A hybrid compensatory-noncompensatory model of residential
preference structures
Citation for published version (APA):
Borgers, A. W. J., Timmermans, H. J. P., & Veldhuisen, K. J. (1986). A hybrid compensatory-noncompensatory
model of residential preference structures. Netherlands Journal of Housing and Environmental Research, 1(3),
227-233. https://doi.org/10.1007/BF02505798
DOI:
10.1007/BF02505798
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Published: 01/01/1986
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A H Y B R I D C O M P E N S A T O R Y - N O N C O M P E N S A T O R Y M O D E L O F R E S I - D E N T I A L P R E F E R E N C E S T R U C T U R E S A l o y s B o r g e r s , H a r r y T i m m e r m a n s a n d J a n V e l d h u i s e n I n t r o d u c t i o n T h e m o d e l l i n g of r e s i d e n t i a l a n d h o u s i n g c h o i c e b e h a v i o u r a n d p r e f e r e n c e s t r u c t u r e s h a s c o n t i n u o u s l y b e e n a n a r e a of m a j o r a t t e n t i o n in h o u s i n g a n d b u i l d i n g r e s e a r c h o v e r t h e l a s t d e c a d e s . E s p e c i a l l y d i s c r e t e c h o i c e m o d e l s h a v e f r e q u e n t l y b e e n a d o p t e d to p o r t r a y t h e s e p r o c e s s e s . E x a m p l e s i n c l u d e O n a k a (1983), O n a k a and C l a r k (1983), Van L i e r o p (1981, 1985), Van L i e r o p a n d N i j k a m p (1984), Van L i e r o p a n d R i m a (1984), L o n g l e y (1984), V e l d h u i s e n (1984, 1985). B o t h t h e s t a n d a r d m u l t i n o m i a l l o g i t m o d e l a n d t h e n e s t e d l o g i t m o d e l h a v e r e c e i v e d m a j o r a t t e n t i o n , t h e l a t t e r t y p e e n a b l i n g t h e r e s e a r c h e r t o i n c o r p o r a t e t h e s i m i l a r i t y b e t w e e n t h e c h o i c e a l t e r n a t i v e s in t h e m o d e l (see M c . F a d d e n , 1978 for d e t a i l s ) . B o t h t h e s e t y p e s of m o d e l s i m p l i c i t l y a s s u m e s o m e k i n d o f c o m p e n s a t o r y d e c i s i o n - m a k i n g p r o c e s s . T h a t is, low s c o r e s on s o m e a t t r i b u t e m a y , in t h e o - ry a t l e a s t , b e c o m p e n s a t e d by h i g h s c o r e s on o n e o r m o r e of t h e r e m a i n i n g a t t r i b u t e s . A l t h o u g h s a t i s f a c t o r y p r e d i c t i v e r e s u l t s h a v e b e e n o b t a i n e d w i t h t h e s e m o d e l s in t h e p a s t , t h e a s s u m p t i o n o f c o m p e n s a t o r y d e c i s i o n - m a k i n g s e e m s a t l e a s t to s o m e d e g r e e c o u n t e r i n t u i t i v e . P e o p l e m a y s c r e e n t h e a v a i l - a b l e c h o i c e a l t e r n a t i v e s a c c o r d i n g to s o m e a t t r i b u t e s , a n d c h o i c e a l t e r n a - t i v e s f a i l i n g s u c h a t e s t a r e no l o n g e r c o n s i d e r e d as v i a b l e a l t e r n a t i v e s . In t h e o r y , n o n c o m p e n s a t o r y d e c i s i o n r u l e s , s u c h as t h e c o n j u n c t i v e r u l e a n d t h e l e x i c o g r a p h i c r u l e , m a y d e s c r i b e s u c h d e c i s i o n p r o c e s s e s . T h e c o n j u n c t i v e r u l e s t a t e s t h a t in o r d e r to b e c h o s e n a n a l t e r n a t i v e m u s t e x c e e d s p e c i f i c a c c e p t a b l e a t t r i b u t e v a l