comparison of three multivariate calibration methods as an approach to arsenic (2)

8/13/2019 Comparison of Three Multivariate Calibration Methods as an Approach to Arsenic (2)

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Mikro ch im. A c ta 126 , 257-262 (1997) Mikrochimica cta9 Spr inger -Ver lag 1997Pr in ted in u s t r i a

Co m par i son o f Three Mul t ivar ia te C al ibrat ion M et hod s as an App roach to Arsen icS p e c ia t io n by H G A A SR o s a r i o T o r r a l b a 1 , M i l a g r o s B o n i l l a 1 , L u i s V . P ~ r e z - A r r i b a s 2 *, M a r i a A . P a l a c i o s 2 , a n d C a r m e n C ~ im a r a 21 Depar tam en to de Ingen ie r ia C iv i l , Tecno log ia Hid r~u l ica y Energ6 tica, E .U. I .T . Obras P f ib l icas, Un ivers ida d Po l i t6cn ica de Madr id ,

C /Alfon so XII n ~ 3 , E -28014 Mad r id , Spa in2 Depar tamen to de Quimica Ana l i t ica , Facu l tad de C ienc ias Quimicas , Un ivers idad Complu tense de Madr id , E -28040 Madr id , Spa in

A b s t r a c t . This paper co mp ares th ree mul t ivar i a t e ca li -b ra t io n m ethod s , nam ely c l as si ca l l eas t squares (CLS),inverse l eas t squares ( ILS) and Kalman f i l t e r , app l i edt o c o n t i n u o u s - f l o w h y d r i d e g e n e r a t i o n w i t h s o d i u mt e t r a h y d r o b o r a t e ( I I I ) r e d u c i n g a g e n t a n d A A S d e t e c -t ion fo r the purp oses o f spec ia t ion o f As( II I) , As (V) ,mo n o m e t h y l a r s o n i c a c i d ( MMA ) , a n d d i me t h y l a r s in i ca c i d ( D MA ) . T h e p r e c i si o n o f t h e t h r e e m u l t iv a r i a t eme t h o d s w a s c o mp a r e d i n t h e c a l i b r a t i o n a n d p r e d i c -t i o n s t e p s b y s t a n d a r d e r r o r o f p r e d i c t i o n ( SE P) a n dre la t ive e r ro r o f p red ic t ion (REP) , respec t ive ly , fo reach a na ly te an d no s ign if i can t d if fe rences have bee nf o u n d f o r A s( II I) , A s ( V ) , M M A , a n d D M A w h e n t h eF - t e s t w a s a p p l i e d t o c o mp a r e t h e t h r e e mu l t i v a r i a t ec a l i b r a t i o n me t h o d s i n p a i r s a t t h e 9 5 % c o n f i d e n c eleve l. Dete rm ina t ion o f the As spec ies was car r i ed ou ti n s p i k e d d r i n k i n g a n d s e a w a t e r i n t h e r a n g e7-3 5 ~tg 1 - 1 . Rec over i es were in a l l cases a ro und 100%and the de tec t ion l imi t fo r the l eas t sens i t ive spec ieswas c lose to 5 gg 1 - 1Key words: a r sen ic spec ia t ion , hydr ide genera t ion -AA S, mul t iva r i -a te ca l ib ra t ion , sea w a te r , d r ink ing wa te r .

The spec ia t ion o f a rsen ica l s is o f g rea t in t e res t to m anyresearchers , beca use o f the i r tox ic i ty . The m os t tox icspec ies in so f t and sea w aters a re As(I II ), As (V) , m ono -me t h y l a r s o n i c a c i d ( MMA ) a n d d i me t h y l a r s i n i c a c i d( D MA ) . O t h e r me t h y l a r s e n i c c o mp o u n d s , s u c h a sarsenobeta ine (AsB) o r a rsenocho l ine (AsC) , a re a l so

* T o w h o m c o r r e s p o n d e n c e s h o u ld b e a d d r e ss e d

p r e s e n t in ma r i n e o r g a n i s ms , b u t t h e y a r e n o t c o n s i d e r -ed to be tox ic . The spec ia t ion o f these a rsen ica ls i susua l ly d i f f i cu l t because they mus t be chemica l ly o rphys ica l ly separa ted p r io r to quan t i f i ca t ion .

