Advances in Psychology Volume 20 Trends in Mathematical Psychology

TRENDS IN MATHEMATICAL PSYCHOLOGY

ADVANCES IN PSYCHOLOGY 20 Editors

G . E. STELMACH

P. A . VROON

NORTH-HOLLAND AMSTERDAM ' N E W YORK'OXFOKD

TRENDS IN MATHEMATICAL PSYCHOLOGY

Edited by

E. DEGREEF and

J. VAN BUGGENHAUT Centrefor Statistics and Operational Research Brussels, Belgium

1984

NORTH-HOLLAND AMSTERDAM. NEW YORK . OXFORD

0 Elsevier Science

Publishers B.V.. 1984

All rights reserved. No part of this publication may be reproduced. stored in a retrieval system. or transmitted. in any form o r by any means. electronic. mechanical. photocopying. recording o r otherwise. without the prior permissionof thecopyright owner.

ISBN: 0 4 4 87512 3

Publishers: ELSEVIER SCIENCE PUBLISHERS B . V . P.O. Box 1991 1ocN) B Z Amsterdam The Netherlands

Sole disiribur0r.rfor the U.S.A. und (briadu. ELSEVIER SCIENCE PUBLISHING COMPANY. INC. 52 Vanderbilt Avenue New York. N.Y. 1OUI7 U.S.A.

Library of Comgmm Catmlogl~g11 PmbUeathm Datm

MBin.entry under title: Trends in mathematical psychology. (Advances in psychology ; 2 0 ) Papers presented at the 14th European Mathematical Ssychology Group Meeting, held in Brussels, Sept. 12-14,

1983. Includes indexes. Psychometrics--Congresses. I. Degreef, E., 1953TI. Buggenhaut, J. van, 1937111. European Mathematical Psychology Group. IV. European Mathematicd' Psychology Group. Meeting (14th : 1983 : Brussels, Belgium) V. Series: Advances in psychology ( h t e r d a m , Netherlands) 4 20.

.

BF39.T74 1984 150' .28'7 ISBN 0-444-87512-3 ( U . S . )

84-6032

PRINTED IN THE NETHERLANDS

V

PREFACE

T h i s volume g a t h e r s most o f t h e papers p r e s e n t e d a t t h e 1 4 t h Eurooean Mathem a t i c a l Psychology Grouo Meetinq. Sentember 12 t o t e i t Brussel.

The m e e t i n g took p l a c e i n B r u s s e l s f r o m

September 14, 1983 and was h o s t e d by t h e V r i j e U n i v e r s i -

F i n a n c i a l s u p n o r t was a l s o p r o v i d e d by; t h e p e l q i a n " N a t i o -

n a a l Fonds voor wetenschanpeli j k Dnderzoek", t h e B e l g i a n " t c i n i s t e r i e van N a t i o n a l e Opvoeding", t h e E e l F i a n " C u l t u r e l e B e t r e k k i n g e n " and t h e " N a t i o n a l e Bank van B e l g i e " . The i d e a o f t h e Groun i s t o b r i n g t o g e t h e r once a y e a r , neoDle i n Europe w o r k i n g i n t h e f i e l d o f V a t h e m a t i c a l Psychology,

Taken i n t o a c c o u n t t h e

growing importance a t t a c h e d t o mathematical models i n human s c i e n c e s , t h e exaeriences a c q u i r e d i n Drevious meetings and t h e presence, besides o t h e r we1 1-known p a r t i c i p a n t s , o f f o u r i n v i t e d l e c t u r e r s , namely S. Crossberg (Boston U n i v e r s i t y ) , F.S. and V.F.

Venda

-

V.Y.

