Jou nal P e-p oo
Impac o he p e ea men o ATR-FTIR signals on he igu es o me i when PLS is
used
C. Mas, L. Rubio, L. Val e de-Som, L.A. Sa abia, M.C. O iz
PII: S0169-7439(19)30816-0
DOI: h ps://doi.o g/10.1016/j.chemolab.2020.104006
Re e ence: CHEMOM 104006
To appea in: Chemome ics and In elligen Labo a o y Sys ems
Recei ed Da e: 13 Decembe 2019
Re ised Da e: 17 Ma ch 2020
Accep ed Da e: 19 Ma ch 2020
Please ci e his a icle as: C. Mas, L. Rubio, L. Val e de-Som, L.A. Sa abia, M.C. O iz, Impac o
he p e ea men o ATR-FTIR signals on he igu es o me i when PLS is used, Chemome ics and
In elligen Labo a o y Sys ems (2020), doi: h ps://doi.o g/10.1016/j.chemolab.2020.104006.
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C edi Au ho S a emen :
C. Mas: Analy ical me hodology
L. Rubio: In es iga ion, Analy ical Me hodology W i ing - O iginal D a , W i ing,
Supe ision
L. Val e de-Som: In es iga ion, Analy ical Me hodology, Supe ision, W i ing - Re iew
& Edi ing
L.A. Sa abia Concep ualiza ion, Me hodology,Fo mal analysis, So wa e, Supe ision,
W i ing - Re iew & Edi ing
M.C. O iz: Concep ualiza ion, Supe ision, W i ing - Re iew & Edi ing
1
IMPACT OF THE PRETREATMENT OF ATR-FTIR SIGNALS ON
THE FIGURES OF MERIT WHEN PLS IS USED
C. Mas
a
, L. Rubio
a
, L. Val e de-Som
a
, L.A. Sa abia
b
, M.C. O iz
a,1
a
Depa men o Chemis y,
b
Depa men o Ma hema ics and Compu a ion
Facul y o Sciences, Uni e sidad de Bu gos
Plaza Misael Bañuelos s/n, 09001 Bu gos (Spain)
Abb e ia ions
2
Abs ac
The e iciency o he analy ical me hods based on ib a ional spec oscopy has been
widely e i ied in a high numbe o publica ions. In addi ion, i has been ecognized ha
he p e ea men o he o iginal signals is absolu ely necessa y o ob ain enough quali y
in he subsequen classi ica ion and/o eg ession models. In ac , an inapp op ia e
p e ea men makes he esul s wo se. I is also impossible o gi e “a p io i” ules ha
gua an ee he adequacy o a p e ea men o speci ic da a.
The e ec o he p e ea men s is e alua ed h ough hei impac on he quali y o he
classi ica ion and /o eg ession models buil om hem due o he double dependence
(on he da a and on he pu pose o he analysis). The e ec o he p e ea men has been
e alua ed using pa ial leas squa es eg ession (PLSR) in some wo ks and he oo
mean squa es in p edic ion o in c oss- alida ion has been always used as a c i e ion o
e alua e he eg ession in all hese cases. Howe e , i seems app op ia e o use quali y
c i e ia o he calib a ion o he analy ical me hod h ough he igu es o me i : he
signi icance o he eg ession, he absence o cons an o p opo ional bias, he esidual
s anda d de ia ion, he mean o he absolu e alues o he ela i e e o s and he
capabili y o de ec ion.
In his wo k, he use o hese analy ical c i e ia in a desi abili y unc ion is p oposed o
he i s ime wi h calib a ion da a o oxybenzone ob ained by ATR-FTIR and PLSR.
1
Co esponding au ho . Telephone numbe : +34-947-259571. E-mail add ess: mco [email protected]
(M.C. O iz).
2
A enua ed o al e lec ance-Fou ie ans o m in a ed (ATR-FTIR), oxybenzone (BP3),
capabili y o de ec ion (CCβ) da a p ep ocessing (DP), design o expe imen s (DoE), di ec
o hogonal signal co ec ion (DOSC), ex ended mul iplica i e sca e co ec ion (EMSC),
in a ed (IR), la en a iable (LV), mul iplica i e sca e co ec ion (MSC), nea in a ed (NIR),
o hogonal signal co ec ion (OSC), pa ial leas squa es eg ession (PLSR), oo mean squa e
e o (RMSEC), oo mean squa e e o o c oss- alida ion (RMSEC_CV), S anda d e o in
p edic ion
(
SEP), s anda d no mal a ia e (SNV).
