D I M ENS I ONAL S C A LING ANALY S ES - A quantitative model for the design of nutritious and

The ob j e c t iv e of thi s s t age of th e re s e ar c h was t o derive a

l inear func t i on r e la t ing r�w ma t e r ia ls to f o o d d ish a c c e ptability .

Nonm e tr i c mul t i d imens i ona l s c a l i ng was chosen a s a t e chniqli e t o derive

m e t r i c s c a le values for the raw ma terials and food d i sh e s wh ich migh t

b e u s e C in th is func t io n . For t h is purpose a numb e r o f dif f e r e n t

me th � ds o f da ta c oJ.le c t ion w e r e employed in Tha iland t o o b ta i n

pr oximity me a s u r e R for b o t h t h e raw ma ter i a ls and f o o d d ish e s . The s e

da ta w e r e as follows :

1 . Raw ma t e r ia l s im ilar i t i e s - show i ng the r e la t ive s u b s t i t u t a b i l i t i e s o f pa i1 s o f the 40 raw ma t c r ia lc .

2 . Raw ma t e r i a l ass o c iation - showing the r e la t iv e a cce p t a b ilities

o f pa irs o f the raw mat e rial s i n assoc ia t io n i n t h e same f o o d d ish .

3 .

'Raw ma t e r ial by u G o ; in f o o d dishes - show ing t he a c c e p t a b i l i t y o f e a ch o f t h e � 0 raw ma t e r ia l s a s a n ingredient i n e a ch of 1 5

categories o f f o o d d ish .

4 .

Food

d ish s im i la r i t i e s - showing t h e r e la t iv e s im ilar i ti e s o f pa i r s o f 20 Tha i food dishe s .

Ea ch s e t o f da ta was s c a l e d in 5 throu gh t o 1 d imens i o ns us ing the nonmetric mul t id imens i o n a l s caling programme, KYS T. Th e point o f

' e lbow ing ' in the p l o t o f s tr e s s versus d imen s i on toge th e r w i th a

graph ic a l methc � des c r ib e d by S penc e and Gra e f ( 1 87 ) w e r e us e d t o

choose t h e underlying dime n s i ona lity o f the da t a . P l o t s o f the i t e�s (raw ma t e r ia ls or food dishe s ) were obtained in th e s pa c e of the chos en d i mens iona l i t y .

I n e a c h c a s e , a t temp ts w e r e ma de t o ide n t i fy the axes of the

spa t ia l c o nfigur a t io n . Axi8 id e n_ti f i cation was done e i th e r ob j e c t

ive ly b y c orrelat ion w ith e x t e rnal information o r sub j e c t iv e ly u s ing

the pr i o r know le dge of the r e s e archer . I n a l l cas e s the c onf iguration o f i t e ms was s e n c ib l e within t h e c o ntext o f the collec ted data .

Although the s e parate s pa c e s o f raw ma t e ria ls ani f o od d is h e s pro v e d i n teresting in i n terpr e ta t ion , there was no means

of tying the t w o t o ge th e r int o a s i ngl e l inear func t ion a s r e quir e d

for the l ine ar pr ogramme . T o this e n d , a n unf old i ng a na lys is was per forme d on the ' raw m� terial by us e ' data in an a t tempt to dis

play the raw ma tcriaJ s and food di sh e s i n the s a me mul t i d im e n s ional

s pa c e . U n f or tu n a t e l y the s o lu t ion to t h is ana l y s i s was d e ge nera t e .

A fur the r a t tempt was ma de t o pr o v ide a common ba s i s for th e r aw m3 teria ls and food dis h e s by l o c ating an i deal p o i nt in a raw material spa c e . This point _{w a s} d_efined a s r e pr e s en t i n g t h e

opt imum c o mb i n a t i o n o f r a w _{ma t e r i a l}pr ope r t i e s req_{uir e}d in a f o o d

d i sh . A l th ough thr e e mu l t id i m e n s i o n a l spac e s were deri v e d , o nly

the one obta ine d from th e s im ila rity m e a su r e s show e d s pat i a l

din1 e ns i ons w h i c h w e re r e la t e d s o le l y t o t he r a w ma t e r ial pr o p e r t ie s .

The sp� c e s derive d from the association and ' raw Ma terial b y u s e '

data w e r e r e la t e d t o both the proper t i c G of the ruw ma t eria ls and

the chara c te r i s t i c R of the food dis h e s in whi c h the r aw ma t e r j als

ar e c o �monly us_ed. H e nc e , t h e spa c e der ived fr o m th e similar ities

measures was c h o s e n a s t h e ba sis fo r loca tion o f t h e i d e a l p o i nt .