A t a n d e m o n -l in e p r o c e s s u s in g c h r o m a t o g r a p h i csepara t ion wi th spec i f i c a tomic de tec t ion i s the mos tu s u a l w a y t o t a c k l e t h e p r o b l e m [ 1 , 2 ] . A n i o n -e x c h a n g e H P L C o r io n - p a i r r e v e r s e -p h a s e c h r o m a t o g -r a p h y c o m b i n e d w i t h G F - A A S [ 3 ] , p o s t - c o l u m nh y d r i d e g e n e r a t i o n a t o mi c a b s o r p t i o n s p e c t r o me t r y[4 , 5 ] , i nduct ive ly coup led p lasm a a tom ic em iss ions p e c t r o me t r y ( I CP- A E S) [ 6 ] , o r m i c r o w a v e i n d u c e dp l a s ma a t o mi c e mi s s i o n s p e c t r o me t r y ( MI P- A E S) [ 7 ]a r e t h e u s u a l c o mb i n a t i o n s .

Al though mul t ivar i a t e ca l ib ra t ion has been ex ten-s iv e l y u s e d i n mo l e c u l a r s p e c t r o p h o t o m e t r i c me t h o d sb a s e d o n p h o t o d i o d e a r r a y s p e c t r o m e t r y [ 8 ] , i t i s l es sc o mmo n i n a t o mi c s p e c t r o s c o p y . N e v e r t h e l e s s , t h i sma t h e ma t i c a l a p p r o a c h i s u s e d b y s o me a u t h o r s f o rd i f fe ren t reasons . For example , in a tomic emiss ionspec t roscopy , chemica l sys tems exh ib i t ing var iousobs tac les to quan t i t a t ion , inc lud ing spec t ra l - lineover l ap , in t e r fe rences due to b roadened spec t ra l l i nesand s t ray l igh t f rom a l ine o f h igh in tens i ty , have beensuccess fu l ly overcome by mul t ip le l inear reg ress ion(MLR) [9 ] . Kalman f i l t e r ing has been used in induc-t i v e l y c o u p l e d p l a s ma a t o mi c e mi s s i o n s p e c t r o me t r yf o r b a c k g r o u n d c o r r e c t i o n a n d f o r so l v in g o t h e r p r o b -l e ms [ 1 0 ] , b u t t h e r e a r e n o r e p o r t s o f th e u s e o fmul t ivar i a t e ca l ib ra t ion to s tudy spec ia t ion .

A n e a r l i e r b r ie f p a p e r [ 1 1 ] b y t h e a u t h o r s r e p o r t e d ,unde r idea l cond i t ions , the spec ia t ion o f tox ic a rsen ic


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258 R. Torralba et al.s p e ci e s s u c h a s A s (I II ), A s ( V ) , M M A a n d D M A b yd i r e c t c o n t i n u o u s - f l o w h y d r i d e - g e n e r a t i o n a t o mi cabsorp t ion . The p rocedure invo lves d i f fe ren t i a l reduc-t ion o f the spec ies to the i r hydr ide fo rm , depend ing ont h e r e d u c t i o n me d i u m, a n d t h e u s e o f a ma t h e m a t i c a lmul t ivar i a t e ca l ib ra t ion model to reso lve the d i f fe ren tspec ies . The mu l t ivar i a t e me thod p rop ose d was inverseleas t squares ( ILS) , wh ich i s espec ia l ly recommendedwhen the m ain source o f e r ro r in the f ina l resu l t s ise r ro rs in concen t ra t ion dur ing ca l ib ra t ion [12] . In thep r o p o s e d mo d e l , s u c h e r ro r s m i g h t b e d u e t o t h e l o wconc en t ra t ion o f each a rsen ic spec ies used in the ca l i -b ra t ion s t ep ( l es s than 35 gg 1 -1 ) and /o r to s l igh tchanges in the e ff ic iency o f hydr ide genera t ion fo r eachc a l i b r a ti o n me a s u r e m e n t . T h e I L S c h o i c e w a s b a s e d o nthese cons idera t ions and on ou r exper i ence , bu t cer t a ina u t h o r s , i. e . T h o m a s a n d H a a l a n d [ 1 3 ] a n d K a l i v a s[ 1 4 ] , p o i n t o u t t h a t t h e mu l t i v a ri a t e me t h o d s mu s t b etes t ed em pi r i ca l ly b ecaus e o f the d i f f icu l ty o f p red ic t ingt h e ir p e r f o r ma n c e b a s e d o n t h e o r e t i c al c o n s i d e r a t i o napr ior i Therefo re , the a im of th i s wor k i s to exp lo re theab i l i ty o f o ther m ul t ivar i a t e ca l ib ra t ion m ethod s fo rma t h e ma t i c a l s p e c i a t i o n b y c o mp a r i n g t h r e e mu l t i -v a r i a te c a l i b r a t io n me t h o d s a p p l i e d t o c o n t i n u o u s h y -d r i d e g e n e r a t i o n w i t h s o d i u m t e t r a h y d r o b o r a t e ( I I I )r e d u c i ng a g e n t a n d A A S d e t e c t i o n f o r t h e p u r p o s e s o fs p e c i a ti o n o f A s( II I) , A s ( V ) , M M A a n d D M A . T h emul t ivar i a t e ca l ib ra t ion methods app l i ed were c l as s i -cal least squares (CLS), inverse least square s (ILS), andKalman f i l t e r . CLS i s a mul t ivar i a t e l eas t squaresproce dure b ased d i rec t ly on Beer s l aw [12 , 15]. ILS i sa l eas t squares method , somet imes ca l l ed the P-mat r ixme thod , base d o n the inverse o f Beer s l aw [16 , 17].Ka lm an f il te r is a recurs ive mul t ivar i a t e m etho d bas edon B eer s l aw wi th s imi la r goa l s to those o f the C LSme t h o d , b u t i t h a s t h e a d v a n t a g e o v e r CL S t h a t i tavo ids m at r ix inve rs ion [8 , 18 ].

