M u l t idi me nsi ona l s c a l ing, although da ti ng b a c k to 1 938 , has only receive d Didesprea d r e c ognition sinc e the exposition o f
the nonme t :r i c form of th e te chnique by S hepar d ( 1 6 7 , 1 68 ) and
Kruskal ( 1 02 , 1 03 ) i n the e a r l y 1 9 60 ' s . Nonm e t r i c mu l t i
diwensio nal s c a ling has r e c e i v e d much a t ten t i o n from b o th the
me thodo l o gi s t and the appl ied s c ient is t . A gre a t deal o f work has pr o du c e d impr ovements i n th e me tho ds of c omp1zta t i on w i th m o r e ef ficie nt a n d ve r s a t i le computer pro gramme s . I n s p i t e o f the s e c o mpu t a t i o na l impr o ve o e n t s , s e veral limitati o ns s t i l l e xi s t ,
inc lu d i n g the pr obl e�s o f c h o i c e o f di � e ns i ona l i t y 1 a x i s d e f i n i t i o n
and sub-op tima l s o l u t i o ns .
The l im i t a t i o n s o f nonme tric mul t i dime ns i o na l � c al inc h a v e n o t preven ted the behavioural s c ientis t from apply ing it to
a w i de variety o f pr ob l ems . I t s advent wa s par t ic u l a r ly w e l c omed
by mar ke t r e search ers b e c ause o f i t s a b i l i t y to pro du c e a
pict oria l r· epr e s e n ta t ion o f it e ms w ith a me tric s c a le from
or d i na l infor �at ion a b o u t the i t G ms. Par ticular emptas ic has b e e n p la c e d on th e l o c a ti o n of pro du c t brands within a mul t i dime ns i onal spa c e . I de n t i f i c a tion o f ' ho les ' o r 'gaps' i n t he sp& c e ha s then b e en u s e d to i d en t i f y p o t ent ial f o r n e w bran d s .
Although s ome � �rker s ( 1 90 ) have repor t e d su c c e s s e s i n th is f orm o f new pr o duc t d e v e l opme nt , mos t ha ve b e en c o nfront e d with t he
problem o f trans f o rm ing the psycho l o gi c a l scale value s o f a point
in the p roduc t spa c e int o the physic a l prope r t ie s of a new product. T h i s thesis ov e r c am e t his problem b y posi ti o ning food
raw materials in a mult i dimens i onal sp a c e an d s e l e c ting raw
ma teria l c ombina t i ons , as a b as is f or new fo o d dishe s , a c c or ding t o the inhe r e nt a t tr ib utes of the materials as the y i nf luenc e foo d dish chara c te r is t ic s . Tha t is , raw ma t e r i a ls w e r e l o c a t e d
o f th e domina nt a t tr ib � t e s ( s pa tial dimensi ons ) c ontaine d i n e a ch . A p o int was i de nt i f i e d in th e spa c e r e pr e s enting t h e ideal c ombina t io n of a t t r ib u t e s as a bas is f or a food d ish . R aw
ma t e r i a ls were then sele c t e d t o giv e th is r e qu ir e d a t tr i bu t e c ombina t io n .
5 . 1 Wha t is mu l t i dimens iona l
The t e rm mu lti dime ns ional scal ing is ra the r loos e an d
inc J u de s a l is t o f varie d a nd pow e rful t e chniques for the a nalys is o f da ta of s e veral type s c o l le c te d in the behav iour a l s c i e nc e s . De spite the �r d iv e r s i ty , the s e t e chnique s sha r e the du a l purp os e
o f der iving wha t e v e r pa t te rn or s tru c tu r e e x is t s in a ma trix o f e mp i r i c a l data , and of repre s e n t i ng tha t s tru c tur e i n n f o rm tha t
i s mor e a c c ep ta b le to th e human e y e - name ly a ge ome tri c al or pic t or ia l mode l . T h e o b j e c ts u n d er s tu dy are r e pr e s en t e d a s
points in th e spa tia l mode l in s u ch a w a y as to r e v e a l t h e ir domina n t f e a tur e s through the g eo me tri c a l r e l&. t i ons a mong the point s . T h e r e su l t ing spa t ia l r e pr e s e nta t i o n is j n r� c t a ' s c a le ' and r e s e mbles mor e tra di t ional s c ale s such a s llia s s and t e mpera ture ,
