are in all the cases of the Microgynon resulted to be better in the 250–300 nm wavelength
same order of magnitude than those obtained by application interval than in 220–300 nm range (see below), using three
of PLSR. Bias in the case of etinilestradiol is higher than the components, either for PLSR or MCR-ALS. Obtained errors
bias obtained for levonorgestrel, which might be due to the were of the same order for MCR-ALS and PLSR. These errors
lower concentrations used for this analyte in the mixtures. In were slightly higher than those obtained for synthetic mixtures,
the case of etinilestradiol the 230–300 nm interval gave the opti- which is reasonable, since in synthetic mixtures no excipient
mal quantification results and for levonorgestrel the best interval interferences were present. Also since etinilestradiol is a minor
was 220–300 nm. Once the wavelength interval was chosen for component, it was more affected by the presence of these inter-
the analysis of the two analytes in their synthetic mixtures, ferences. For levonorgestrel, rather good quantification results
commercial drugs were analyzed using the same conditions. were obtained at the same wavelength intervals than with syn-

Table 2
Figures of merit in the quantitative analysis of etinilestradiol and levonorgestrel analytes, in Microgynon, Neogynona and Triagynon (brown and ochre) commercial
drugs, using UV spectrophotometry (at different wavelength ranges) and PLS and MCR-ALS methods
Etinilestradiol (250–300 nm) Levonorgestrel (220–300 nm)

RMSEP SEP Bias RE (%) r2 RMSEP SEP Bias RE (%) r2

Microgynon
ALS 0.149 0.086 0.129 4.534 0.9919 0.284 0.279 0.150 1.723 0.9998
PLS 0.143 0.081 0.125 4.366 0.9931 0.282 0.278 0.146 1.706 0.9998
Neogynona
ALS 0.062 0.073 0.017 1.856 0.9963 0.184 0.226 0.002 1.007 0.9979
PLS 0.088 0.075 0.063 2.642 0.9964 0.200 0.229 −0.071 1.094 0.9980
Triagynon (brown)
ALS 0.439 0.304 −0.361 4.457 0.9907 0.685 0.522 −0.551 3.747 0.9947
PLS 0.422 0.289 −0.349 4.287 0.9906 0.704 0.528 −0.557 3.856 0.9936
Triagynon (ochre)
ALS 0.092 0.064 6.38é−2 2.909 0.9921 0.165 0.206 −3.21e−3 1.226 0.9970
PLS 0.124 0.071 1.09e−1 3.927 0.9873 0.159 0.181 −6.0ê−2 1.183 0.9986

See Table 1 for the meaning of RMSEP, SEP, bias, r2 and RE (%).
 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210 1207