u e s w h i c h a r e d e f i n e d o n e a c h a t t r i b u t e . A l t e r n a - t i v e s t h a t h a v e v a l u e s o u t s i d e t h e a c c e p t a b l e r a n g e a r e r e j e c t e d as u n a c - c e p t a b l e , w h i c h i m p l i e s t h a t t h e w o r s t a t t r i b u t e o f a n a l t e r n a t i v e is v i t a l in t h e d e c i s i o n - m a k i n g p r o c e s s . N o t e t h a t c o m p e n s a t i o n is n o t a d m i t t e d . T h e l e x i c o g r a p h i c r u l e s t a t e s t h a t t h e a l t e r n a t i v e s a r e f i r s t c o m p a r e d o n t h e m o s t i m p o r t a n t a t t r i b u t e . If t w o or m o r e a l t e r n a t i v e s a r e e q u i v a l e n t a t t h i s s t a g e , t h e y a r e c o m p a r e d on t h e n e x t m o s t i m p o r t a n t a t t r i b u t e . T h i s p r o c e s s is a s s u m e d t o c o n t i n u e u n t i l all a l t e r n a t i v e s a r e ( w e a k l y ) r a n k e d or u n t i l all a l t e r n a t i v e s h a v e b e e n c o n s i d e r e d . P r e v i o u s w o r k of t h e a u t h o r s h a s i n d i - c a t e d h o w e v e r t h a t t h e s e s t r i c t l y n o n c o m p e n s a t o r y d e c i s i o n r u l e s w e r e u n - a b l e t o r e p r o d u c e i n d i v i d u a l c h o i c e b e h a v i o u r a n d p r e f e r e n c e s t r u c t u r e s . So
i n d i v i d u a l s m a y a p p a r e n t l y u s e c e r t a i n a t t r i b u t e s as s c r e e n i n g d e v i c e s for d e l i m i t i n g t h e i r c h o i c e s e t , w h i l e o t h e r a t t r i b u t e s a r e u s e d in a c o m p e n s a - t o r y f a s h i o n to a r r i v e a t s o m e o v e r a l l u t i l i t y for t h o s e a l t e r n a t i v e s t h a t r e - m a i n in t h e i r c h o i c e s e t s . If s u c h b e h a v i o u r is p r e v a l e n t , a h y b r i d c o m p e n s a - t o r y - n o n c o m p e n s a t o r y m o d e l is n e e d e d t o u n c o v e r r e s i d e n t i a l a n d h o u s i n g c h o i c e p r o c e s s e s a n d p r e f e r e n c e s t r u c t u r e s . T h e a i m of t h i s a r t i c l e is to d e v e l o p a n d t e s t s u c h a h y b r i d m o d e l . T h e a r t i c l e i s o r g a n i s e d as follows. F i r s t , in t h e n e x t s e c t i o n , t h e h y b r i d c o m p e n - s a t o r y - n o n c o m p e n s a t o r y m o d e l of r e s i d e n t i a l a n d h o u s i n g p r e f e r e n c e f o r m a - t i o n will b e o u t l i n e d . T h i s is f o l l o w e d in s e c t i o n 3 by a d e s c r i p t i o n of t h e d a t a and t h e r e s u l t s of a t e s t of t h e m o d e l on t h e s e d a t a r e f e r r i n g to r e s i - d e n t i a l p r e f e r e n c e s in t h e p r o v i n c e of Z u i d - H o l l a n d , T h e N e t h e r l a n d s . T h e p a p e r is c o n c l u d e d by d i s c u s s i n g t h e i m p l i c a t i o n s of t h e e m p i r i c a l f i n d i n g s a n d s o m e p o s s i b l e i m p r o v e m e n t s of t h e m o d e l . T h e m o d e l A s s u m e t h a t r e s i d e n t i a l p r e f e r e n c e f o r m a t i o n is r e g u l a t e d by a m i x t u r e of c o m p e n s a t o r y a n d n o n c o m p e n s a t o r y m e c h a n i s m s . S u p p o s e an i n d i v i d u a l a t - t a c h e s to e a c h a t t r i b u t e s o m e t h r e s h o l d Tj. If a c h o i c e a l t e r n a t i