E stab lish ing Syn thesis Evaluation Index

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1 (2004) PL S, (, ) PL S (partial least square),, ;,,,, PL S,, PL S ; ; O 212 A T he A pp lication R esearch of Partial L east Square Path M odeling on E stab lish ing Syn thesis Evaluation Index W AN G H u i2w en, FU L ing2hu i (Schoo l of Econom icsm anagem ent, BeiH ang U niversity of A eronautics and A stronautics,beijing , Ch ina) Abstract In th is paper, a m ethod fo r establish ing m ultivariable evaluation index is p ropo sed by com bining Partial L east Square Path M odeling w ith M ultip le T ables A nalysiṡ T he relation betw een every laten t variab le and co rresponding ob servab le variab les is investigated and the relation betw een every latent variable and m ultivariable evaluation index is analyzed w ith the p ropo sed m ethod. O n the o ther hand, the im po rtan t info rm ation of ob servab le variab les is ex tracted and the m u ltivariab le evaluation index w h ich rep resents the latent variables and observable variables app rop riately is found w ith the m ethod. A s a case research, th ree variable sets w h ich reflect econom ic developm ent level, life level and urbanization level are adop ted and partial least square path modeling is app lied fo r establish ing city synthesis evaluation index on city developm ent level of Ch ina. T h rough the evaluation of different city, it is consistent betw een the result and econom ic geography know ledge. Key words partial least square path modeling; m ultip le tables analysis; synthesis evaluation index 1,,,,,,,,,,, ( ), ( ),,,, PL S (app roach PL S), ( ); ( ) (1957- ),,,, F lh07@ sina. com,

2 10 PL S 81,, PL S ;,, ;, 2PL S W o ld (1975, 1982, 1985) PL S ( ) ; ( ) ( 1) 1) PL S n J X j = {x j1, x j2,, x jk j }, x jh, ( ), (un idim en tionnelity), Νj j x jh Νj ( ) x jh = ΠjhΝj + Εjh, (1), Νj 0, 1; Εjh 0, Νj ; Πjh un idim en tionnelity,, 1, 1, un idim en tionnelity,, J Νj Νj = 6 ij Βj i Νi + Μj, (2) Μj 0 Νi (i j ), Βj i 0g1, j i, 1PL S ( i, j ) 1, 0 2) PL S Νj Νj j x jh, Yj, Νj Yj = 6 h w jh x jh = X jw j, (3), X j x jh, w j w jh, Yi (ij ) Νj Νi, Yi Νj. Z j, Νj Z j 6 ej i Y i. (4) i Ν i is connected w ith Ν j (4),, Z j 1. ej i, Yj Yi eij = sign (co r (Y j, Y i) ), (5), sign (x ) = 1 x Ε 0, - 1x < 0, co r (Y j, Y i) Yj Yi

3 W o ld (3) w jh, A B A w j x jh Z j w j = 1 n X jzj, (6) B w j Νj Z j x jh w j =, PL S (X jx j) - 1 X jzj (7) 1 Yj x j1 (4), Z j ; 2 Z j, (6) (7), w j; 3 w j, (3), Yj; 1, Yj Νj Ν δ j 4, Ν δ j Νj,, (2) C. Gu ino t, J. L atreille & M. T enenhau s PL S (analysis of m u ltip le tab les),,,,,,, ( 2),, PL S PL S, () () (). () () ( ) (.,, 1. 1 (Ν1) (Ν2) (Ν3) (x 11) (x 21) (x 31) (x 12) (x 22) (x 32) (x 13) (x 23) (x 33) (x 14) (x 34), U n idim en sionality 2. 2, U n idim en sionality

4 10 PL S 83, PL S 2 2U n idim en sionality (Ν1, Ν2, Ν3) x 11- x 14 x 21- x 23x 31- x 34,, x 11- x 34, Ν , , Ν4, Ν Ν3,, 2, PL S 3 ( 2) 3,, Ν4 Ν1Ν3 R 2 = 0. 99, Ν4 Ν1Ν3, w jh 3 w jh x x x x 14 x x x 23 x x x x x 11 x 12 x 13 x 14 x 21 x 22 x 23 x 31 x 32 x 33 x

5 , Ν4,,, 88 ; 74% - 87% ;, 70% Ν4,, Ν , ,,, 66% 103%,,,,, , ; , ; , 5. 5 () () () () () ( ) () () ( ) ,,, ;, ;,,, 4

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