in tha t it a t tempts to c aptur e the fundam e nt a l prope r ti e s o f t h e ob j e c ts b y s e t t ing them w ithin a s p2 tial c ont inuum . l t i s , in fa c t , an e xt e ns i o n of t h e s e more simple unidime n s iona l s c a l e s , a s the points are a l l ow e d t o assume p o s i t ions w i th in a t w o - d i me n s i ona l plane or e ven w i th in a thr e e , four o r h i gher dimens i onal spa c e . 5 . 1 . 1 The pr ob l em o f dime nsiona li ty and interpre ta t ion
I n mos t c a s e s , an a t tempt is ma de to find a r ep r e s e n ta t ion of the l ow e s t d ime n s iona lity , c o ns is t e nt w ith the data . A low e r dime ns iona l r ep r e s en t at ion dis p la ys the same d a t a b y me ans of a sma ll e r numb er o f parame ters a n d he n c e t o the e xtent tha t f e w e r param e t e rs are e s t i ma te d from t h e same da t a , great e r s t a ti s ti ca l r e lia b il i t y will � e obta ine d . P erha ps the mo s t impor tant
c ons ide r a t ion in the achieve m en t o f a low dimensi ona l c on f igu r a t ion is the i nabilit y o f the human eye to v isua l i z e pa s t thr e e
w i t h ou t so me loss o f informa tion a b ou t the orj gi nal dat� . T h e
number o f d i me ns i ons sh ould a lways b e s u f f i c j e n t to display t h e
full c o mp l e x i t y o f t h e r e la t i ons in t h e gi ven d a t a . Gen e r ally,
n o mor e than three d im e n s i o n s ha ve b e e n a dop t e d in p r e vious
pra cti ca l applications .
The pr ima r y pu r p o s e o f the r e pr e s e nt a t i o n i s to e na b l e t h e in ve s t ig a t o r t o ga i n a b e t t e r und e r s t a n d i n g o f t h e t o t al u n d e r l y in g pat t e rn o f i n t e r r e la t ions i n h i s da t a . The obtaini ng o f a sp a t i a l c on f i gura tio n s h o u l d no t be c ons ider e d a n e nd i n i t s e l f . I n t e rpr e ta t i o n o f t h e a x e s c a n lea d t o t h e de fin it ion o f the d o m i nant p r o p e r t i e s or char a c t e r is t i c s o f the ob j d c t s which ga v e r is e t o the sp a tial mo d e l . A ga in , a lowe r dime n s i o n a l i t y i s mo r e su i t a b le a s the pr ocedure o f f i n d i ng i n t e r p r etab le a x e s b e co mes m o r e d i f f i cu l t and unc e r t a i n w h e n t h e number o f dimens i o n s e xc e e d s wha t c an n or ma l ly b e appre hen ti e d iu a ll i c t u r e o r mo de l .
5 . 1 . 2 The d e v e lopme nt o f mu l t idime n s i o na l sc aling
M u l t i d ime n s i o na l scaling da t e s back t o 1 938 when You ng a n d Househo lder ( 2 4 0 ) lai d s o me o f th e ma the ma t i c a l grou ndwor k
f o r th e fu l ly me tr j c m o d e l s . T h is w o rk w a s e x tend e d in th e e a r ly 1 950 ' s by T orgers o n ( 2 05 ) and l a t e r by Messick an d A b e lson ( 1 1 5 )
who fir s t a c h i e v e d a g e n e r a l l y w0 rkable me thod for mu l t i d imen s i o na l scaling pr o pe r . Torger son ( 2 0 7 ) g iv e s a c ompr e h e n s i v e
r e p r e s e n t a t i o n o f t h i s f ir s t pha s e of d e v e l o p m en t . The r e q u ir e ments o f the s e fully me t r i c m o d e l s for a me t ric input o f r a t i o s c a le d da t� p r ov e d t o o seve re f or m o s t s o c i a l s c i e nc e app lica t i o ns a n d le d t o th e d e v e l o p m e n t o f the n o nme tric varie t i e s o f multi d i m e n s i o na l scaling . T h e s e fa l l into t w o c a t e gorie s . The f ir s t group w a s pr opos e d by C o ombs ( 3 1 ) for th e spatial r epr e s e nta t io n
o f or dina l or nonme t r i c d a ta . The s e t e chnique s h av e no t b e e n w i d e ly us e d . One r e a s o n for t h i s ma y b e tha t t h e me th ods lacke d s uffic ient forma liza t i o n to b e c onv e r t e d in c o c ompu t er programm e s a nd a r e n o t manageable , e x c e p t with a r e lat ive ly smal l numb e r o f o b j e c ts . A no ther r e a s o n is the ir fai lure to e xtra c t sub s tan ti a l m e tric i n f o r ma t io n c o nt a ine d i n the or d ina l date. , a de f e c t whic h