v e ' s a t t r i - b u t e l e v e l is g r e a t e r t h a n or e q u a l to t h e c o r r e s p o n d i n g t h r e s h o l d , t h e a l t e r - n a t i v e p a s s e s t h e n o n c o m p e n s a t o r y t e s t a n d e n t e r s t h e c o m p e n s a t o r y p a r t of t h e d e c i s i o n m a k i n g p r o c e s s . If it d o e s n o t p a s s t h i s t e s t , t h e c h o i c e a l t e r n a - t i v e is no l o n g e r c o n s i d e r e d . A s s u m e t h a t t h e t h r e s h o l d s a r e s t o c h a s t i c v a r i a - b l e s to a c c o u n t for m e a s u r e m e n t e r r o r s , i n s t a b i l i t y or h e t e r o g e n e i t y a t t h e a g g r e g a t e l e v e l . It f o l l o w s t h a t t h e p r o b a b i l i t y of t h e i - t h c h o i c e a l t e r n a t i v e p a s s i n g t h e t e s t is e q u a l to:
Pij = Pr (
Xij
> Tj + ~j)(i)
w h e r e , Pij is t h e p r o b a b i l i t y t h a t t h e i - t h c h o i c e a l t e r n a t i v e p a s s e s t h e t e s t on t h e j - t h a t t r i b u t e ; Xi] d e n o t e s t h e j - t h a t t r i b u t e l e v e l of a l t e r n a t i v e i; j is t h e t h r e s h o l d a s s o c i a t e d w i t h t h e j - t h a t t r i b u t e ; ~j Is an e r r o r t e r m It is a s s u m e d t h a t t h e z :'s a r e n o r m a l l y d i s t r i b u t e d . T h e p r o b a b i l i t y t h a t c h o i c e a l t e r n a t i v e i s a t i s } i e s all s e l e c t i o n c r i t e r i a , chat is t h e p r o b a b i l i t y t h a t c h o i c e a l t e r n a t i v e i b e l o n g s t o t h e s e t ~ of f e a s i b l e c h o i c e a l t e r n a t i v e s u n d e r t h e a s s u m p t i o n of i n d e p e n d e n t s c r e e n i n g o f t h e a t t r i b u t e s t h e n e q u a l s : p( i~c~ ) = ][jPij (2)
T h e p r o b a b i l i t y t h a t t h e c h o i c e is m a d e f r o m a p a r t i c u l a r c h o i c e s e t A t h u s e q u a l s : P A = E i { P ( i s - p ( i ' s i ' z i
(3)
T h e a b o v e e q u a t i o n r e s u l t s a f t e r f i n i s h i n g t h e n o n c o m p e n s a t o r y p a r t of t h e c h o i c e p r o c e s s . T h e s e c o n d c o m p o n e n t o f t h e a s s u m e d d e c i s i o n - m a k i n g p r o c - ess c o n s i s t s of a c o m p e n s a t o r y c h o i c e p r o c e s s in w h i c h t h e a t t r i b u t e s of t h e a l t e r n a t i v e s r e m a i n i n g in t h e c h o i c e s e t s a r e e v a l u a t e d in a c o m p e n s a t o r y f a s h i o n . It is a s s u m e d t h a t t h e h y b r i d c h o i c e m o d e l m a y b e w r i t t e n as: Pi = h A { ( e x p ( g j { g j X i j ) / g i , c A ( e x p ( Z j S j X i , j ) } P A(4)
T h e a b o v e e q u a t i o n a s s u m e s t h e s t a n d a r d logit e x p r e s s i o n for t h e u t i l i t i e s of t h e c h o i c e a l t e r n a t i v e s , b u t o t h e r f u n c t i o n a l r e l a t i o n s h i p s c o u l d be a s s u m e d as well. A l t h o u g h t h e m o d e l i t s e l f is new, s o m e of i t s c o m p o n e n t s c a n b e f o u n d in o t h e r w o r k on d e c i s i o n - m a k i n g a n d c h o i c e p r o c e s s e s . T h r e s h o l d s h a v e b e e n u s e d in t h e f i e l d of s p a t i a l a n a l y s i s on s e v e r a l o c c a s i o n s (Young, 1986). E s p e c i a l l y t h e c o n c e p t has b e e n u s e d in s t u d i e s of a c c