2
This desi abili y unc ion enables o choose he bes p e ea men among he 39
possibili ies s udied. In addi ion, i is shown ha he same op imum is no ob ained i
he minimum o RMSEC_CV is conside ed as a c i e ion.
Keywo ds
P e ea men da a; ATR-FTIR; PLS; oxybenzone; desi abili y unc ion; igu es o me i
1. In oduc ion
Da a p ep ocessing (DP) has been ecognized as a c i ical s age o high dimensional
da a analysis, pa icula ly o da a ob ained using ib a ional spec oscopy echniques.
The e a e a lo o scien i ic wo ks abou di e en DP me hods which can be classi ied in
wo la ge g oups: i) p e ea men by means o o hogonal p ojec ions o ex ac he
ele an in o ma ion o a aining se [1] using pu e spec a and in o ma ion ex ac ed
om expe imen al design and calib a ion da ase s ha includes he O hogonal Signal
Co ec ion (OSC) amily; ii) p e ea men by ans o ma ion o he spec al signal
emo ing undesi ed physical phenomena [2,3]. This las g oup can be di ided in o wo
ca ego ies. The i s one, sca e co ec ion, includes Mul iplica i e Sca e Co ec ion
(MSC), In e se MSC, Ex ended MSC (EMSC) [4,5], Ex ended In e se MSC,
no maliza ion, and S anda d No mal Va ia e (SNV). The second g oup belongs o he
spec al de i a iza ion g oup which includes he No is-Williams de i a i es and
Sa i zky-Golay polynomial de i a i es. The ela ion be ween MSC and SNV [6] has
been s udied because a e he p e ea men s mos employed in p ac ice, also hei e ec
on he signals [7] and he chemical in e p e abili y o p e ea ed spec a [8]. A he same
ime, he e a e di e en e iew a icles [5,9] and many u o ials ha ha e been
published o show he p ac ical aspec s o using DP, o example wi h nea in a ed
(NIR) [2], Raman and in a ed (IR) [3,5,10,11] o a enua ed o al e lec ance-Fou ie
ans o m in a ed (ATR-FTIR) [12] da a.
Howe e , despi e he emphasis on he impo ance o he p e ea men o spec a da a,
he e a e ew con ibu ions on he sea ch o he op imal p e ea men o a da a se . The
c i ical e ision o he mos common h ee s a egies used o he da a p e ea men
concludes ha "all h ee ha e se ious d awbacks: hey may be ime-consuming beyond
p ac icabili y o may p o ide misleading esul s" [13]. Then, i is necessa y o conside
join ly successi e ypes o p e ea men . Fo his eason, J. Engel e al. [13] ha e used a
sea ch space o med by 7x10x10x7 p e ea men s o baseline, sca e , noise, smoo hing
and scaling/ ans o ma ions, espec i ely. O he 7 p e ea men s a e added o OSC and
Di ec O hogonal Signal Co ec ion (DOSC). A simila s a egy includes binning,
smoo hing, no maliza ion and baseline co ec ion wi h 3528 di e en p e ea men s ha
could be pa ially pe mu ed [14]. In o he wo k, expe imen al design (DoE), speci ically
a ull ac o ial (2
4
), is used as a s a egy o explo e he e ec o hese same ypes o
p e ea men s [15]. In e e ence [16] his s a egy o p e ea men is linked wi h
3
a iable selec ion o imp o e he in e p e a ion and he p edic i e capaci y o a
eg ession model. On he o he hand, a ac o ial design 2
4
is used wi h h ee di e en
me hods applied in a iable selec ion o he ou p e ea men s selec ed in [17]. A D-
op imal design o op imize he p e ea men in h ee in e media e s ages is also used o
a me abolomic da a usion o u ine and se um in [18].