O n c e t h e t h r e e mu l t i v a r ia t e c a l i b r a t io n m e t h o d s h a db e e n c o mp a r e d b y ma t h e ma t i c a l a n d s t a t i s t i c a l p r o -cedures , t he ab i l i ty o f the m etho d to de te rmine As(I II ),A s (V ) , M M A a n d D M A s p e ci e s i n r ea l w a t e r s a mp l e swas s tud ied , espec ia l ly in water samples wi th h ighlevels of salts.

xperimentalppara tus

A model 2380 Perkin-Elmer atomic absorption spectrophotometerequipped with an electrodeless discharge lamp operated at 8 W froman external power supply was used for arsenic determinations.

S a m p l e : M i x t u r e s ofAs Ill),As V),M M A a n d D M AS e l t c t e d b y f a c t o r i a l design)

A c i d media:H C I : 0 .5 M , 1 M a n d 6 MH A c : I MCItrlcJCitrate uffer: H 2 and4

N a B H 4 : 3 ( w / v )

Acid > ~ sePa~r~t~ INaBH4Peristalticpump

Data processingFig 1. Manifold used for continuous-hydride generation

A spectral ba ndwidth of 0.7 nm was selected to isolate the 193.7 nmarsenic line. The signals were recorded on a model 56 Perkin-Elmerrecorder set at the 10 mV range. A quartz atomization cell heated byan acetylene-air flame was used. The continuous-flow system usedfor hydride generation is shown in Fig. 1.

Data processing was performed on a 486DX computer equippedwith a mathematical co-proces sor (640 kB base memory size and 50MHz speed) and the mathematical algorithms were written in stan-dard BASIC (Microsoft GW-BASIC| 62147 bytes free of minimummemory required).

ChemicalsAll reagents were of analytical reagent grade or higher purity a nddeionized water from a Mil li-Q system (Millipore) was used.

Stock solutions (1000 mg 1-1) of As(III), As(V), monomethyla r-sonic acid (MMA) and dimethylarsinic acid (DMA) were preparedby dissolving the appropria te amount of ultrapure AszO 3 (Merck),AszO 5 (Aldrich), disodium salt of monomethyla rson ic acid (CarloErba) and sodium salt of dimethylar sinic acid (Sigma), respectively.As(III) and As(V) were dissolved in 10ml of 1 M sodium hydroxidesolut ion and d iluted to a final volume of 250 ml with 2 M HC1. MMAand D MA were prepared by dissolving the reagents in water.

Sodium tetrahydrobo rate solution (3 w/v) was prepared inwater, from Aldrich reagent, and stabilized with 1 (w/v) sodiumhydroxide. The solution was filtered before use to eliminate turbidity.

Solutions of 6, 1 and 0.5 M HC1 were prepared by approp riat edilut ion of 37 (w/v) HC1 (Carlo Erba). A1 M HAc solut ion wasprepared from glacial acetic acid (d = 1.050 g ml - 1). Buffer solutionsfor pH 2 and pH 4 were prepared from 40 (w/v) citric acid andsodium hydroxide (10 w/v).