e s s i b i l i t y . H o w e v e r , t h r e s h o l d s h a v e also b e e n i n c o r p o r a t e d in m o d e l s of c h o i c e b e h a v i o u r . K r i s h - n a n (1977) d e v e l o p e d a logit m o d e l w h i c h p o s t u l a t e d t h a t a n i n d i v i d u a l will o n l y p r e f e r a n a l t e r n a t i v e o v e r a n o t h e r , if its u t i l i t y e x c e e d s t h a t of t h e o t h e r a l t e r n a t i v e by a t l e a s t a p o s i t i v e v a l u e . His m o d e l h a s b e e n e x t e n d e d b y L i o u k a s (1984) to t h e c a s e of m o r e t h a n t w o c h o i c e a l t e r n a t i v e s . In t h e s a m e way, Y o u n g a n d his a s s o c i a t e s h a v e i n c o r p o r a t e d t h r e s h o l d s in e l i m i n a - t i o n - b y - a s p e c t m o d e l s , w h i c h t h e y a p p l i e d t o l o c a t i o n p r o b l e m s and r e s i d e n - t i a l c h o i c e b e h a v i o u r (Young, 1983, 1984; Y o u n g a n d O g d e n , 1983; Y o u n g a n d R i c h a r d s o n , 1980, 1983}, w h i l e R e c k e r a n d G o l o b (1979) a n d G e n s c h a n d S v e s t k a (1979) i n c l u d e d t h r e s h o l d s in l e x i c o g r a p h i c d e c i s i o n r u l e s . F i n a l l y , M e y e r a n d J o h n s o n ' s s t o c h a s t i c e l i m i n a t i o n m o d e l is also b a s e d on t h e i d e a t h a t c h o i c e a l t e r n a t i v e s s h o u l d m e e t c e r t a i n t h r e s h o l d v a l u e s to r e m a i n in an i n d i v i d u a l ' s c h o i c e s e t ( J o h n s o n a n d M e y e r , 1984). T h e i d e a o f d e t e r m i n i n g all p o s s i b l e c h o i c e s e t s is s i m i l a r to t h e a p p r o a c h a d o p t e d by S m i t h a n d S l a t e r (1981) f o r i n c l u d i n g c h o i c e s e t c o n s t r a i n t s in m o d e l s of l a b o u r flows. D a t a T h e h y b r i d c h o i c e m o d e l was t e s t e d o n d a t a p e r t a i n i n g t o r e s p o n d e n t s r e - s i d i n g in t h e p r o v i n c e of Z u i d - H o l l a n d , T h e N e t h e r l a n d s . A v a r i e t y o f d a t a w a s c o l l e c t e d but for t h e p r e s e n t s t u d y o n l y f e w of t h e s e w e r e r e l e v a n t . As p o i n t e d o u t in t h e i n t r o d u c t o r y s e c t i o n t h e m o d e l c o u l d b e a p p l i e d w i t h m i - n o r m o d i f i c a t i o n s to a c t u a l c h o i c e p r o c e s s e s , b u t in t h e p r e s e n t c a s e t h e m o d e l w a s u s e d t o u n c o v e r r e s i d e n t i a l p r e f e r e n c e f o r m a t i o n s i n c e d a t a on a c t u a l c h o i c e b e h a v i o u r w e r e not c o l l e c t e d in t h e Z u i d - H o l l a n d s a m p l e . O n l yif o n e a s s u m e s t h a t p e o p l e will c h o o s e t h e i r m o s t p r e f e r r e d r e s i d e n t i a l e n v i - r o n m e n t , t h e r e s u l t s o f t h e p r e s e n t s t u d y c a n b e i n t e r p r e t e d in t e r m s o f r e s i - d e n t i a l c h o i c e b e h a v i o u r . H o u s e h o l d ' s p r e f e r e n c e s w e r e e l i c i t e d in t h e f o l - l o w i n g way. To e a c h r e s p o n d e n t a s e t o f 13 d e s c r i p t i o n s o f r e s i d e n t i a l e n v i - r o n m e n t s , s e l e c t e d a c c o r d i n g to t h e p r i n c i p a l s of e x p e r i m e n t a l d e s i g n w a s s h o w n . In a