Many wo ks analyse o op imise he da a p e ea men be o e applying a classi ica ion
echnique. In gene al, a c i e ion o e alua e he classi ie (e.g. he % o
misclassi ica ion) is used. Only H.J. Bu le e al. [14] used se e al c i e ia combined
addi i ely in one unique alue.
The need o ca ying ou a p e ea men o he spec a p o ided by ib a ional
spec oscopic echniques be o e applying a eg ession me hod, which is usually a Pa ial
Leas Squa es Reg ession (PLSR), is comple ely accep ed. In he li e a u e consul ed,
he e ec o changing he p e ea men is analysed h ough he change caused in he
PLSR quali y pa ame e s.
In his case, Roo Mean Squa e E o o P edic ion (RMSEP)
[15,17], Roo Mean Squa e E o o C oss-Valida ion (RMSEC_CV) [16] and a
es ima ion o Roo Mean Squa e E o (RMSEC) based on boo s ap [2] a e used. In
hese wo ks, he use o quali y c i e ia o an analy ical me hod e alua ed by means o
he eg ession “p edic ed concen a ion wi h PLSR e sus ue concen a ion o he es
sample”, which is named as he accu acy line in p edic ion, is no ackled. This wo k
p oposes o s udy he e ec o he p e ea men on he quali y pa ame e s o he PLSR
model and on he accu acy line in p edic ion by means o ATR-FTIR da a o he
de e mina ion o oxybenzone, benzophenone-3 (BP3). BP3 is an addi i e used in he
manu ac u e o sunsc een cosme ic c eams and i s de e mina ion by ATR-FTIR is
possible due o he amoun ound in c eams.
2. Ma e ial and me hods
2.1 Chemicals
2-hyd oxy-4-me hoxybenzophenone (oxybenzone, CAS no. 131-57-7, 98% pu i y) was
pu chased om Sigma-Ald ich (S einheim, Ge many).
E hanol (96% ol., CAS no. 64-17-5, HiPe Sol CHROMANORM®, g adien g ade o
HPLC) was supplied by VWR In e na ional (Radno , Pennsyl ania, USA) and ace one
(CAS no. 67-64-1) o liquid ch oma og aphy Lich osol ® was om Me ck KGaA
(Da ms ad , Ge many).
2.2 S anda d solu ions
A s ock solu ion o BP3 a 30275 mg L
-1
was p epa ed in e hanol and in e media e
solu ions a concen a ions o 5000, 10000, 15000 and 20000 mg L
-1
we e p epa ed
om ha s ock solu ion in e hanol as calib a ion s anda ds. All solu ions, whose

4
weigh s we e con olled o e i y ha he sol en had no e apo a ed, we e s o ed in
c imp ials a 4ºC and p o ec ed om ligh . The s abili y o he solu ions o BP3 has
been e i ied by GC/MS, being he s ock and in e media e solu ions o BP3 s able o
15 days as can be seen in e . [19].
2.3. Ins umen al
An Agilen Ca y 630 FTIR spec ome e coupled o a ZnSe ATR module o measu ing
liquids samples (Agilen Technologies, San a Cla a, CA, USA) was used o pe o m he
analyses. The numbe o e lec ions o he c ys al wi h his module was 5. The main
op ical uni dimensions we e only 16 × 22 × 13 cm. The Ca y 630 FTIR spec ome e
con ained a unique Michelson in e e ome e .
The spec al ange o collec he abso bance signal was om 650 o 4000 cm
-1
wi h 32
scans and he spec al esolu ion was ixed o 4 cm
-1
using Happ-Genzel as apodiza ion
unc ion [20]. The me hod gain was se a 255.
2.4. S eps o measu e he sample
Fi s , ai collec ion as backg ound was selec ed wi h 16 scans. The backg ound was
collec ed a he beginning o he sequence and i was no measu ed again be ween
samples. Then, a olume o 100 µL o he sample was pu on he c ys al. In his s ep,
he abso bance signal was collec ed. Finally, wo sol en s (e hanol and ace one) we e
used o clean he c ys al using delica e ask wipe s (Kimwipes®, om Sigma-Ald ich).
A olume o 100 µL o e hanol was pu on he c ys al and he signal was eco ded o
check i he c ys al was clean.