Roberts (Rutoers, S t a t e U n i v e r s i t y o f New J e r s e y )

K r y l o v (Floscow, USSR Academy o f Sciences), gave us

t h e i d e a t o make a s e l e c t i o n o f t h e c o n t r i b u t i o n s and t o g a t h e r them i n a book. I n o r d e r t o s t r u c t u r e t h e whole, we t o o k t h e l i b e r t y t o groun t h e papers i n t o t h r e e p a r t s , knowing t h a t t h e c l a s s i f i c a t i o n can be discussed; o f t h e papers, indeed, can f i n d a p l a c e i n more than one p a r t .

some

So y o u w i l l

find: Part I

: P e r c e p t i o n , l e a r n i n g and memory

P a r t I 1 : Order and measurement P a r t 111: Data a n a l y s i s . ble hope t h a t t h e s t u d i e s c o l l e c t e d here, f a i r l y r e o r e s e n t t h e d i f f e r e n t p e r s p e c t i v e s and t h a t t h e volume as a whole w i l l be a dynamic r e s o u r c e f o r those who want t o keeD a b r e a s t o f f l a t h e m a t i c a l Psychology i n g e n e r a l and t h e Eurooean one i n p a r t i c u l a r . We f i n a l l y w i s h t o thank F r a n c i s Gheys f o r t h e e x c e l l e n t t y p i n g o f t h e manuscript.

I t was a l o t o f work, b u t we e n j o y e d i t .

The e d i t o r s B r u s s e l s , February 1984

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Vii

CONTENTS

v

Preface P a r t i cioants

xi

PART I: PERCEPTION, LFARNINI; AND MEMORY

1

Tree r e n r e s e n t a t i o n s o f a s s o c i a t i v e s t r u c t u r e s i n semantic and e n i s o d i c memory r e s e a r c h 11. b b d i , J.-P.

FivLRhUtrny,

Y.

Luong

3

Task-denendent r e p r e s e n t a t i o n o f c a t e g o r i e s and memory-ouided inference duri nq c lassi f ication

H. R U ~ ~ W L . ~ti.-(;. ,

&?hAeet

33

O u t l i n e o f a t h e o r y o f b r i g h t n e s s , c o l o r , and f o r m n e r c e n t i o n

s.

h044bUg

59

A t t e n t i on i n d e t e c t i o n t h e o r v E.C. b!icbo

a7

I m n o s s i b l e o b j e c t s and i n c o n s i s t e n t i n t e r p r e t a t i o n s

E. TLtoianne

105

I n s e a r c h i n g o f general r e g u l a r i t i e s o f a d a p t a t i o n dynamics: on t h e t r a n s f o r m a t i o n l e a r n i n g t h e o r y V.F.

Venda

121

A D r o h a b i l i s t i c choice model adanted f o r t h e a n g l e D e r c e n t i o n experiment

N.P. VenheL5.t

159

PART I 1 : ORDER AND MEASUREPIEKT

175

About t h e a s y m t r i e s o f s i m i l a r i t y judgments: an o r d i n a l n o i n t o f view

J.-P. Rah.thaePrnu

177

The a x i o m a t i z a t i o n o f a d d i t i v e d i f f e r e n c e models for p r e f e r e n c e judgments

M.A. Cnoon

193

Contents

Viii

Generalizations o f i n t e r v a l orders

1.- 7 .

209

poiqnon

Reseaux s o c i a u x g e n e r a l i s e s : en combinant graphes e t hyperoranher C.

2 19

FLnment

On conceots o f t h e dimension o f a r e l a t i c n and a g e n e r a l i z e d r e copnition e x p c r i m n t

227

K . IJe?rh4t I s o t o n i c r e g r e s s i o n a n a l y s i s and a d d i t i v i t y

239

‘Inc Patiold

7.p.

T e s t i n g Fechnerian s c a l a b i l i t y b v Faximum l i k e l i h o o d e s t i m a t i o n

of o r d e r e d b i n o m i a l narameters

25 5

?. “ n t ~ 6 4 e f d

Prnbahi l i s t i c c o n s i s t e n c y , homoaeneous fami l i e s o f r e 1 a t i o n s and

1i n e a r 1-re1 a t i ons 271

B. V o n j m d c t A o p l i c a t i o n s o f t h e t h e o r v o f meaninafulness t o o r d e r and matching e x o e r i men t s

283

F.S. Robem2 A new d e r i v a t i o n o f t h e Rasch model

E . E . Ra.ikn~i, P.C.W.