d d i t i o n p h o t o g r a p h s w e r e u s e d to v i s u a l i s e t h e d e s c r i p t i o n s o f t h e h y p o t h e t i c a l e n v i r o n m e n t s , w h i c h d i f f e r e d in t e r m s of t h e f o l l o w i n g f o u r a t - t r i b u t e s : t e n u r e , t y p e o f d w e l l i n g , n u m b e r o f r o o m s , a n d t r a f f i c s i t u a t i o n ( s e e V e l d h u i s e n a n d H a c f o o r t , 1985). T h e s e a t t r i b u t e s w e r e s e l e c t e d b e c a u s e p r e - v i o u s a n a l y s i s on t h e s a m e s a m p l e h a d s h o w n t h e s e to b e a m o n g t h e m o s t i m p o r t a n t a t t r i b u t e s i n f l u e n c i n g r e s i d e n t i a l d e c i s i o n - m a k i n g . R e s p o n d e n t s w e r e r e q u e s t e d to s o r t t h e t h i r t e e n d e s c r i p t i o n s i n t o t w o s e t s , o n e c o n s i s t i n g o f r e s i d e n t i a l e n v i r o n m e n t s w h i c h t h e y l i k e d less t h a n t h e i r p r e s e n t e n v i r o n - m e n t a n d t h e o t h e r c o n s i s t i n g o f t h o s e e n v i r o n m e n t s for w h i c h t h e i r e v a l u a - t i o n w a s h i g h e r t h a n for t h e i r p r e s e n t r e s i d e n c e . E a c h r e s p o n d e n t w a s a s k e d to r a n k t h e l a t t e r s e t of h y p o t h e t i c a l r e s i d e n t i a l e n v i r o n m e n t s in t e r m s of o v e r a l l p r e f e r e n c e . T h i s p r o c e d u r e y i e l d s a r a n k i n g of t h e r e s i d e n t i a l e n v i - r o n m e n t s in t e r m s of o v e r a l l p r e f e r e n c e . T h e a l t e r n a t i v e w i t h t h e h i g h e s t o v e r a l l p r e f e r e n c e w a s u s e d t o f o r m t h e d e p e n d e n t v a r i a b l e . T A B L E I. P a r a m e t e r v a l u e s of t h e h y b r i d m o d e l . a t t r i b u t e p a r a m e t e r t h r e s h o l d e r r o r t e n u r e 4.090 6.764 0 . 1 3 5 t r a f f i c s i t u a t i o n 2.978 6.002 0.032 n u m b e r o f r o o m s 4 . 9 1 0 7.120 1.431 t y p e o f d w e l l i n g 4 . 5 0 0 7.810 0 . 8 5 3 A s d e s c r i b e d in t h e p r e v i o u s s e c t i o n , t h e a c t u a l a t t r i b u t e s o f t h e c h o i c e a l t e r n a t i v e s c a n b e t a k e n as t h e i n d e p e n d e n t v a r i a b l e s of t h e m o d e l . T h e a d v a n t a g e of s u c h an a p p r o a c h would b e t h a t t h e f i n d i n g s o f t h e m o d e l c a n b e i n t e r p r e t e d d i r e c t l y in t e r m s of h o u s i n g c h a r a c t e r i s t i c s . On t h e o t h e r h a n d , h o u s e h o l d s m a y e v a l u a t e a p a r t i c u l a r e n v i r o n m e n t d i f f e r e n t l y a n d h e n c e s u b j e c t i v e e v a l u a t i o n s c o u l d b e u s e d as well. In t h e p r e s e n t s t u d y t h e l a t t e r a p p r o a c h was t h e r e f o r e a d o p t e d . R e s p o n d e n t s w e r e i n v i t e d t o e x p r e s s t h e i r e v a l u a t i o n of t h e s e t of h o u s i n g a t t r i b u t e s a n d t h e s e t o f a t t r i b u t e s d e s c r i b i n g t h e r e s i d e n t i a l e n v i r o n m e n t on a n i n e p o i n t c a t e g o r y s c a l e r a n g i n g f r o m e x c e l l e n t to e x t r e m e l y bad. T h e s e m e a s u r e m e n t s c o n s t i t u t e t h e i n d e - p e n d e n t v a r i a b l e s of t h e m o d e l .