2.5. So wa e
Mic oLab PC, e sion 5.3.1748 (Agilen Technologies, Inc.) wi h Da a Analysis
so wa e was used o acqui ing da a. The di e en p e ea men s o he signals and
PLSR models we e pe o med wi h he PLS_Toolbox [21] used unde MATLAB
en i onmen [22]. The eg ession models we e i ed and alida ed using
STATGRAPHICS Cen u ion XVI [23]. Capabili y o de ec ion (CCβ) was calcula ed
using he DETARCHI p og am [24].
3. Calcula ions
3.1. Da a
A wide calib a ion ange and ew concen a ion le els we e used as in ou ine analyses.
The calib a ion se was made up o ou samples a concen a ions o 5000, 10000,
15000 and 20000 mg L
-1
o BP3 and a blank. The es se was made up o o he samples
o he same concen a ions o BP3 which we e p epa ed again and independen ly o he
calib a ion s anda ds. The ma ix dimensions in bo h cases a e 5×1798.
5
3.2. P e ea men
The in oduc ion sec ion desc ibed di e en da a p e ea men s. In his wo k, he mos
common da a p e ea men is chosen o ATR-FTIR spec oscopy da a wi h liquid
samples:
1) Mul iplica i e Sca e Co ec ion (MSC) o S anda d No mal Va ia e (SNV) o
co ec he sca e ing signal.
2) Sa i zky-Golay smoo hing (SG) wi h windows o 15 (o 25) poin s, a second o de
polynomial and second de i a i e.
3) Mean cen e ing o Au oscaling o scale co ec ion.
In addi ion,
he possibili y o applying only one, wo o no co ec ion has been included.
Scaling is he only p e ea men o he h ee ones desc ibed abo e ha is no di ec ly
ela ed o he elimina ion o any signal a e ac . I scaling is used, i should be he las
s ep o he p e ea men because i s e ec is o uni y he s a is ical scale o he a iables
(mean and/o a iances). The e o e, i scaling is used p io o sca e co ec ion, he
scaling e ec will be pa ially a enua ed by he sca e co ec ion me hod. Howe e , he
o he wo s eps may be changed in o de . This may be impo an , e.g., he e ec o
exchanging he MSC and SG p e ea men s is checked in e . [25]. Table 1 shows he
code o he di e en p e ea men s used. By way o example, he code "253" means ha
SNV has been applied in he i s s ep, Sa i zky-Golay smoo hing wi h windows o 15
poin s in he second s ep, and Au oscaling in he las s ep. The code “141” means ha
no p e ea men has been pe o med. When he change o o de be ween sca e and
smoo hing is conside ed, duplica ion mus be a oided when one o hem is no applied.
By way o example, he p e ea men “153” (which means using he code o Table 1: do
no apply sca e co ec ion, SG wi h 15 poin s and au oscaling) would be he same
p e ea men as "513". The e o e, only a o al o 39 di e en p e ea men s ha e been
applied.
Gi en a se o spec a S
i
, i=1,.., n (e.g. a se o calib a ion samples), e . [6] shows ha
he e is a linea ela ionship be ween each spec um ans o med by SNV and he one
ans o med by MSC, al hough ha linea ela ionship is di e en o each S
i
.
The e o e, he p e ea ed spec a a e simila excep o a o a ion and an o se
co ec ion and i is gene ally assumed ha “MSC and SNV a e he same o he mos
p ac ical applica ions” [9,26] bu he esul s a e no always e y simila . Fea n e al. [7]
ob ained “ e y di e en esul s when NIR spec al da a we e p e- ea ed wi h SNV and
MSC, he o me leading o a s iking ellipsoidal s uc u e in a plo o p incipal
componen sco es and he la e o a plo wi h many ex eme ou lie s”. In addi ion, e .
[8] shows ha MSC (and o he p e ea men s o he same amily including non-linea
app oaches as EMSC) p oduces a shi along he signal p o ile which leads o a e ac s
in he p incipal componen analysis o he spec a. Bo h p e ea men s ha e been
included since he aim o his wo k is he analysis o he e ec o he p e ea men s on
6
he PLSR calib a ions and he e a e no compa a i e s udies in li e a u e abou he
di e ences caused by SNV and MSC in he igu es o me i .