thetic mixtures (220–300 nm), either using MCR-ALS or PLSR, better control of the factors that can influence these small dif-
using three components in each case. ferences. Nevertheless, it is possible to conclude that at least
In Table 2 (middle part), results in the quantification of the in the analysis of synthetic mixtures and in the analysis of the
same analytes in Neogynona drug are given. The optimal interval investigated commercial drugs, MCR-ALS provided quantita-
for the quantification of etinilestradiol in Neogynona commer- tive results of similar quality to those provided by the application
cial drug was the same than for the quantification of Microgynon of PLSR. The obvious advantage of MCR-ALS compared to
(250–300 nm). The use of the more restricted 250–300 nm spec- PLSR is, however, that MCR-ALS recovers the qualitative infor-
tral range for the analysis of these two commercial drugs instead mation as well, including the pure spectra of the components
of the 220–300 nm spectral range used during the analysis of the (Fig. 1), and also of the interferents, allowing their possible
synthetic mixtures was due to the presence of drug interferences identification/confirmation.
(excipient) that also absorb in the 220–250 nm spectral range.
The inclusion of the 220–250 range would affect negatively the 4.2. MCR-ALS resolution and quantification of humidity
quantification of etinilestradiol in the commercial drugs. So, and protein content on natural samples (Ray-Grass)
finally the 250–300 nm spectral range was considered to be the analyzed by NIR spectrophotometry
best one for the quantification of this analyte. Obtained errors
were of the same order for MCR-ALS and for PLSR, and a little NIR spectroscopy has been widely applied as an analyti-
higher than for the synthetic mixtures. For levonorgestrel also cal technique in the agricultural food sector, using partial least
a good quantification was obtained in the same wavelengths squares (PLS) to develop calibration equations for the determi-
interval than for synthetic mixtures (220–300 nm), either for nation of the humidity and protein content [39–41]. In this work,
MCR-ALS or for PLSR. The number of components used to MCR-ALS and PLS methods have been applied and compared
explain the model for each analyte, were in this case (like for in the analysis of natural Ray-Grass forage samples using NIR
Microgynon) three components, either for PLSR or MCR-ALS. spectrophotometry, with the purpose of obtaining both quali-
And finally, also in Table 2 (lower part), obtained results for tative and quantitative information of the humidity and protein
the quantification of the two steroids in Triagynon (brown and present in these samples. Obviously, in this case, difficulties for a
ochre color), using MCR-ALS and PLS are also given. Optimal proper calibration will be more important because of the larger
wavelength interval for the quantification of etinilestradiol in contribution of unknown physical contributions and chemical
Triagynon (ochre and brown color pills) was at 250–300 nm, interferents in the measured NIR spectra of the analyzed forage
and obtained errors were of the same order for MCR-ALS and samples. This example will probably illustrate the limits of the
for PLSR. For levonorgestrel, the optimal quantification was use of the proposed MCR-ALS method for quantitative determi-
obtained in the wavelength interval of 230–300 nm, either for nations of natural samples using first order spectrophotometric
MCR-ALS or for PLSR. The number of components used to data. Comparison of MCR-ALS results with PLSR results is per-
explain the model, for each analyte, was again three components, tinent since this is a much extended method used for calibration
either for PLSR or for MCR-ALS. of NIR spectrophotometric data [37].
Differences observed in the results obtained in all cases by In Table 3, obtained results in the quantification of humidity
application of MCR-ALS or PLSR were considered to be little and protein in Ray-Grass forage samples using NIR spectropho-
significant. A deeper interpretation of these small differences tometric data and MCR-ALS and PLS are given. A summary of
would require the study of a larger number of samples with a prediction errors for these two analytes, using different number

Table 3
Figures of merit in the quantitative analysis of humidity and protein analytes in Ray-Grass samples using NIR spectrophotometry and PLS and MCR-ALS methods
Number of factors RMSEP SEP Bias r2 RE (%)

ALS PLS ALS PLS ALS PLS ALS PLS ALS PLS

Humidity
5 0.391 0.313 0.370 0.316 0.045 0.008 0.962 0.973 4.383 3.721
6 0.369 0.301 0.370 0.305 0.046 0.009 0.962 0.975 4.387 3.585
7 0.358 0.307 0.360 0.311 0.043 0.006 0.964 0.974 4.260 3.654
8 0.361 0.289 0.363 0.292 0.030 0.008 0.963 0.977 4.287 3.432
9 0.285 0.313 0.289 0.313 0.004 0.004 0.977 0.973 3.394 3.724
10 0.286 0.269 0.290 0.268 −0.005 0.004 0.977 0.980 3.406 3.199
Protein
5 1.286 0.789 1.300 0.797 0.013 0.026 0.957 0.984 7.656 4.695
6 0.808 0.724 0.816 0.730 0.046 0.061 0.983 0.986 4.813 4.314
7 0.841 0.623 0.850 0.628 0.002 0.049 0.982 0.990 5.008 3.711
8 0.871 0.560 0.880 0.555 0.003 0.011 0.980 0.992 5.184 3.334
9 0.973 0.559 0.981 0.559 0.074 0.083 0.976 0.992 5.792 3.327
10 0.748 0.559 0.755 0.560 0.050 0.070 0.986 0.992 4.45 3.327