Findings
T h e c a l i b r a t i o n of t h e m o d e l i n v o l v e d a t i m e - c o n s u m i n g p r o c e s s . S i n c e t h e p r o p e r t i e s o f t h e p a r a m e t e r s p a c e a r e n o t well k n o w n a n d a r e l i k e l y t o b e r a t h e r i r r e g u l a r , a s e r i e s o f s e a r c h e s w a s u s e d t o e x p l o r e t h e p a r a m e t e r s p a c e . In p a r t i c u l a r a c o m b i n a t i o n o f s e q u e n t i a l l i n e a r s e a r c h e s a n d g r a d i e n t s e a r c h e s w a s u s e d t o c a l i b r a t e t h e m o d e l . F i r s t , t h e t h r e s h o l d s a n d e r r o r t e r m s w e r e c a l i b r a t e d . T h e s e t e r m s g i v e n , t h e p r o b a b i l i t i e s a s s o c i a t e d w i t hd i f f e r e n t c h o i c e s e t s could be c a l c u l a t e d in a s t r a i g h t f o r w a r d way. N e x t , t h e p a r a m e t e r s for t h e u t i l i t y e x p r e s s i o n w e r e c a l i b r a t e d , g i v e n t h e s e c h o i c e p r o b a b i l i t i e s . This p r o c e s s was r e p e a t e d until no f u r t h e r i m p r o v e m e n t of m o d e l fit was o b t a i n e d . To i n v e s t i g a t e t h e s t a b i l i t y of t h e r e s u l t i n g s o l u t i o n , t h e c a l i b r a t i o n p r o c e s s was r e p e a t e d a n u m b e r of t i m e s w i t h d i f f e r e n t s t a r t i n g values. S q u a r e d d e v i a n c e was used as t h e o p t i m i z a t i o n c r i t e r i u m .
