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« 3 M T M M f - » ( Ä 2 ) A Compoï; Trait Components T r a i t T 1 T 2 T 3 Impiilsivitv fil '14 Kxtravesion 52 M -1!) \. h M o t i v a t i o n 1 A n x i e t y 33 fil .62 'loportion V a r i a b i l i t y .37 .22 13 It ( o r e Matrix Method Trait ( iMiiiioii' Components T 1 (Common)

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Kionnrnl.

X Mt

A i a l u e . l ' , C a i i o l l . J D, & DeSatbo. W S ( 1 9 8 7 ) . Thrci-miv sailing, ««</ n;.i; He\ e r l v H i l l s . ( A '

Hcutlcr. I ' M . * l .cc. S V ( 1 9 7 9 ) . A s t a t i s t i c a l d e v e l o p m e n t ol three mode I . K loi . m . i l v s i s H n / i s l i Journal «I Mulhi'tniitiftil mul Slu/is/inil I'svc/ioloxv. 32, 87 101

H i o u w c r I ' . X' kroonenheit;. l ' M ( 1 9 9 1 ) . Some noirs o n I h r c l i . : i o n o l r x l r n d r i l r o t r m a t i n e s Jimninl ol Cliissi/ii'ii/ioti. <S'. 93 98

B u r d i c k . D S (199S). A T I i n t r o d u c t i o n to lensoi products w i t h a p p h c . l i i o n s to m u l l i w a v d . i l , i a n a l y s i s ('hi'tnonit'trii's anil InlrlliKi'til l.nhi>t<itor\ Svali'nr-229 237.

( ' a t h c r . A. cK- K t o o n r u h r i v . . I' M ( 1 9 ' H i ) . D r i o n i p o s i l i o n s and b i p l o l s in tlircc w a y ' orrcspondciK c a n a l y s i s l\\chimn'ttikd. d I

( ' a i i o l l . I I ' X1 C h a n t ; . I I ( 1 9 7 0 ) A n a l y s i s of i n d i v i d u a l d i f f e r e n c e s in i n t i l l i

d i m e n s i o n a l scahiu; v i a an N way t ; c n c r a l i / a t i o n of " I ' j k a i l V o u n t ; " de< 0111 position l\\chomrlnk<i.'.Ui.2H'.\ : t l 9

C a i i o l l . J . D . . A Chants'. .1 .1 ( 1 9 7 2 ) . //)/(>.SV.1 / 1 wm'xihxitwn <>t IMWM..

iilloH'inK iniO^vni'ulii i i ' l i ' t i ' i i i i xvs/cw, us U'cll us uti iinulvttc <it>t»'<ninui linn to l,\'l)S( AI. l'apei p i e s e n l e d al the Spnnt; M e e t i n g of the I'syclionirt

l i e S o c i e t y , 1'micelon. N e w .leisev

P ' t a n c , A (199:!) i'.luili- nlnchin/ui' </cs niHltildhlrdu*- Afifiorl* tic I'tilwbrc trnsn

nt'lli' Thèse l ' n i y e i s i l é d e M o n t p e l l i e r I I . F i a n c e

( . a b i i c l . K R. ( 1 9 7 1 ) The hiplot «eowraphu al d i s p l a y ol i n a l i i i c s \ \ i t h a p p h i a

lion« to principal components niomcinkn. :>s. i ; > : t 167.

( . a l i i i e l . K l\ ( K I H 1 ) . H i p l o t d i s p l a y of i n u l l u ai l a t e i n a l r i c c s lor i n s p e c t i o n ol d a t a and diai;nosis In Y I t a i n e l l ( I'.d \ Intfipit'tuin niulliruruiti• tlutii . pp

H7 173), Chicester, ri< \ \ i i e \

l l a i ' . h i n a n . K A, X' DeSarho, W S ( 1 9 8 1 ' . An applu alion of 1 ' A R A K A C to a s m a l l sample p i o h l r i n . d c i n o n s l i a l i n t ; p i e i ' t ' o c essint;. o r t h o K o i u i h U c o n s t i a i n l s . a n d s p l i t h a l l d i a g n o s t i c t e c h n i i i i i e s I n I I ( , l a « . C \\ Snvder. Jr., J. A l l a l t i e . X- K I' M c D o n a l d ( K d s \ A'CMV/IC/I mrtlioils lor mullimotlc tltilu

innilvsis (pp (i()2 <v12). New York TracKcr

I I . u s I n n , in. K A. X l . u n d v , M K ( I 9 8 1 a > . The I ' A K A K A C ' model for t h r e e WaJ

i , n toi analTiUand multidimensional scaling in II i. Law,C \\' s n \ < i e i . ii

.1 A l l a l t i e . ,<• K' I' Mi Donald ( K d s ) , h'escuxli nu-lhixh lor mnlttm<nl<- lintn

tnid/vsis ( p p 122 2 I ! > ) . N r w Y o t k l ' i a i - . i

l l a i s l i i n a n . K' A . ,<> l . u n d v . M !•'. (198.1hl. Data preprocessing and t h e e x l r n d r d 1 ' A R A K A C model In 1 1 1 , L a w . C \V S n v d e r . l i . .1 A l l a t t i e . \- R P. M c D o n a l d ( K d s ) . Ki'sctniii mclhoi/s Im mnltimotli' ilnla mtulvsis (pp 28/1). New Y o i k Prat)

l l a i s h m a n . R A. & l u n c h . M V ( 1 9 9 1 ) . 1 ' A R A K A C 1 ' a r a l l e l l a c loi ai

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metrika, 56, 449 470.

II. A . I . . . Kroonenberg, P.M.. & Ten Dergc, J . M . F . (1992). An e f l i c i c - n t a l g o r i t h m for TUCKALS3 on data with large n u m b e r s of observation u n i t s

1'sychometrika. 57, 415 422.

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mode!', Leiden D S W O I ' n

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and applications Leiden D S W O I '

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mode d a t a by m e a n s o t a l t e r n a t i n g l e a - . I Squares .ilv.nl i t I n i i ' . /\v<lin»ii'/nifii.

1:, ( i ' l ' ) (

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»rTr **W1*»fAfr«ft, /M. I 7.

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Abstract

Three-Way Data Analysis and Us Recent Developments

Pu r K R M. KROONI NIII-RC.

Leuten l'ntretsth'

HISAO M I Y A N O

('hihn

In this papei. I h t e e w a y (l.il.i , i n . i l \ M S m e t h o d s .in- r e v i e w e d and explained Ironi the viewpoint ol T u c k e t models A simple description of ;i three vv.iv d a t a set is followed by an introduction ol t y p i c a l Tucki-r models. including the Tucker 2, Tucker H. and l'aial.ic models Next the (-slimation alKonthni d e x e l oped liv KroonenheiK is explained somewlial in d e t a i l especially loi the Tucker 3 (or Tucker 2) model, alon« w i t h discussions on pn-pnx c-ssin« ol U n . ' d a t a The algorithm is then applied t o growth curve data to show w h a t infor Illation is obtained l>v t l u e e w . u d a t a a n a l y s i s The linal i devoted to

|| d e v e l o p m e n t s in three w a v d a t a analysis

Key w o i d s Ihicemode l h r e i - « a \ model, individual dilleiences scaling model, a l t e r n a t m i ! leas! sipiaies e s t i m a t i o n , g r o w t h c u i \ e d a t a . MTMM d a t a

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