WHAT IS STRUCTURAL EQUATION MODELING SEM 1 LINEAR

WHAT IS STRUCTURAL EQUATION MODELING (SEM)? 1

LINEAR STRUCTURAL RELATIONS 2

Terminología • LINEAR LATENT VARIABLE MODELS • T. W. Anderson (1989), Journal of Econometrics • MULTIVARIATE LINEAR RELATIONS • T. W. Anderson (1987), 2 nd International Temp. Conference in Statistics • LINEAR STATISTICAL RELATIONSHIPS • T. W. Anderson (1984), Annals of Statistics, 12 • COVARIANCE STRUCTURES • • • Browne, Shapiro, Satorra, . . . Jöreskog (1973, 1977) Wiley (1979) Keesling (1972) Koopmans and Hovel (1953) 3

Computer programs • • • LISREL EQS LISCOMP / Mplus COSAN MOMENTS CALIS AMOS RAMONA Mx • • • Jöreskog and Sörbom Bentler Muthén Mc. Donalds Schoenberg SAS Arbunckle Browne Neale 4

Computer programs • SEM software: – EQS – LISREL – MPLUS – AMOS – Mx http: //www. mvsoft. com http: //www. ssicentral. com http: //www. statmodel. com/index 2. html http: //smallwaters. com/amos/ http: //www. vipbg. vcu. edu/~vipbg/dr/MNEALE. shtml 5

. . . books • • • Bollen (1989) Dwyer (1983) Hayduk (1987) Mueller (1996) Saris and Stronkhorst (1984). . 6

. . . many research papers • Austin and Wolfle (1991): Annotated bibliography of structural equation modeling: Technical Works. BJMSP, 99, pp. 85 -152. • Austin, J. T. and Calteron, R. F. (1996). Theoretical and technical contributions to structural equation modeling: An updated annotated bibliography. SEM, pp. 105 -175. 7

Information on SEM: bibliography, courses. . General information on SEM: http: //allserv. rug. ac. be/~flievens/stat. htm#Structural Jason Newsom's Structural Equation Modeling Reference List http: //www. ioa. pdx. edu/newsom/semrefs. htm David A. Kenny’s course http: //users. rcn. com/dakenny/causalm. htm Jouni Kuha’s Model Assessment and Model Choice: An Annotated Bibliography http: //www. stat. psu. edu/~jkuha/msbib/biblio. html 8

. . . web sites • SEM webs: – http: //www. gsu. edu/~mkteer/semfaq. html – http: //www. ssicentral. com/lisrel/ref. htm • http: //www. psyc. abdn. ac. uk/homedir/jcrawf ord/psychom. htm computing the scaling factor for the difference of chi squares 9

Introduction to SEM: • Data matrix (“raw data”) • Sufficient statistics (sample means, variances and covariances) vars Indiv. Data Matrix (n x p) Sample Moments: • Vector of means • Variance and covariance matrix (p x p) • Fourth order moments: G (p* x p*) p* = p(p+1)/2, p=20 --> p* =210 10

Moment Structure S sample covariance matrix S population covariance matrix S = S(q) 11

Fitting S to S(q): Min f(S, S) ^ ^ S = S(q) ^ S ≈ S ^ S – S ≈ 0 12

Type of variables Manifest Variables: Yi , Xi Measurement Model: e 3 X 3 e 4 X 4 l 32 x 2 l 42 Measurement error, disturbances: ei , di 13

The form of structural equation models Latent constructs: - Endogenous - Exogenous hi xi Structural Model: - Regression of h 1 on x 2: g 12 - Regression of h 1 on h 2: b 12 Structural Error: zi 14

LISREL model: h(m x 1) = B(m x m) h(m x 1) + G(m x n) x(n x 1) + z(m x 1) y(p x 1) = Ly(p x m) h(m x 1) + e(p x 1) x(q x 1) = Lx(q x n) x(n x 1) + d(q x 1) 15

. . . path diagram (LISREL) d 1 X 1 d 2 X 2 d 3 x 1 X 4 d 5 X 5 e 2 e 3 Y 1 Y 2 Y 3 g 11 z 1 h 1 b 31 q 21 X 3 d 4 e 1 x 2 z 2 h 3 g 22 b 32 h 2 Y 4 e 4 Y 6 e 6 Y 7 e 7 z 3 Y 5 e 5 16