<Table 1>
3.3. PLSR model
The PLSR model is buil wi h he aining da a se and each o he 39 di e en
p e ea men s. The numbe o la en a iables is he one ha p o ides he minimum
RMSEC_CV wi h lea e-one-ou as c oss- alida ion. Then, he model is applied o he
es se . In bo h cases, Ho elling's T
2
and Q- esidual s a is ic a a 95% con idence le el
a e used o check i he e is any ou lie .
No ou lie da a was ound in he buil models.
4. Resul s and discussion
4.1. E ec o he p e ea men on PLSR models
Table 2 shows all he p e ea men s wi h di e en in o ma ion abou he PLSR models.
The second column o his able indica es he numbe o la en a iables in he model,
whe eas oo mean squa e in calib a ion (RMSEC) and in c oss- alida ion
(RMSEC_CV) a e collec ed in he hi d and ou h columns, espec i ely. In addi ion,
s anda d e o in p edic ion (SEP) has been calcula ed.
<Table 2>
The p e ea men s wi h Sa i zky-Golay smoo hing wi h windows o 15 poin s and
wi hou scaling (codes 151, 251 and 351) show he g ea es alues o RMSEC_CV, SEP
and RMSEC. On he o he hand, he p e ea men s wi hou Sa i zky-Golay smoo hing
and no au oscaling (codes 342, 341, 241, 242, 142 and 141) show he lowes alues o
RMSEC_CV wi h alues be ween 2881.7 and 3002.9, bu in e media e alues o
RMSEC (be ween 900 and 1000). In hose cases, he selec ion o sca e co ec ion (1, 2
o 3 in he i s posi ion o he code) is indi e en . The e ec o no scaling o mean
cen e ing (1 o 2 in he hi d posi ion o he code) is e y small and i is only obse ed
when he sca e co ec ion is used, in which case mean cen e ing p o ides be e alues
o RMSEC, RMSEC_CV and SEP, bu inc eases ERROR, s
yx
, and CCβ. The absolu e
minimum is achie ed wi h a alue o 2881.7 o RMSEC_CV wi h he p e ea men 342.
4.2. E ec o he p e ea men on he igu es o me i o he analy ical me hod
In he scope o chemical analysis, i is impo an o alida e he calib a ion model o an
analy ical me hod as well as o ob ain he igu es o me i . The s a is ical p ocedu e o
his ask can be ound in e e ence [27]. I is in e es ing o know, h ough he PLSR
7
model, he impac on hese igu es o me i o e alua e he di e en p e ea men s
ca ied ou . Fi s , he PLSR model is buil ; hen, he eg ession line "p edic ed
concen a ion wi h PLSR e sus ue concen a ion o BP3" which is known as accu acy
line is alida ed. The es se samples o hese eg essions we e no used o build he
p e ious PLSR model.
Table 2 shows he pa ame e s o he accu acy lines in columns 6, 7, 8 and 9 such as he
co ela ion coe icien ( ), esidual s anda d de ia ion (s
yx
), in e cep (b
0
) and slope (b
1
),
espec i ely.
4.2.1. Signi icance o he accu acy line
The hypo hesis es o e alua e he signi icance o he accu acy line in ol es:
H
0
: he eg ession does no explain a a iance bigge han he esidual.
H
a
: he eg ession explains he a iabili y o he esponse, so he eg ession is
signi ican .
The null hypo hesis (H
0
) is ejec ed i he p- alue o es is lowe han 0.05, in which
case he al e na i e hypo hesis (H
a
) is accep ed. Table 2 shows he p- alues o he
signi icance es (p-s, column 10) which a e signi ican and H
0
is ejec ed. These esul s
a e cohe en wi h he co ela ion coe icien s which ha e alues be ween 0.96 and 1.00
(Table 2, column 6).
4.2.2. Bias o he accu acy line
The accu acy line should ha e he in e cep equal o ze o and he slope equal o one.
O he wise, he analy ical p ocedu e has cons an and/o p opo ional bias.