Jnmen

293

A d e f i n i t i o n o f p a r t i a l i n t e r v a l orders

? I . ?oubeno, Ph. VLncke

309

Causal l i n e a r s t o c h a s t i c deDendencies: t h e f o r m a l t h e o r y

317

?. Sfelreh

F a c t o r i z a t i o n and a d d i t i v e decomposition o f a weak o r d e r

”.

347

Suck

PADT

363

111: DATA A N A L Y S I S

The oroblem o f r e p r e s e n t a t i o n based u m n two c r i t e r i a

365

G. De Ueut, hl. G ~ 4 n e ~X. , HubaLLt Tree r e p r e s e n t a t i o n s o f r e c t a n g u t a r p r o x i m i t y m a t r i c e s

G, Oe S o e t e , W.S. DCa.tbo, C.Pl.

FUMLU,

J.D. CmoU

377

ifleak and s t r o n g models i n o r d e r t o d e t e c t and measure o o v e r t y ?.

Picken

393

Contents

ix

Am1 ic a t i o n s o f a Bayes an Poisson model f o r misreadings M.G.f/.

Jan6en

405

The polychotomous Rasch model and d i c h o t o m i z a t i o n o f graded resnonses P.G.P!.

.TanAeen, E.E. Qobkam

413

Comnonent a n a l y s i s o f t r a n s i t i o n n r o b a b i l i t i e s and i t s a n o l i c a t i o n to prisoner's d i l e m a

K. R a i n i o

433

An a n p l i c a t i o n o f mu1 t i d i m e n s i o n a l s c a l i n g on D r e d i c t i o n : t h e Radex structure

F. Van O v W e

449

Author i n d e x

473

Subject index

477

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xi

PARTICIPANTS

H. A B D I , L a b o r a t o i r e de p s y c h o l o g i e , Ancienne Facul t e , Rue Chabot Charny, 21000 Di j o n , France