ProcedureSolutions conta ining the four arsenic species, 3 (w/v) NaBH 4 anddifferent acid media were introduced in the continuous-flow systemthrough a peristalti c pump. The experimental parameters are givenin an earlier work [11] where experimental conditions for arsine


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Comp arison o f Three Mult iva r ia te Ca l ib ra t ion Methodsgeneration from the arsenicals As(III), As(V), M M A and DM A indifferent reaction media such as 0.5, 1 and 6 M HC1, 1 M, HA c andpH 2 and pH 4 citric/citrate buffer were shown.

R e s u l t s a n d D i s c u s s i o nT h e a r s i n e g e n e r a t i o n r e s ul t s, w h i c h d e p e n d e d o n t h ec h e m i c a l f o r m o f t h e a n a l y t e , c a n b e e x p r e s s e d a sa p e r c e n t a g e o f t h e s i g n a l o b t a i n e d f r o m A s ( I I I ) , a s w a sd o n e b e f o r e [ 11 ] . I n 6 M H C 1 c o n t a i n i n g 3 % ( w /v )N a B H 4 , a r s i n e is g e n e r a t e d f r o m A s ( I I I ) , A s ( V ), a n dM M A w i t h t h e s a m e e f fi c ie n c y. T h e a r s i n e y i e l d f r o mD M A w a s 5 0 % t h a t o f t h e o t h e r s p ec i es i n t h e 2 0 -1 40 t ag 1 - 1 r a n g e t e s t ed . O t h e r a c i d i c m e d i a s u c h a s1 a n d 0 . 5 M H C 1 r e d u c e t h e e f f i c ie n c y o f h y d r i d eg e n e r a t i o n f r o m A s ( V ) a n d M M A , a n d i n c r e a s e i t f r o mD M A , w i t h r e s p e c t to t h a t i n 6 M H C 1 . T h e A s ( I I I ) a n dD M A s i gn a l s w e r e s i m i l a r i n 1 M H A c a n d a r s i ne w a sn o t g e n e r a t e d f r o m A s (V ) or M M A i n ci t r i c / c i tr a t em e d i u m a t p H 4 .

259Table 1. Correspondence between As species and the factor levelsapplied in our design

Fac tor level (gg 1-1)Species 1 2 3 4 5As(III) 0 10 20 30 40As(V) 0 10 20 30 40M M A 10 20 30 40 50DMA 10 20 30 40 50

Table 2. Ca libra tion design for the 35 mixtures, based on simplexlatticeConcen tration (gg I - 1)

Mixture Level As(III) As(V) M M A D M A

23456Exper imenta l Design for Calibration and Prediction 78I n m u l t i v a r i a t e a n a l y s i s , a g o o d d e s i g n i s e s s e n t i a l f o r 9