The findings of t h e c a l i b r a t i o n a r e g i v e n in t a b l e I. T a b l e I s u g g e s t s t h a t t h e hybrid c o m p e n s a t o r y - n o n c o m p e n s a t o r y m o d e l is c a p a b l e of r e p r o d u c i n g t h e p r e f e r e n c e f o r m a t i o n p r o c e s s in a s a t i s f a c t o r y m a n n e r . T h e s q u a r e d d e v i a n c e is equal to 0.0029, i m p l y i n g t h a t t h e a v e r a g e p e r c e n t a g e e r r o r is only 0.05. T a b l e l also i n d i c a t e s t h a t t h e t r a f f i c s i t u a t i o n a t t r i b u t e is t h e m o s t c r i t i c a l s c r e e n i n g a t t r i b u t e in t h e s e n s e t h a t it has a low a s s o c i a t e d e r r o r t e r m , which i m p l i e s t h a t a r e l a t i v e l y low s c o r e on this a t t r i b u t e will e x c l u d e t h e c h o i c e a l t e r n a t i v e f r o m t h e c h o i c e s e t . The h i g h e s t t h r e s h o l d v a l u e is a s s o c i a t e d w i t h the a t t r i b u t e ' t y p e of d w e l l i n g ' , but t h e e r r o r t e r m s u g g e s t s a c o n s i d e r i b l e d e g r e e of h e t e r o g e n e i t y w i t h r e s p e c t to this a t t r i - bute. T A B L E 2. P a r a m e t e r v a l u e s of t h e m u l t i n o m i a l logit model. a t t r i b u t e p a r a m e t e r t e n u r e 1.749 t r a f f i c s i t u a t i o n 0.798 n u m b e r of r o o m s 1.912 t y p e of d w e l l i n g 1.964 As s t a t e d in the i n t r o d u c t o r y s e c t i o n of t h e p r e s e n t a r t i c l e , t h e r a t i o n a l e behind t h e hybrid m o d e l is to adjust for s o m e p r o p e r t i e s of t h e s t a n d a r d m u l - t i n o m i a l logit (MNL) m o d e l in o r d e r to i m p r o v e its p r e d i c t i v e a b i l i t y . T h e r e - f o r e it s e e m s logical to c o m p a r e t h e r e s u l t s o b t a i n e d for t h e hybrid m o d e l w i t h t h o s e found when the s t a n d a r d m u l t i n o m i a l logit m o d e l is a p p l i e d to t h e d a t a . T h e MNL m o d e l has b e e n a p p l i e d in a s t r a i g h t f o r w a r d m a n n e r . T h e first p r e f e r e n c e p r o b a b i l i t i e s t h a t w e r e d e r i v e d c o n s t i t u t e d t h e d e p e n d e n t v a r i a b l e . A g a i n s q u a r e d d e v i a n c e was used as a g o o d n e s s - o f - f i t c r i t e r i u m . T h e d e r i v e d p a r a m e t e r v a l u e s of t h e m o d e l a r e g i v e n in t a b l e 2. T a b l e 2 shows t h a t a c c o r d i n g to t h e m u l t i n o m i a l logit m o d e l t h e t y p e of d w e l l i n g is t h e m o s t i m p o r t a n t a t t r i b u t e , f o l l o w e d by n u m b e r of rooms, t e n u r e and t r a f - f i c s i t u a t i o n r e s p e c t i v e l y . N o t e t h a t this o r d e r i n g d i f f e r s s o m e w h a t f r o m t h e r a n k o r d e r i n g o b t a i n e d for t h e hybrid m o d e l in t h a t t h e a t t r i b u t e s t y p e of d w e l l i n g and n u m b e r of r o o m s h a v e c h a n g e d p l a c e s . T h e m u l t i n o m i a l l o g i t m o d e l is a b l e to r e p r o d u c e t h e d a t a in a v e r y s a t i s f a c t o r y m a n n e r : t h e s q u a r e d d e v i a n c e is only 0.00333, which is just s l i g h t l y w o r s e t h a n t h e v a l u e o b t a i n e d for t h e hybrid model. T h e s e r e s u l t s i n d i c a t e t h a t , a l t h o u g h t h e h y b r i d m o d e l p e r f o r m s s o m e w h a t b e t t e r , (and o n e should k e e p in m i n d t h e l a r g e r n u m b e r of p a r a m e t e r s a s s o c i a t e d w i t h t h e h y b r i d model), t h e MNL m o d e l p e r f o r m s a l m o s t e q u a l l y well. H e n c e , it c o u l d be a r g u e d t h a t t h e o r e t i - c a l l y t h e hybrid m o d e l should be p r e f e r r e d , but t h a t f r o m a p r a c t i c a l p o i n t o f
v i e w o n e s h o u l d p r e f e r a b l y use t h e MNL m o d e l , s i n c e it r e q u i r e s c o n s i d e r a b l y l e s s c o m p u t i n g t i m e and is f a r m o r e e a s y to use. In f a c t t h e s e r e s u l t s c a n b e t a k e n as a n o t h e r p i e c e of e v i d e n c e s h o w i n g t h e r o b u s t n e s s of t h e MNL m o d e l .