The hypo hesis es is he ollowing one (page 141 o e . [27]):
H
0
: in e cep and slope a e equal o ze o and one, espec i ely (b
0
=0 and b
1
=1).
H
a
: is no he case, he accu acy line is biased.
The null hypo hesis (H
0
) is ejec ed i he p- alue is lowe han 0.05, in which case he
al e na i e hypo hesis (H
a
) is accep ed. Table 2 shows he p- alues (p-F, column 11).
The nine p e ea men s wi h Sa i zky-Golay smoo hing wi h windows o 15 poin s (all
o hem ma ked wi h numbe 5 in he second posi ion o he code in PRET o Table 2)
show alues lowe han 0.05, he e o e, H
0
is ejec ed.
These p e ea men s (151, 152, 153, 251, 252, 253, 351, 352 and 353) a e no
conside ed accep able om an analy ical poin o iew; in addi ion, he g ea es alues
o RMSEC_CV and SEP a e among hem.
4.2.3. Rela i e e o
14
[26] T. Fea n, The e ec o spec al p e- ea men s on in e p e a ion, NIR News 20
(2009) 15.16. 15e16, h ps://doi.o g/10.1255/ni n.1146.
[27] M.C. O iz, M.S. Sánchez, L.A. Sa abia, Quali y o analy ical measu emen s:
uni a ia e eg ession, in: S.D. B own, R. Taule , B. Walczak (Eds.),
Comp ehensi e chemome ics. Chemical and biochemical da a analysis. Else ie ,
1, Ams e dam, 2009, pp. 127-169. h ps://doi.o g/10.1016/B978-044452701-
1.00091-0.
[28] In e na ional O ganiza ion o S anda diza ion, ISO 11843-1:1997, Capabili y o
de ec ion - Pa 1: Te ms and de ini ions, Genè e, Swi ze land, 1997.
[29] In e na ional O ganiza ion o S anda diza ion, ISO 11843-2:2000, Capabili y o
de ec ion – Pa 2: Me hodology in he linea calib a ion case, Genè e,
Swi ze land, 2000.
[30] J. Inczédy, T. Lengyel, A.M. U e, A. Gelencsé , A. Hulanicki, In e na ional Union
o Pu e and Applied Chemis y, IUPAC Compendium o analy ical nomencla u e,
hi d ed., Bal imo e, Po Ci y P ess Inc., 2000.
[31] G. De inge , R. Suich, Simul aneous op imiza ion o se e al esponse a iables,
J. Qual. Technol. 12 (1980) 214-219.
[32] M.C. O iz, L.A. Sa abia, M.S. Sánchez, Tu o ial on e alua ion o ype I and ype
II e o s in chemical analyses: F om he analy ical de ec ion o au hen ica ion o
p oduc s and p ocess con ol, Anal. Chim. Ac a 674 (2010) 123-142,
h ps://doi.o g/10.1016/j.aca.2010.06.026
[33] R.G. B e e on, The use and misuse o p alues and ela ed concep s, Chemom.
In ell. Lab. Sys . 195 (2019) 103884
h ps://doi.o g/10.1016/j.chemolab.2019.103884

15
FIGURE CAPTIONS
Figu e 1 Pa allel coo dina es plo o he alues o he quali y a iables o he
PLSR model and he accu acy line. The codi ica ion o a iables is he
same as in Table 2.
Figu e 2 P incipal componen analysis o he a iables RMSEC, RMSEC_CV,
SEP, , s
yx
, b
0
, b
1
, ERROR and CCβ o Table 2. A) Loadings on he i s
and second PC and B) loadings on he i s and hi d PC.
Table 1
P e ea men s and hei codi ica ion.
Code / Sca e co ec ion Code / Noise co ec ion Code / Scaling
1
No sca e co ec ion 4 No noise emo al 1 No scaling
2
SNV 5 S-G smoo hing, window 15 poin s 2 Mean cen e ing
3
MSC 6 S-G smoo hing, window 25 poin s 3 Au oscaling
SNV, S anda d No mal Va ia e; MSC, Mul iplica i e Sca e Co ec ion; S-G, Sa i zky-Golay.