t r a i n i n g - s e t s y s t e m s ( c a l i b r a t i o n ) . I n p r e p a r i n g a s e t o f 10c a l i b r a t i o n m i x t u r e s f o r a n a l y t i c a l p r o j e c t i o n o f d a t a , i t 11i s f u n d a m e n t a l t h a t th i s s e t o f o b j e c t s ( s t a n d a r d m i x - 1213t u r e s ) s p a n s t h e p e r t i n e n t e x p e r i m e n t a l r e g i o n p r o p e r l y 14i n o r d e r t o a v o i d l a t e r p o o r p r e d i c ti o n s . T h ~ c ; o r e , t h e 15s e t o f c a l i b r a t i o n m i x t u r e s m u s t b e s e l e c t e d a c c o r d i n g 1617t o a s t a t i s t i c a l d e s i g n . T h e s e d e s i g n s a r e b a s e d o n 18s i m u l t a n e o u s l y c h a n g i n g t h e c o n c e n t r a t i o n o f a l l c o r n - 19p o n e n t s i n t h e s t a n d a r d c a l i b r a t i o n m i x t u r e s . T h e 20s i m p l e s t d e s i g n i s p r o b a b l y t h e s o - c a l l e d f a c t o r i a l d e - 2122s i gn , w h i c h r e q u i r e s t h e c o d i n g o f a l l t h e v a r i a b l e s . T h i s 23c o d i n g , w h i c h c a n b e l o g a r i t h m i c o r l i n e a r , g i v e s r i s e t o 24s e v e r a l l e v el s o f e a c h f a c t o r. U n f o r t u n a t e l y , m a n y v a r i - 2526a b l e s c a n l e a d t o a l a r g e n u m b e r o f s t a n d a r d c a l i b r a - 27t i o n m i x t u r e s kP; k = l e v e l s , p = f a c t o r s ) a n d , c o n s e - 28q u e n t l y , t o u n n e c e s s a ri l y t i m e - c o n s u m i n g c a l i b r a t i o n 2930e x p e r i m e n t s . A g o o d w a y t o s i m p l i f y t h e d e s i g n i s t o 31r e d u c e t h e n u m b e r o f e x p e r i m e n t s b y u s i n g t h e s o 32c a l l e d f r a c t i o n a l f a c t o r i a l d e s i g n , o f w h i c h t h e r e a r e 33s e v e r a l v a r i a n t s [ 1 9 ] ; a l t e r n a t i v e l y , i n t h e c a s e o f c l o - 3435s u r e, a s i m p l e x l a t ti c e d e s i g n c a n b e u s e d [ 2 0 ] . F o r o u rw o r k , w e u s e d a s i m p l e x l a t t i c e d e s i g n b a s e d o n f o u rf a c t o r s ( o n e p e r c o m p o n e n t ) a n d f iv e v a r i a b l e s ( c o n c e n -t r a t i o n s ) c o d e d a s , 1 , 2 , 3 , 4 a n d 5 . T a b l e 1 s h o w s t h ec o n c e n t r a t i o n f o r e a c h a r s e n i c a l a n d l e ve l . T h i s d e s i g n ,w h i c h l e d t o a se t o f 3 5 c a l i b r a t i o n s t a n d a r d m i x t u r e s( T a b l e 2 ), a ll o w s f o r t h e p o s s i b l e a b s e n c e o f i n o r g a n i c

1:1:1:5 0 0 10 501:1:2:4 0 0 20 401:1:3:3 0 0 30 301:1:4:2 0 0 40 201:1:5:1 0 0 50 101:2:1:4 0 10 10 401:2:2:3 0 10 20 301:2:3:2 0 10 30 201:2:4:1 0 10 40 101:3:1:3 0 20 10 301:3:2:2 0 20 20 201:3:3:1 0 20 30 101:4:1:2 0 30 10 201:4:2:1 0 30 20 101:5:1:1 0 40 10 102:1:1:4 10 0 10 402:1:2:3 10 0 20 302:1:3:2 10 0 30 202:1:4:1 10 0 40 102:2:1:3 10 10 10 302:2:2:2 10 10 20 202:2:3:1 10 10 30 102:3:1:2 10 20 10 202:3:2:1 10 20 20 102:4:1:1 10 30 10 103:1:1:3 20 0 10 303:1:2:2 20 0 20 203:1:3:1 20 0 30 103:2:1:2 20 10 10 203:2:2:1 20 10 20 103:3:1:1 20 20 10 104:1:1:2 30 0 10 204:1:2:1 30 0 20 104:2:1:1 30 10 10 105:1:1:1 40 0 10 10

s p ec i es d u e t o m i c r o b i a l m e t h y l a t i o n o r r e d u c t i o n , s o i ti n c lu d e s s o m e c a l i b r a t i o n s t a n d a r d s w i t h o u t A s ( I I I)a n d / o r A s (V ) . T h e p r e d i c t i o n s t e p f or e a c h m u l t i v a r i a t em e t h o d w a s c a r r i e d o u t a f t e r c a l i b r a t i o n b y u s i n g a s e t


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260 R. Torralba et al.

A = K C

i t l i i)A r t A rm / \ K r l . .. K r n J \ G r i tr x m r x n n x m~ j CaIibration

~ ~ ILSK : A C t ( C C I ) - 1 ] C : P h ]

(If r = n, P = K - l)I P = C A ' a A r ' ] I

~ a l m a n F ilte rI A ' = C ' K t I

or each r selected medium do:k(0) = 0, P(0) = 106I, R = 1 x 1 0- s J

g ( i + 1 ) = P ( i ) % t ( i + 1 ) / J R + c c ( i + 1 ) P ( i ) c o t ( i + 1 ) ]P(i + 1) = 1-I - g(i + 1) 0 + 1)] P(i) [ I - g (i + 1) (i + 1 )] + g(i + 1) Rg'(i + 1)k(i + 1) = k (i) + g(i + 1)[aJi + 1) - cc(i + 1)k(i)]for i = 1, 2, ...., m stand ard mix tures Fig 2a