H. ALGAYER, D o n n d o r f o r s t r . 93, D-8580 Bayreuth, Federal R e p u b l i c Germany J. ANDRES, R a t h a u s s t r . 53, 53 Bonn 3, Federal R e p u b l i c Germany J.-P. BARTHELEMY, ENST, Deoartement d ' I n f o r m a t i q u e , 46 Rw B a r r a u l t 75634 P a r i s Cedex 13, France A. BOHRER. CRS, S e c t i e voor P s y c h o l o g i s c h Onderzoek, Kazerne K l e i n K a s t e e l t j e , 1000 B r u s s e l , Belgium H. F. J .M. BUFFART, P s y c h o l o g i sch L a b o r a t o r i urn , Kathol i e k e U n i v e r s i t e i t Nijmegen, Postbus 9104, 6500HE Nijmegen, The N e t h e r l a n d s M.A. CROON, K a t h o l i e k e Hopeschool T i l b u r g , Hogeschoollaan 225, T i l b u r g , The Nether1ands E. DEGREEF, CSOO, V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2, 1050 B r u s s e l , Belgium L. DELBEKE, P s y c h o l o g i s c h I n s t i t u u t , K a t h o l i e k e U n i v e r s i t e i t Leuven, T i e n s e s t r a a t 102, 3000 Leuven, Belgium G. DE MEUR, U n i v e r s i t e L i b r e de B r u x e l l e s , CP 135, 1050 B r u x e l l e s , Belgium G. DE SOETE, D i e n s t v o o r Psychologie, R i j k s u n i v e r s i t e i t Gent, H e n r i Dunantlaan 2, 9000 Gent, Belgium M. DESPONTIN, CSOO, V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2, 1050 B r u s s e l , Be1 gium P. DICKES, U n i v e r s i t e de Nancy 11, Bd A l b e r t I, BP 3397, 54015 Nancy-Cedex, France J.-P. DOIGNON, U n i v e r s i t e L i b r e de B r u x e l l e s , CP 216, 1050 B r u x e l l e s , Belgium C. FLAMENT, Departement de P s y c h o l o g i e , U n i v e r s i t e de Provence, Les Blaques, Cereste, F-04110 R e i l l a n n e , France H.-G. GEISSLER, S e k t i o n Psychologie, K a r l - M a r x - U n i v e r s i t a t L e i p z i g , T i e c k s t r . 2, 7030 L e i p z i g , German Democratic R e p u b l i c M. GASSNER, U n i v e r s i t e L i b r e de B r u x e l l e s , CP 135, 1050 B r u x e l l e s , Belgium C.A.W. GLAS, C.I.T.O., Postbus 1034, 6801 MG Arnhem, The N e t h e r l a n d s S. GROSSBERG, Center f o r A d a p t i v e Systems, Boston U n i v e r s i t y , 111 C u m i n g t o n S t r e e t , Boston, Massachusetts 02215, USA P.K.G. GUNTHER, S i e b e n g e b i r g s t r . 11, D-5330 K o n i g s w i n t e r 41, F e d e r a l R e p u b l i c Germany M. HAHN, M o l l w i t z s t r . 5, D-1000 B e r l i n 19, Federal R e p u b l i c Germany K. HERBST, I n s t i t u t filr Psychologie, U n i v e r s i t a t Regensburg, U n i v e r s i t a t s t r . 31, D-8400 Regensburg, Federal R e p u b l i c Germany D. HEYER, I n s t i t u t f i r P s y c h o l o g i e , U n i v e r s i t a t K i e l , Ohlshausenstr. 40/60, D-2300 K i e l , Federal R e p u b l i c Germany M.G.H. JANSEN, I n s t i t u u t voor Onderwi jskunde, R i j k s u n i v e r s i t e i t Groningen, Westerhaven 16, 9718 AW Groningen , The N e t h e r l a n d s V.Y. KRYLOV, Department o f Mathematical Psychology, I n s t i t u t e o f Psychology, USSR, Academy o f Sciences, Moscow 129366, 13 Yaroslavskaya, USSR N. LAKENBRINK, A u f dem Kampf 11, D-2000 Hamburg 63, Federal R e p u b l i c Germany X. LUONG, L a b o r a t o i r e de Mathematiques, U n i v e r s i t e de Besancon, Besancon, France R.R. MAC DONALD, Department o f Psychology, U n i v e r s i t y o f S t i r l i n g , S t i r l i n g FK94LA. S c o t l a n d

xii

A.W.