See Table 1 for the meaning of RMSEP, SEP, Bias, r2 and RE (%).
1208 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210

of factors for PLS and MCR-ALS are given. The optimal num- factors for PLS and six factors for MCR-ALS. Prediction errors
ber of components was selected in each case by considering the (RMSEP) were 0.560 and 0.808 for PLS and MCR-ALS, respec-
minimal RMSEP values. Errors in Table 3 are calculated for tively. In this case, PLSR clearly outperformed MCR-ALS. This
external validation samples. In the case of the PLSR method, improvement was probably due to the possibility to incorporate
results shown in Table 3 correspond to the application of the a larger number of components in PLSR models compared to
model to mean centered spectra. And in the case of the MCR- MCR-ALS models. MCR-ALS could not resolve more compo-
ALS, results shown in Table 3 correspond to data without any nents as PLSR for a better quantification of protein because of the
data pretreatment. Constraints applied during the ALS optimiza- intrinsic difficulties resolving minor components by MCR-ALS,
tion were non-negativity (for concentration and spectra profiles) whereas they could still have some effect improving quantitative
and the new correlation constraint discussed in this work. estimations in PLSR. On the other hand, if RMSEP values are
According to results shown in Table 3, it is difficult to decide compared using the same number of factors, for PLS and MCR-
about the optimal number of components for the determination ALS, some differences in the prediction error results are always
of humidity. Whereas in the determination of humidity by PLS, encountered which can be due to the fact that PLS, maximizes
six components gave a first minimum of RMSEP (0.301) and of relevant information in the first factors, and fits better calibration
relative error RE (%) (3.58) in the case of MCR-ALS, seven com- and validation data. In Fig. 5, regression of humidity and protein
ponents were needed from RMSEP (0.358) and RE% (4.26%) contents predicted by MCR-ALS and PLS versus the concen-
values. This first selection of components should be considered tration reference values, using the optimal number of factors in
rather parsimonious since lower RMSEP and RE% values could each case, are given. In caption of Fig. 5 results of the elliptic
still be obtained (Table 3) if a larger number of components joint confidence region F test [42] for the slope and the intercept
were considered, for both PLS and ALS. However, since these of these regressions are given. This test considers that if no sys-
differences were not large, this first selection estimation was tematic errors are present, the theoretical point intercept should
considered good enough for the purposes of this comparative be zero and the theoretical slope should be equal to one and that
work. For protein, the best number of components was eight their uncertainties should be located inside the corresponding

Fig. 5. Humidity and protein concentrations values predicted by MCR-ALS and PLS models vs. concentration reference values in validation samples. (a) Humidity
values predicted by MCR-ALS vs. their reference values (F = 0.18, α = 0.91), (b) humidity predicted values by PLSR vs. their reference values (F = 0.24, α = 0.87),
(c) protein predicted values by MCR-ALS vs. reference values of protein (F = 0.43, ␣=0.73), (d) protein predicted values by PLSR versus reference values of protein
(F = 2.06, α = 0.12). In parenthesis, calculated F values and significance levels for the regression slope and offset confidence region test (see Ref. [42]) are given.
Tabulated F value at the same degrees of freedom (ν1 = 2 + 1 = 3 and ν2 = 46 − 2 − 1 = 43) and α = 0.05 significance level is F = 2.82.
 T. Azzouz, R. Tauler / Talanta 74 (2008) 1201–1210 1209

Fig. 6. Pure spectra of moisture and protein estimated by MCR-ALS (two top plots) and the same pure spectra of moisture and protein taken from the literature [43].

elliptic joint confidence region. In all cases, F test confirmed the in general comparable to the results obtained using PLSR cal-
adequacy of the postulated models. ibration approaches. The main advantage of using MCR-ALS
Nevertheless and in general, the determination of humidity instead of PLSR is, however, the simultaneous recovery of qual-
and protein in Ray-Grass forage samples using MCR-ALS were itative information (spectra confirmation) about the analyte and
also rather good and close to the optimal ones obtained by PLSR. possible unknown intereferents. In this work, we have presented
This is especially relevant if it is taken into account the intrin- a preliminary contribution to this problem and further work is
sic difficulties inherent to MCR-ALS to properly resolve and needed to confirm the results here obtained.
quantificate components contributing very little to the measured
spectroscopic signal and also to the fact that neither sample References
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