Table 3. P rediction design mixtures.Conce ntration (ggl 1)

M ixtu re As( II I) As(V) MM A DM A1 0 20 35 352 20 25 15 353 30 25 20 154 25 0 20 255 20 30 30 306 25 15 35 257 30 30 25 208 15 20 30 309 30 15 15 3010 26 20 25 15

o f t e n r a n d o m l y s e l e c te d m i x t u r e s c o n t a i n i n g t h e f o u rA s s p e c i e s a t b e t w e e n 0 a n d 3 5 g g 1 - 1 ( T a b l e 3 ). T h et o t a l c o n c e n t r a t i o n s o f A s s e le c te d f o r t h e f o u r a r s e n i cs p e ci es w e r e s im i l a r t o t h e m a x i m u m e s t a b li s h e d b y t h eE C i n w a t e r s f o r h u m a n u s e ( 5 0 g g 1 - 1).

A l l t h e m a t h e m a t i c a l a l g o r i t h m s a p p l i e d f o r t h e sem u l t i v a r i a t e m e t h o d s w e r e w r it t e n i n - h o u s e a n d b a s e do n t h o s e r e p o r t e d b y C . W . B r o w n e t a l. [ 1 6 ] f o r C L Sa n d I L S a n d b y S . D . B r o w n [ 1 8 ] f o r K a l m a n f il te r.A s c h e m e f o r t h es e a l g o r i t h m s i s s h o w n i n F i g . 2 . T h eA - m a t r i x is bu i lt f r o m t h e a b s o r b a n c e s o f t h e m s ta n -d a r d c a l i b r a t i o n m i x t u r e s ( o n e f o r e a c h c o l u m n ) f o r

e a c h o f t h e r g e n e r a t i o n m e d i a ( o n e f o r e a c h r o w ), a n dt h e C - m a t r i x c o n t a i n s t h e c o n c e n t r a t i o n s o f t h e n c o m -p o n e n t s ( o n e f o r e a c h r o w ) i n th e m s t a n d a r d c a l i b ra -t i o n m i x t u r e s . T h e m a i n d i f fe r e n c e b e t w e e n t h e t h r e em e t h o d s i s i n h o w t o o b t a i n t h e K - m a t r i x w h i c h r e la t e st h e m e a s u r e d a b s o r b a n c e s v e r s u s a n a ly t e c o n c e n t r a -t i o n ; C L S a n d I L S a r e r e g r e s s i o n m e t h o d s w h i c h i n -v o l v e m a t r i x i n v e r s i o n ( p r o d u c t C C t i n C L S a n d A A ti n I L S ) a n d K a l m a n f il te r is a r e c u rs i v e m e t h o d w h o s em a i n a d v a n t a g e i s t o a v o i d m a t r i x i n v e r s i o n .

O v e r a l l P e r f o r m a n c e C o m p a r i s o n sT h e p r e c i s i o n o f t h e t h r e e m u l t i v a r i a te m e t h o d s ( C L S ,I L S , a n d K a l m a n f il te r) w a s c o m p a r e d i n t h e c a li b r a -t i o n a n d p r e d i c t i o n s t e ps . R e c o v e r y w a s t e s t e d b yd e t e r m i n i n g t h e R E P ( re l at iv e e r r o r o f p r e d i c ti o n ) f o re a c h c o m p o n e n t . T h e R E P is a m e a s u r e o f a c c u ra c ya n d p r e c i s i o n , s i n c e t h e d i f f e r e n c e b e t w e e n p r e d i c t e da n d a c t u a l c o n c e n t r a t i o n r e p r e s e n t s t h e a c c u r a c y o f t h em e t h o d .

^ . __ i ) 2R E P = x 1 0 0

1I t s h o u l d b e b o r n e i n m i n d t h a t t h e R E P g i ve s o n l y a n


5/6

Comparison of Three Multivariate Calibration Methods 261

a = K c / l * LS

c = (KtK) 1Kta

Prediction I

Kalman Filter

] c 0 ) = 0 , P 0 ) = 1 0 6 I , R = 1 x 1 0 - ~

g(i + 1) = P(i)kt(i + 1)/[R + k(i + 1)P(i)k'(i + 1)]P(i+ 1)= [I -g (i + l )k(i + 1)]P(i) [ I - g ( i + 1)k(i + 1)] '+ g(i + 1) Rgt(i + 1)c(i + 1) = c(i) + g(i + 1) [a(i + 1) - k(i + 1)c(i)]for i = 1, 2, ...., r selected mediu m F i g . 2 b