Participants

MAC RAE, U n i v e r s i t y o f Birmingham, Box 363, Birmingham 615 ZTT, Great B r i t a i n R. MAUSFELD, U n i v e r s i t a t Bonn, Auf den S t e i n e n 13A, 53 Bonn 1, Federal R e p u b l i c Germany H.C. MICKO, I n s t i t u t f u r P s y c h o l o g i e , Technische U n i v e r s i t a t Braunschweig, Spielmannstrasse 12A, 0-3300 Braunschweig, F e d e r a l R e p u b l i c Germany B. MONJARDET, C e n t r e de M a t h h a t i q u e S o c i a l e , 54 Bd R a s p a i l , 75270 P a r i s Cedex 06, France C. MULLER, L e h r s t u h l fur P s y c h o l o g i e 111, U n i v e r s i t a t Regensburg, Postfach 397, D-8400 Regensburg, F e d e r a l R e p u b l i c Germany p . PLENNIGER. Seminar fiir P h i l o s o n h i e und E r r i c h u n g s w i s s e n s c 5 a f t d e r U n i v e r s i t a t F r e i b u r g , IJerthmannnlatz, D-7800 F r e i b u r o , F e d e r a l R e p u b l i c Germany B. ORTH. I n s t i t u t f u r P s y c h o l o g i e , U n i v e r s i t a t Hamburg, Von-Melle-Park 6, D-2000 Hamburg 13, F e d e r a l R e p u b l i c Germany M. PIRLOT, U n i v e r s i t e de 1 ' E t a t a Mons, 17 P l a c e Warocque, 7000 Mons, Belgium J .G.W. RAAIJMAKERS, P s y c h o l o g i s c h L a b o r a t o r i u m , K a t h o l i e k e U n i v e r s i t e i t Nijmegen, Postbus 9104, 6500 HE Nijmegen. The N e t h e r l a n d s K. R A I N I O , U n i v e r s i t y o f H e l s i n k i , P e t a k s e n t i e 44, 00630 H e l s i n k i , F i n l a n d F.S. ROBERTS. Qutqers, S t a t e U n i v e r s i t y c f f'ew Jersey. Deep. o f 'lath. a t New Brunswick, H i l l Center f o r t h e '4athematical Sciences, Rush Camous, New Rrunswick, New J e r s e y 08903, 1J.S.A. E.E. ROSKAM, Vakgroep Mathematische P s y c h o l o g i e , K a t h o l i e k e U n i v e r s i t e i t Nijmegen. Postbus 9104, 6500 HE Nijmegen, The N e t h e r l a n d s M. ROUBENS, F a c u l t e P o l y t e c h n i q u e de Mons, 9 Rue de Houdain, 8-7000 Mons, Belgium U. SCHULZ, F a k u l t a t f u r P s y c h o l o g i e und S p o r t w i s s e n s c h a f t , A b t . f u r e x p e r i m e n t e l l e und angew. P s y c h o l o g i e , U n i v e r s i t a t B i e l e f e l d , P o s t f a c h 8640, 4800 B i e l e f e l d , Federal R e p u b l i c Germany A . J . SMOLENAARS, P s y c h o l o g i s c h L a b o r a t o r i u m , U n i v e r s i t e i t Amsterdam, WeesDerolein 8 . 1018 XA Amsterdam, The N e t h e r l a n d s R. STEYER,' F a c h b e r e i c h I - P s y c h o l o g i e , U n i v e r s i t a t T r i e r , Schoeidershof, 0-5500 T r i e r , Federal R e p u b l i c Germany R. SUCK, U n i v e r s i t a t Osnabruck, P o s t f a c h 4469, 45 Osnabruck, F e d e r a l Republ i c Germany E . TEROUANNE, UER Mathematiques, U n i v e r s i t e Paul V a l e r y , BP 5043, 34032 M o n t p e l l i e r - Cedex, France P. VAN ACKER, 1 Chaussee de Wavre, 1050 B r u x e l l e s , B e l g i u m J . VAN BUGGENHAUT, CSOO. V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2. 1050 B r u s s e l , B e l g i u m A . VAN DER WILDT, CSOO, V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2, 1050 B r u s s e l , Be1g i um A. VAN DINGENEN, CSOO, V r i j e U n i v e r s i t e i t B r u s s e l , P1 e i n l a a n 2 , 1050 B r u s s e l , Belgium L . VAN LANGENHOVE, F a c u l t e i t P s y c h o l o g i e en Opvoedkunde, V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2, 1050 B r u s s e l , Belgium F. VAN OVERWALLE, EDUCO, V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2 , 1050 B r u s s e l , B e l g i u m J.C. VAN SNICK. F a c u l t 6 des Sciences Economiques e t S o c i a l e s . U n i v e r s i t e de 1 ' E t a t a Mons, 17 P l a c e Warocque, 7000 Mons, Belgium V.F. VENDA. Department o f E n g i n e e r i n g Psychology, I n s t i t u t e of Psychology, USSR Academy o f Sciences, Moscow 129366, 13 Yaroslavskaya. USSR R . VERHAERT, CSOO, V r i j e U n i v e r s i t e i t B r u s s e l , P l e i n l a a n 2 , 1050 B r u s s e l , Belgium

Participants

N . D . VERHELST, Subfacul t e i t der psychologie, vakgroep PSM, R i jksuniversit e i t Utrecht, Sint-Jacobsstraat 14, 3511 BS Utrecht, The Netherlands Ph. VINCKE, I n s t i t u t de Statistique, Universite Libre de Bruxelles, CP 210, 8-1050 Bruxelles, Belgium

xiii

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PARTI PERCEPTION, LEARNING AND MEMOR Y