Conclusion and discussion
T h e m a i n t h r u s t of t h e p r e s e n t a r t i c l e h a s b e e n to a d v a n c e a n e w h y b r i d c o m p e n s a t o r y - n o n c o m p e n s a t o r y m o d e l o f h o u s i n g a n d r e s i d e n t i a l p r e f e r e n c e s t r u c t u r e s . T h e m o d e l is b a s e d on t h e i d e a t h a t h o u s e h o l d s f i r s t s c r e e n c a n d i - d a t e h o u s i n g e n v i r o n m e n t s on a s e r i e s of a t t r i b u t e s in a n o n c o m p e n s a t o r y f a s h i o n . If c h o i c e a l t e r n a t i v e s do n o t m e e t s u c h a s e t of m i n i m u m c o n d i t i o n s t h e y will n o t b e c o n s i d e r e d as c a n d i d a t e s for c h o i c e . T h e r e m a i n i n g a l t e r n a - t i v e s a r e t h e n e v a l u a t e d in a c o m p e n s a t o r y f a s h i o n in w h i c h t h e i r a d v a n t a g e s a n d d i s a d v a n t a g e s a r e c o m p a r e d . T h e r e s u l t s o b t a i n e d in t h e e m p i r i c a l p a r t of t h e p a p e r s u g g e s t t h e t h e o - r e t i c a l v a l u e of t h e h y b r i d m o d e l . T h e m o d e l ' s p r e d i c t i v e v a l i d i t y a p p e a r s to b e s a t i s f a c t o r y . H o w e v e r , f u t u r e r e s e a r c h m a y t e l l w h e t h e r t h e h y b r i d m o d e l p e r f o r m s b e t t e r t h a n t h e m o r e c o m m o n l y u s e d m u l t i n o m i a l a n d n e s t e d l o g i t m o d e l s on o t h e r d a t a s e t s as well. It s h o u l d also b e s t r e s s e d t h a t t h e m o d e l as o u t l i n e d in t h e p r e s e n t p a p e r is o n l y t h e m o s t s i m p l e f o r m o n e c o u l d t h i n k o f f . T h e m o d e l m a y b e e x t e n d e d by i n c l u d i n g o t h e r e f f e c t s , w h i c h m a y i n f l u - e n c e r e s i d e n t i a l c h o i c e b e h a v i o u r s u c h as a g g l o m e r a t i o n a n d c o m p e t i t i o n e f f e c t s , e f f e c t s of s u b s t i t u t a b i l i t y , i d e a l p o i n t s e t c . Such e x t e n s i o n s m a y i n c r e a s e t h e p r e d i c t i v e p e r f o r m a n c e o f t h e m o d e l a n d will p r o b a b l y i n c r e a s e i t s t h e o r e t i c a l r i c h n e s s , but a t t h e s a m e t i m e t h e y will i n c r e a s e e v e n f u r t h e r t h e c o m p u t i n g d i f f i c u l t i e s in t h e c a l i b r a t i o n p r o c e s s . A c k n o w l e d g e m e n t T h i s r e s e a r c h p r o j e c t h a s b e e n c a r r i e d o u t p a r t l y w i t h t h e f i n a n c i a l a s s i s t - a n c e of T h e N a t i o n a l F o u n d a t i o n f o r t h e A d v a n c e m e n t of P u r e S c i e n t i f i c R e s e a r c h ( Z W O / S R O ) . R e f e r e n c e s G e n s c h , D.H. a n d J . A . S v e s t k a (1979) " A n e x a c t h i e r a r c h i c a l a l g o r i t h m for d e t e r m i n i n g a g g r e g a t e s t a t i s t i c s f r o m i n d i v i d u a l c h o i c e d a t a " , Management Science, vol.25: 9 3 9 - 9 5 2 .
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