F i g 2. M odels and algo rithms of the three multivariate methods app lied: a Calibration step and b prediction step. i: index of the iteration g (i):n x 1 matrix ca lled the Kalma n gain factor, k(i): vector containing the propo rtionality constant estim ated in calibration or established inprediction step. P(i): n x n variance-covarian cematrix, c(i): vector of the concen trations established in calibration or p redicted in predictionstep. a(/): vector of the m easured absorb ance scalar giving the p redicted variance of the w hite noise. I: n x n identity matrix. Subscript c denotescalibration, superscript t denotes the transpo se of the ma trix or vecto r superscript - 1 denotes the inverse of the matrix

i d e a o f th e a c t u a l p r e d i c t i o n e r r o r f o r t h e d i f f e r e n ts p e c i e s s t u d i e d a n d e a c h m e t h o d t e s t e d [ 2 1 , 2 2 ] .

A n o t h e r w a y t o d e t e r m i n e t h e p r e c i si o n f o r e a c hc o m p o n e n t i s t o c a l cu l a te t h e S E P ( s t a n d a r d e r r o r o fp r e d i c t i o n ) , w h i c h i s a s o r t o f s t a n d a r d d e v i a t i o n

z ~~ i c i ) 2SEPw h e r e in b o t h e q u a t i o n s ~i a n d q a r e t h e g i v e n a n d t h ec a l c u l a te d c o n c e n t r a t i o n s o f e a c h c o m p o n e n t , r e s p ec -t i v el y , a n d m is th e n u m b e r o f m i x t u r e s i n t h e c a l i b r a -t i o n o r p r e d i c t i o n s e t .

T h e S E P c a n p r o v i d e a g o o d m e a s u r e o f h o w w e ll , o na v e r a g e , th e c a l i b r a t i o n m o d e l p e r f o r m s . O f t en , h o w -e v e r, th e p e r f o r m a n c e o f t h e c a l i b r a t i o n m o d e l v a r i e sd e p e n d i n g o n t h e a n a l y t e l e v e l [ 2 3 ] .

T a b l e 4 s h o w s t h e r e s u l t s o b t a i n e d f o r t h e f o u r a r -s e n i c s p e c i e s i n t h e c a l i b r a t i o n a n d p r e d i c t i o n s t e p su s i n g t h e th r e e m u l t i v a r i a t e c a l i b r a t i o n m e t h o d s . T h eI L S m e t h o d y i el d s t h e m o s t p r e c is e r e su l ts i n b o t h t h ec a l i b r a t i o n a n d p r e d i c t i o n s t e p s. H o w e v e r , a f t e r t a k i n gi n t o a c c o u n t t h e S E P c a l c u l a t e d i n t h e p r e d i c t i o n s t e p ,t h e r e w e r e n o s i g n i f i c a n t d i f f e r e n c e s f o r A s ( I I I ) , A s ( V ) ,M M A a n d D M A w h e n th e F - t e st w a s u s ed to c o m p a r et h e m u l t i v a r i a t e c a l i b r a t i o n m e t h o d s i n p a i r s a t t h e9 5 c o n f i d e n c e l e v el . S e v e r a l w a y s h a v e b e e n p r o -