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TRENDS IN MATHEMATICAL PSYCHOLOGY E. Degreef and J . Van Bu genhaut (editors) 0 Elsevier Science Dublisfers B. V. (North-Holland), 1984

3

TREE REPRESENTPTIONS OF ASSOCIATIVE STPUCTUpE5 I N SFFWNTIC AND E P J SOD1 C VFF1ORY RE SF ARCH Herve Abdi Laboratoi r e de Ps.vcholoaie, D i j o n Jean-Pierre Barth12l&ny F.PJ.q.T., Paris Xuan Luona L a b o r a t o i r e de Mathematioues, Besanqon lnle exnose some research i n the area o f psycholorry o f memory i n v o l v i n q o r o x i m i t v o r d i s t a n c e m a t r i c e s . nronose some ways o f b u i l d i n g LIP such r a t r i c e s .

Then

we d e t a i l an a l a o r i t h m allowinc! the r e n r e s e n t a t i o n o f p r o x i m i t y matrices b y an a d d i t i v e t r e e , and c o n t r a s t t h i s new a l o o r i thm w i t h orevious ones,

F i n a l l v , we

examine some r e s u l t s obtained w i t h t h s method.

1. INTRODUCTION The general ournose o f t h i s naner i s t o emphasize the u t i l i t y and describe the use o f a d d i t i v e t r e e s i n o r d e r t o describe data c o l l e c t e d i n the f i e l d of the nsychology o f Femory.

This naner i s t h r e e f o l d : we f i r s t describe

some research l e a d i n o t o the c o n s t r u c t i o n o f distance o r n r o x i m i t y matrices; secondly we expose and d e t a i l the c o n s t r u c t i o n o f an a d d i t i v e t r e e as a r e n r e s e n t a t i o n o f the o r i o i n a l r i a t r i x : f i n a l l y , we examine the r e s u l t s o b t a i n ed. The u t i l i z a t i o n o f c l u s t e r i n q methods f o r a t t e s t i n a t h e o r a a n i r a t i o n o f memor v o r r e v e a l i n g i t s s t r u c t u r e has been s t r o n y l y advocated r e c e n t l y by some authors i n d i f f e r e n t areas o f c o g n i t i v e Fsycholooy (see, among others:

M i l l e r (1969) (1982)).

, Henley

(1969), F r i e n d l y (19781, Rosenbera e t a1 (1968)

,

(1972),

Most o f the used methods amount t o r e n r e s e n t the o r i g i n a l m a t r i x

by an U l t r a w t r i c Tree.

Recently, t h e r e has been an attempt t o b u i l d sow

methods l e a d i n g t o r e n r e s e n t a t i o n s l e s s s t r i n g e n t than the c l a s s i c a l U1 t r a m e t r i c Tree, i.e. the A d d i t i v e Tree (see Carroll & Chang (1973), Cunningham (1974), (1978); S a t t a t h R Tversky (1977)).

Ye nronose h e r e a f t e r an (econo-

m i c a l ) h e u r i s t i c g i v i n a an A d d i t i v e Tree from a o r o x i m i t y m a t r i x and i l l u s t r a te i t with c a l oaners.

some examples borrowing from our c u r r e n t research o r from c l a s s i -

H. ,4bdi, J.-P. Burthhlhmy und X. Long

4

2. A RUNCH OF EXAWLES

2.1. RAPTLET': : " ' i l ' f

T C THE GHOSTS"

I n 1932, R a r t l e t t asked

i:

few suhdects t o read an l r w r i c a n I n d i a n f o l k t a l e

(named "The '.tar o f the chosts"! and t o r e c a l l the s t o r i t on r e v e r a l occasions ( a w t h o d c a l l e d "rerleatec' r e n r o d u c t i o n " ) ; i n a v a r i a n t o f the method ( i . e . "yerial

r e n r o d u c t i o n " ) a chain o f d i f f e r e n t s u h i e c t s i s used, the f i r s t

heinq shown the o r i c l i n a l t e x t and then r e c a l l i n n f o r the second s u b j e c t who

would nass i t t o a t h i r d and s o on.