The a v e r a ge d s c or e s f or the gen e ral u s e o f the 4 0 raw materials in

Tha_i fe e d dis he s pr ovid e d th e bas is for _{i deal} f e int l oc a ti o n .

7 . 1 Th e _{o f ffiul t i dime nsi o na l}

A ll mul t i d ime nsi onal s c a li ng a na ly s e s w e r e pe r fo r me d us ing

the c omputer pr ogram�e , KYS T ( 1 05 ) , and �he Burr ough's B6700 c ompu t e r . �YST was chosen be cause o f i ts versa t i l it y in u s e and robus tness a ga in s t sub-optimal s o lu t i ons . I t i s an amalgam a t i on

o f two w e ll known a nd pr oven programue s , TORSCA 9 and 11-D -SC AL 5M .

I t gives the u s e r a numb e r o f opti ons , b o th i n th e input of da ta , i t s analys is a nd the output o f r e s u lt s . S ome o f the s e opt i o ns are d e s cribe d b e l ow :

1 . I t gives the choice o f 5 m e thods for pro ducing a s tar t ing c o nf igura t i on .

2 . I t has

2

s eparate f ormu la e for s tr e s s cal cu la t ion , de p e nd ing

4 . I t pe_{r f}or ms u_{n f}olding a nalyses.

5 . J t p e n;: i t s t h e u s e r t o ob tai n s o lut ions in a number o f M inkowski me tr i c s .

6 . I t giv e s s e v e r a l opti_on_s on out put i_n_clu_d_ing _{a h}istory o f c a lcul? t ions showing t h e pr o gr e s s o f fue iterative nume r i c a l

c a l c u l a. t i on a n d a numb e r o f plots, su ch a s the spatial c o n f i gu r a t i o n o f p o i n t s , dis tances a n d f i t t e d d i s tanc e s v e r s u s data a n d s tr e s s

v e r s u s _{d i tn8 n s i o n .}

The s e a r o on ly a f e w _{o f} t h e gr e a t ma n y options a v a i l a b J e .

F o r t u ca t e l y , th e u s e r is n o t cb l i ge d t o s e l e c t _{f r om} e a c h option.

Wh ere v e 1· s e vera l _{al t e rn a t i v e p o s s i bi l i t j e s} _are avai labl e , one _is a lw ays s e le c t e d to he t h e ' s t a nda r d ' or ' de fau l t ' ch o i c e . In the a b s e nc e of any indicat i on from the u s e r , t h e _{pro gramme u s e s} t h e s e

s tandar d

c h o i c e s . ( Fu r· th e r de .s c r ip t :i on of KYS T is gi v e n i n the

c o mpu t e r oper a t ions manu_al ( 1 05 ) . )

Mu l t i dimen c i ona l s c a l i n g analyses w e r e per f ormed on th e

da t a o b t� j uc d fro m t� s cur v c yo in Thai la Ld . T h e s e da ta w er e

ba� ic all y o f two t y pe s . F i r � t l y , proximity m e a sur e s o f t he raw ma t e r i a l s an d food d is h e s in c l u d i n g a s s o c ia t i o n , si�ilarit_y and

d e � iv e d s i.m i la r i t y . The d e r i v e d s im i la r i t i e s were cal cu l a t e d

f 1· o rn t h e ' raw ma t e r ia l _{b y} _{us e '} survey us ing S te f f lre ' s m e t hod ( 1 9 1 ) .

T h e c e c o r d _type o f data w a s a r e c �angu lar o� t r i x show i ng th e a c c e p ta b i J i t y o f t h e 4 0 raw ma t e r i a ls in 1 5 c J.ass e s o f food dish .

The met hod require_{d t o d i s p la y} _the r aw ma t e :c i a ls an d c la s s e s o f

f o o d d ish i n th e s am e s pa t ia l c o nf igur a t �.on w a s un fo lding analysis. Fur the r d e s �r iption o f th i s analysis is gi ven i n S e c tion 7 . 7 .

A l l s c a l ing ana l y s e s o f th e pr oximity ma tr ic e s w e r e

p e r formed u s i ng the Mink o w s k i - 2 metri c , i . e . , i n Euc lidean spa c e . Th e data w er e pr e p ar e d o n cards in the form o f a n upp e r t r ia ngular ma trix with miss ing d ia g o na l . S olut ions w ere ob taine d in 5 through

t o 1 dimensions ac c or ding t o the c ontro l state m ents s h own in

C ar d numb er 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 C ar d d e s c ript ion TORSCA

UPPERHA LFMA 'I'R I X D I A G ONAL=ABS ENT PRE- I TERATI ONS =3

DIMMAX�5,DIMM I N=1

In document A quantitative model for the design of nutritious and acceptable foods : a thesis presented in partial fulfilment of the requirements for the degree of Ph D in Product Development at Massey University (Page 168-171)