Table 2
PLS models and accu acy line (see he p e ea men s codi ica ion in Table 1)
PRET L.V. RMSEC RMSEC_CV
SEP s
yx
b
0
b
1
p-s p-F ERROR
CCβ
141 3 994.02
3002.91 2422.31 0.9709 1703.7 4020 0.757 0.00590 0.118 24.4 12687
142 2 990.57
2967.13 2367.66 0.9705 1746.1 3976 0.770 0.00610 0.126 24.9 12790
143 2 1098.44
3487.76 1776.56 0.9853 1310.0 2755 0.827 0.00210 0.154 16.0 8928
151 2 1779.22
6266.01 4965.47 0.9650 943.3 7150 0.380 0.00780 0.004 38.1 13975
152 2 167.99
5684.47 3880.48 0.9747 1096.7 5884 0.524 0.00480 0.013 33.8 11796
153 2 89.47
4343.81 3089.47 0.9803 1160.6 4476 0.630 0.00330 0.031 22.0 10376
161 2 912.70
4717.50 2375.71 0.9806 1346.0 3334 0.738 0.00320 0.100 11.8 10279
162 1 660.33
4061.57 1734.71 0.9885 1146.9 2509 0.820 0.00150 0.141 12.8 7883
163 2 738.88
3751.92 2276.04 1.0000 63.7 0 1.000 0.00001 1.000 14.5 359
241 3 899.14
2889.14 2272.84 0.9766 1542.7 3795 0.767 0.00430 0.108 22.7 11331
242 2 900.19
2889.48 2271.66 0.9766 1541.8 3794 0.768 0.00430 0.108 22.7 11323
243 2 865.46
3864.61 2480.90 0.9686 1762.8 4225 0.753 0.00660 0.113 27.4 13202
251 2 1740.41
6257.89 4939.87 0.9666 927.7 7101 0.383 0.00730 0.004 37.8 13637
252 2 105.20
5974.19 4230.66 0.9734 1024.5 6322 0.477 0.00520 0.008 34.2 12113
253 2 84.07
4316.10 3148.11 0.9797 1163.6 4534 0.623 0.00350 0.030 22.1 10533
261 2 928.66
4726.40 2361.94 0.9807 1348.1 3310 0.740 0.00320 0.103 11.5 10265
262 1 811.85
4480.37 2033.53 0.9863 1189.3 2851 0.778 0.00190 0.109 11.3 8614
263 2 20.53
3759.02 2462.69 1.000 26.50
0 1.000 0.00001 1.000 15.3 88
341 3 899.52
2881.97 2273.51 0.9767 1539.4 3801 0.767 0.00430 0.107 22.7 11312
342 2 899.62
2881.71 2273.52 0.9767 1539.4 3801 0.767 0.00430 0.107 22.7 11312
343 2 790.41
3861.69 2408.57 0.9714 1692.4 4140 0.758 0.00580 0.107 27.3 12581
351 2 1743.09
6254.58 4943.96 0.9667 925.6 7112 0.383 0.00730 0.004 37.8 13626
352 2 113.70
5969.39 4236.79 0.9726 1038.6 6340 0.476 0.00540 0.008 34.4 12292
353 2 84.28
4308.06 3151.74 0.9798 1157.6 4554 0.622 0.00340 0.029 22.2 10490
361 2 919.48
4720.54 2363.63 0.9808 1343.9 3319 0.740 0.00320 0.101 11.5 10240
362 2 53.54
4535.90 2110.54 0.9889 3103.8 3102 0.759 0.00140 0.501 13.7 23062
363 2 721.44
3755.32 2461.20 1.0000 63.7 0 1.000 0.00001 1.000 15.4 359
521 3 36.13
6145.40 4518.96 0.9767 46.64
0 1.000 0.00001 1.000 34.2 263
522 2 36.29
6144.19 4519.84 0.9767 46.85
0 1.000 0.00001 1.000 34.3 264
523 2 84.34
4383.23 3070.23 0.9999 108.89
1 1.000 0.00001 1.000 22.5 614
621 2 1679.93
6227.64 4906.01 0.9714 2105.97
522 0.944 0.00580 0.917 37.1 12581
622 2 74.31
4859.11 2353.86 1.0000 15.63
0 1.000 0.00001 1.000 12.5 88