These c l a s s i c a l e x n e r i w n t s o f P a r t l e t t

w i l l serve here t o i l l u s t r a t e a s e t o f i n f o r m a t i c nrocedures, the aim of which i s t o b u i l d s o w distances hetween t e x t s . " ) I n f o m a t i c orocedurw

For reasons o f c o m p a t i h i l i t v , the nroorams are w r i t t e n i n Standard V i c r o s o f t and a t l e a s t 64 K-Bytes o f

Pasic (Vnder C P p ) ,

RAP1

and a d i s k U n i t are need-

Although these n r o n r a m i n c l u d e some various n o s s i h i l i t i e s , we w i l l r e -

ed.

s t r i c t o u r s e l f t o the n a r t d e a l i n a s n e c i f i c a l l y w i t h the c o n s t r u c t i o n o f

metri cs between t e x t s . I t must be c l e a r t h a t when we sneak of t h e t e x t oiven by a s u b i e c t , we c o u l d sqeak as w e l l o f a s e t o f themes o r ideas aiven by a suhdect D r o v i dino an adequate codinc; o f the raw data. The t e x t s are f i r s t t r a n s f o m d i n a d i s k f i l e , then f o r each t e x t we b u i l d the Lexicon associated w i t h i t . This Lexicon c o u l d be e i t h e r a Boolean Lexicon (i.e. i t rnerelv i n d i c a t e s the Presence o r the Absence o f the i t e m

o f Vocabulary) o r an i n t e o e r Lexicon ( i . e . rences o f each i t e m ) .

-

build

by union

-

i t i n d i c a t e s t h e numher o f Occur-

From the d i C f e r e n t Lexicons (Boolean or I n t e g e r ) we

a General Lexicon t h a t d e f i n e s the Vocabularv shared hy

the d i f f e r e n t t e x t s .

R ) Construction o f distances hetween t e x t s k n e n d i n q on the p o i n t o f view adonted, we c o u l d d e f i n e d i f f e r e n t distances; as an i l l u s t r a t i o s we examine t h r e e ways: (i\

the t e x t s as suhsets of the Vocabulary

( i i ) the t e x t s as R i - o a r t i t i n n s o f the Vocahularv ( i i i)a "orobabi 1i s ti c " q e n e r a 1 i t a t i o n . Dpncte by L i the Lexicon associated w i t h a t e x t T i , the aeneral Lexicon hy

V =

0

i

L i . and by

the comlement o f L i i n V.

5

Tree representations of associative structures

( i ) Each (Boolean) Lexicon* i s a subset o f t h e Vocahularv and we c o u l d use, f o r examnle , t h e we1 1-known d i s t a n c e between s e t s , t h e so c a l l e d c a r d i n a l o f t h e symmetric d i f f e r e n c e : d(Ti,Tj) ( i i ) {Li,E}

= ILi A L j l = ILi

nnl

+ l E n Ljl.

d e f i n e s a R i - P a r t i t i o n o f V ( i . e . a P a r t i t i o n w i t h two classes), So, we c o u l d use sow d i s t a n c e s between P a r t i t i o n s

and so does { L j , a l .

( c f . A r a b i e & Roorman ( 1 9 7 3 ) ) o r S i - P a r t i t i o n s , e . q . symmetric d i f f e r e n c e hetween ' i - p a r t i t i o n s d(Ti,Tj)

= =

the distance o f the

t h a t can be expressed as:

2( l L i n L i l + l E q n l ) ( l L i ~ ~ l + l E n L j l ) 2( lT"Kil)(I L i A L j I )

( i i i ) I n o r d e r t o take e x n l i c i t l y account o f t h e I n t e g e r Lexicons we c o u l d l o o k f o r an e x t e n s i o n of ( i ) . Ielith each T i i s a s s o c i a t e d a p r o b a b i l i t y measure on V ( i .e. t h e frequency o f t h e d i f f e r e n t words); denote t h e p r o b a h i l i t y o f i t e m x o f t e x t T i by P i ( x ) ; then we f i n d a f a m i l y o f d i s t a n c e s by d,(Ti

,Tj) =

c

[Pi(x)-Pj(x)I?

