2004 10 10 100026788 (2004) 1020080209 PL S, (, 100083) 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 100083, 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), 2003206225 (70371007); (70125003) (1957- ),,,, F lh07@ sina. com,
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
82 2004 10 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) 3 2001 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, 1998 19 () () (). () () ( ) (.,, 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
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, Ν4 3. 8643 0. 1140, 2 2. 8429 0. 1489, Ν4, Ν1-2. 8982 0. 7843 Ν3,, 2, PL S 3 ( 2) 3,, Ν4 Ν1Ν3 R 2 = 0. 99, Ν4 Ν1Ν3, w jh 3 w jh x 11 0. 3092 x 12 0. 3091 x 13 0. 2303 0. 2907 x 14 x 21 0. 3541 x 22 0. 3386 0. 3576 x 23 x 31 0. 3615 x 32 0. 3171 x 33 0. 2858 0. 3066 x 34 0. 9494 0. 9147 0. 7818 0. 9331 0. 9769 0. 9781 0. 9801 0. 9358 0. 8358 0. 5834 0. 8401 x 11 x 12 x 13 x 14 x 21 x 22 x 23 x 31 x 32 x 33 x 34 0. 1192 0. 119 0. 0885 0. 1119 0. 1211 0. 1158 0. 1224 0. 1119 0. 098 0. 0878 0. 0953 0. 9401 0. 9388 0. 701 0. 8827 0. 9506 0. 9089 0. 9607 0. 874 0. 7664 0. 6915 0. 7424
84 2004 10, Ν4,,, 88 ; 74% - 87% ;, 70% Ν4,, Ν4 19 1998, 4 41998 19 2. 575 1-0. 479 11 2. 218 2-0. 585 12 1. 201 3-0. 68 13 0. 372 4-0. 715 14 0. 361 5-0. 722 15 0. 245 6-0. 738 16 0. 139 7-0. 817 17 0. 088 8-0. 922 18-0. 047 9-1. 195 19-0. 299 10,,, 66% 103%,,,,, 0-0. 4, ; - 0. 5-0, ; - 0. 5- - 1. 2, 5. 5 () () () () () ( ) () () ( ) 16002 911 6674 20994 9739 10234 6759 0. 503 10. 4 231. 5 29. 72 14648 876 4257 9962 8711 7623 4948 0. 369 8. 233 267. 6 28. 31 9109 482. 2 3140 8322 7447 5923 3860 0. 361 7. 185 192. 1 24. 02,,, ;, ;,,, 4
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