623 2 34.57
6144.32 3104.53 0.9999 108.74
1 1.000 0.00001 1.000 22.3 613
531 2 958.31
4742.01 2355.93 0.9908 1225.76
185 0.982 0.00110 0.974 11.1 7039
532 2 958.60
4742.02 2355.93 0.9908 1226.13
184 0.982 0.00110 0.974 11.1 7041
533 2 12.10
3788.33 2577.24 1.0000 15.62
0 1.000 0.00001 1.000 17.6 88
631 2 957.54
4741.76 2355.06 0.9908 1224.79
181 0.982 0.00110 0.974 11.1 7033
632 2 74.41
4850.72 2345.98 0.9999 96.06
1 1.000 0.00001 1.000 12.6 542
633 2 12.12
3779.46 2530.69 1.0000 15.64
0 1.000 0.00001 1.000 17.5 88
PRET, spec a da a p e ea men (see he codi ica ion in Table 1); LV, numbe o la en a iable in he PLS model; RMSEC, Roo Mean Squa es E o in
Calib a ion and he same in c oss alida ion, RMSEC_CV; SEP, S anda d E o in P edic ion; , co ela ion coe icien ; s
yx
esidual s anda d de ia ion; b
0
,
in e cep ; b
1
, slope; p-s, p- alue o he signi icance es ; p-b
0
&b
1
, p- alue o join ly es he in e cep = 0 and slope = 1; ERROR (%), mean o he absolu e alues
o he ela i e e o ; CCβ (mg L
-1
), capabili y o de ec ion wi h he p obabili ies o alse posi i e and alse nega i e ixed o 0.05.
Table 3
P incipal componen analysis o he a iables RMSEC, RMSEC_CV, SEP, s
yx
, b
0
, b
1
, ERROR
and CCβ
P incipal Componen Eigen alue Explained a iance (%) Accumula ed a iance (%)
1 3.943 49.29 49.29
2 2.317 28.96 78.25
3 0.773 9.66 87.91

Table 4
Global desi abili y (D) o each p e ea men
(PRET)
PRET D PRET D PRET D
141 0.0000 241 0.0000 341 0.0000
142 0.0000 242 0.0000 342 0.0000
143 0.2898 243 0.0000 343 0.0000
151 0.0000 251 0.0000 351 0.0000
152 0.0000 252 0.0000 352 0.0000
153 0.0000 253 0.0000 353 0.0000
161 0.2511 261 0.2521 361 0.2556
162 0.4269 262 0.3965 362 0.0000
163 0.9188 263 0.9105 363 0.8969
521 0.0000 531 0.4284
522 0.0000 532 0.4281
523 0.6529 533 0.8486
621 0.0000 631 0.4290
622 0.9761 632 0.9497
623 0.6618 633 0.8515
FIGURE 1
RMSEC
S yx
b0
b1
p-s
p-F
ERROR
CCβ
RMSEC_CV
SEP
288112 1734 0.97 15.6 0.0 0.38 0.0 0.0 11.1 88
62661780 4965 1.00 3104 7150 1.00 0.01 1.00 38.1 23062
FIGURE 2
Componen 1
-
0.47
-
0.27
-
0.07
0.13
0.33
0.5
-
0.47
-
0.27
-
0.07
0.13
0.33
0.53
Componen 2
Componen 1
RMSEC
RMSEC_CV SEP
ERROR
b0
CCβ
A)
syx
b1
RMSEC
RMSEC_CV
s
yx
b
0
b
1
ERROR
SEP
-
-
0.27
-
0.07
0.13
0.33
0.53
Componen 1
-
0.4
-
0.1
0.2
0.5
0.8
1.1
Componen 3
CCβ
B)
HIGHLIGHTS
Signal p e ea men mos ly in luences he ib a ional spec oscopy me hods
A p ocedu e o ob ain he bes p e ea men is de eloped o PLSR calib a ion
The p ocedu e is a mul ic i e ia s a egy ha models he accu acy line quali y
The pe o mance o he p ocedu e has been p o ed o calib a ion o BP3 by ATR-FTIR