*V 2.2.

FFnTLJRES OF PFRSONALITY

T h i s r e s e a r c h l a y s on t h e b o r d e r between t h e work on t h e o r o a n i z a t i o n o f t h e semantic memory and t h e work unon the " i m p l i c i t Dsycholoqy".

The ourpose i s

t o describe the subjective orsanization o f the q u a l i f i e r s o f the character. As a m a t t e r o f f a c t , i t has o f t e n been n o t e d t h a t we t e n d t o qroup s u b j e c t i v e l y some f e a t u r e s o f c h a r a c t e r as i f we has an " I m o l i c i t Theory o f Pers o n a l i t y " ( c f . e.a.,

Rosenherrr e t a1 (1972), 'Veoner and V a l l a c h e r ( 1 9 7 7 ) ) .

I n t h i s e x p e r i m e n t we s e l e c t f i f t y e i q h t q u a l i f i e r s o f t h e c h a r a c t e r ( u s i n a some Thesauruses and a b i t o f l i t e r a t u r e , . ..). These q u a l i f i e r s a r e then o r i n t e d on s e o a r a t e cards and a i v e n i n d i v i d u a l l y t o t w e n t y - e i o h t s u b j e c t s w i t h t h e r e q u e s t t h a t he o r she s o r t t h e cards i n t o D i l e s w i t h t h e c o n s t r a i n t t h a t " t h e cards i n a same w i l e g i v e t h e f e e l i n g t o no t o o e t h e r " ; s u b j e c t s were f r e e t o choose t h e numher o f D i l e s f o r s o r t i n n ( f o r a r e v i e w o f t h e p r o and c o n t r a o f t h e s o r t i n a method, see Rosenbern ( 1 9 8 2 ) ) .

*N o t i c e

fuzzy " t h e "boolean" d i s t a n c e i n (i) and ( i i ) by t a k i n g t h e f u z z y e q u i v a l e n t o f t h e u n i o n and i n t e r s e c t i o n , i .e. Min and Max. t h a t one c o u l d

"

6

H. Abdi, j . 2 . Borthdl6my and X. Luong

Hence, each subject exoresses his oninion by a nartition on the s e t of the n u a l i f i e r s , and f o r usino as a 0-rlethodoloay ( c f . Kerlinoer (1973)) the afore evoked distances between nartitions could e a s i l y be used. The p a r t i tion given by a subject i s associated with a matrix whose rolls and columns ren-esert the Q u a l i f i e r s , a n d where we p u t a 1 a t the intersection of a row and a column i f the nualifiers are not sorted i n the same n i l e by the subi e c t . Obviously t h i s i s a distance matrix ( c f . W l l e r ( 1 9 6 9 ) \ , and so will he the matrix definetiby the sum of the matrices of tbe d i f f e r e n t subjects. I n this matrix we simnly count the number of suhjects who do n o t n u t tooether the q u a l i f i e r s . Pually vie could have & f i r e d a matrix o f co-occurences by the sum of the so-called incidence matrix (where a 1 means t + a t the q u a l i f i e r s are i n the same n i l e ) , f n r commodity reasons t h i s i s the m a t r i x we qive l a t e r ( c f . Table 3 ) . I t must be noted, in nassinq, t h a t the Data obtained a n d consenuently the distance matrix denend uoon the w t h o d s desinned f o r o b t a i n i n n such Data. I n n a r t i c u l a r , other wthods ( e . 0 . word associations, o r distances between words in free-recall, e t c . ) lead to other results (see Pbdi (1383)). 2.3. OLRIEP RUT