p o s e d t o c a l c u l a t e t h e l im i t s o f d e t e c t i o n ( L O D ) i nm u l t i v a r i a t e c a l i b r a t i o n a n d a l l o f t h e m a r e s ti ll th es u b je c t o f c o n t r o v e r s y . I n o u r a p p r o a c h w e d e f in e dL O D a s t h e m i n i m u m c o n c e n t r a t i o n t h a t p r o d u ce sa 3 : 1 s i g n a l - t o - n o i s e r a t i o [ 2 4 ] , m e a s u r e d d i r e c t l y i nt h e ca l ib r a t io n m a t r i x ( K - m a t r i x fo r C L S a n d K a l m a nf i l t e r a n d P - m a t r i x f o r C L S ) f o r t h e l e a s t s e n s i t i v ea n a l y t e i n e a c h m e t h o d ( T a b l e 4 ). A s c a n b e s e e n , t h ed e t e c t i o n l i m i t s a r e s i m i l a r t o t h o s e o b t a i n e d u s i n gh y p h e n a t e d t e c hn i q u es .Speciation and Determination of rsenicals in WaterSamplesA l t h o u g h t h e r e w e r e n o s i g n i f i c a n t d i f f er e n c e s b e t w e e nt h e t h r ee m u l t i v a r i a t e c a li b r a t i o n m e t h o d s s t ud i e d, w ec h o s e I L S t o s t u d y t h e p r e d i c t i o n a b i l i t y i n n a t u r a lw a t e r s a m p l e s , w h e r e m a t r i x e f fe c ts c a n a f f e ct th e f i n a lr e s u lt s . I L S w a s c h o s e n o n t h e b a s i s o f t h e r e s u l t sa b o v e , w h e r e , a s c a n b e s e en , it a l m o s t a l w a y s h a s t h el o w e s t R E P a n d S E P . T h e e x p e r i m e n t s w e r e c a r r i e do u t o n t w o w a t e r s a m p l e s , o n e w i t h a l o w le v e l o fi n o r g a n i c m a t t e r ( b o t t l e d w a t e r ) a n d t h e o t h e r w i t ha h i g h l e v e l o f s a l t s ( se a w a t e r ) . I n b o t h c a s e s , f o u ra d d i t i o n s o f A s s p e c i e s b e t w e e n 7 a n d 3 5 g g 1 - 1 w e r em a d e . T h e r e s u l t s a r e s h o w n i n T a b l e 5 . I n a l l c a s e s t h er e c o v e ri e s w e r e a r o u n d 1 0 0 a n d t h e t h e o r e ti c a l t r u ev a l u e o f 1 0 0 w a s w i t h i n t h e l i m i t s o f t h e s t a n d a r dd e v i a t i o n , w h i c h s u g g e s t s t h a t t h e p r o p o s e d m e t h o d


6/6

2 6 2 C o m p a r i s o n o f T h r e e M u l t i v a r i a t e C a l i b r a t i o n M e t h o d s

T a b l e 4. R E P a n d S E P o f t h e t h r e e m u l t i v a r i a te m e t h o d s f o r t h e f o u r s p ec i esC L S I L S K a l m a n f i lt e rR E P ( % ) S E P R E P ( % ) S E P R E P ( % ) S E P

C a l i b r a t i o nAs(I II) 27.3 4 23.7 4 27.2 4As(V) 81.0 12 43.7 7 67.4 10M M A 40.0 9 27 .0 6 38 .3 9D M A 61.8 14 32.3 7 58.3 13P r e d i c t i o nAs( III) 10.9 8 8.9 6 9.9 7As(V) 19.7 12 12.5 8 18.7 12M M A 12.1 10 10.2 8 15.3 12D M A 21.5 8 15.9 13 27.1 22L O D 5 ~ g l 1 4 g g l 1 5 ~ t g l -1

LO D = L im i t o f de te c t ion for the l e a s t - s e ns i tive spec ie s in e a c h m e thod . R EP = Re la t ive e r ror ofpre dic t ion .

S E P = S t a n d a r d e r r o r o f p r e d i c ti o n .

Ta ble 5 . Re c o ve ry f rom two sp ike d sa m ple sBot t l e d wa te r Se a wa te rRecovery S.D. Recovery S.D.( )

As(III) 106 29 109 27As(V) 111 36 107 37M M A 1 0 6 2 2 1 0 3 2 4DM A 118 33 116 33

a M e a n of four a ddi t ions ( a m o unt sp ike d wa s 7 35 gg 1 - 1 or e a c hspecies).

will be useful for As speciation and quantificationwithout previous chemical or chromatographic sepa-ration.

onclusionsThe three multivariate calibration methods studiedcould be useful for the speciation of As(III), As(V),MMA and DMA without previous separation. Al-though there are no significant differences betweenthem, ILS was chosen because it yields the most preciseresults in both the calibration and prediction steps. Itsapplication to two different natural water samples withdifferent saline contents gave recoveries close to 100for the four As species. The proposed arsenic speciationmethod is simple and could be a very good alternativeto hyphenated speciation techniques.Ac k nowle dge me nts . T h e a u t h o r s w i s h t o t h a n k t h e D G I C Y T f o rf i n a n c ia l s u p p o r t ( P B 9 1 -0 3 76 ) a n d M a x G o r m a n n f o r re v i s in g t h em a nusc r ip t .

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comparison of three multivariate calibration methods as an approach to arsenic (2)

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