SEM: i=1, 2, . . , ng, donde: zi: vector de variables observables, hi : vector de variables endógenas xi : vector de variables exógenas vi = (hi’, xi’)’: vector de variables observables y latentes, U(g): matriz de selección completamente especificada, B, G y F = E(xi xi’): matrices de parámetros del modelo 17

El modelo general: donde: F = var x 18

. . . path diagram (EQS) E 1 V 1 E 2 V 2 E 3 F 1 E 6 E 7 E 8 V 6 V 7 V 8 * D 3 F 3 * F 5 V 3 E 4 V 4 E 5 V 5 F 2 D 5 * * F 4 V 9 E 9 * V 11 E 11 V 12 E 12 D 4 V 10 E 10 19

RESEARCH DESINGS 21

Data collection designs • Cross-sectional – N independent units observed or measured at one time • Time-series – One unit observed or measured al T occasions • Longitudinal – N independent units observed or measured at two or more occasions 22

Type of Variables VARIABLES • Continous • Ordinal • Nominal SCALE TYPE • • Interval or ratio Ordinal Ordered categories Underordered caterogies • Censored, truncated … 24

Ordinal Variables Is is assumed that there is a continuous unobserved variable x* underlying the observed ordinal variable x. A threshold model is specified, as in ordinal probit regression, but here we contemplate multivariate regression. It is the underlying variable x* that is acting in the SEM model. 25

Polychorical correlation 26

Polyserial correlation 27

Threshold model 28

Modelling the effect on behaviour Correla =. 83 Affect Cognition. 65. 23 U Behaviour Influence of affect on Behaviour is almost Three times stronger (on a standardized scale) Than the effect of Cognition. A policy that changes Affect will have more influence on B than one that changes cognition Bagozzi and Burnkrant (1979), Attitude organization and the attitude behaviour relationship, Journal Of Personality and Social Psychology, 37, 913 -29 29

Causal model with reciprocal effects U 1 P = price D = demand I = Income W = Wages W I D + - U 2 P 30

Examples with Coupon data (Bagozzi, 1994) 31

Example: Data of Bagozzi, Baumgartner, and Yi (1992), on “coupon usage” : Sample A: Action oriented women (n = 85) Intentions #1 4. 389 Intentions #2 3. 792 4. 410 Behavior 1. 935 1. 855 2. 385 Attitudes #1 1. 454 1. 453 0. 989 1. 914 Attitudes #2 1. 087 1. 309 0. 841 0. 961 Attitudes #3 1. 623 1. 701 1. 175 1. 279 Sample B: State oriented women (n = 64) Intentions #1 3. 730 Intentions #2 3. 208 3. 436 Behavior 1. 687 1. 675 2. 171 Attitudes #1 0. 621 0. 616 0. 605 Attitudes #2 1. 063 0. 864 0. 428 Attitudes #3 0. 895 0. 818 0. 595 1. 373 0. 671 0. 912 1. 480 1. 220 1. 397 0. 663 1. 971 1. 498 32

Variables /LABELS V 1 = Intentions 1; V 2 = Intentions 2; V 3 = Behavior; V 4 = Attitudes 1; V 5 = Attitudes 2; V 6 = Attitudes 3; F 1 = Attitudes F 2 = Intentions V 3 = Behavior 33

SEM multiple indicators E 4 E 5 E 6 D 2 V 4 V 5 V 1 F 2 V 2 E 1 E 2 E 3 V 6 V 3 F 1 = Attitudes F 2 = Intentions V 3 = Behavior 34

INTENTIO=V 1 = 1. 000 F 2 + 1. 000 E 1 INTENTIO=V 2 = 1. 014*F 2 + 1. 000 E 2 . 088 CHI-SQUARE = 5. 426 , 7 DEGREES OF FREEDOM 11. 585 PROBABILITY VALUE IS 0. 60809 BEHAVIOR=V 3 = . 330*F 2 + . 492*F 1 + 1. 000 E 3 . 103 . 204 3. 203 2. 411 VARIANCES OF INDEPENDENT VARIABLES ----------------- E D --- -- ATTITUDE=V 4 = 1. 020*F 1 + 1. 000 E 4 E 1 -INTENTIO . 649*I D 2 -INTENTIO 2. 020*I . 255 I . 437 I . 136 2. 542 I 4. 619 I I 7. 501 E 2 -INTENTIO . 565*I . 257 I 2. 204 I I E 3 -BEHAVIOR 1. 311*I I ATTITUDE=V 5 = . 951*F 1 + 1. 000 E 5 . 213 I 6. 166 I . 117 I E 4 -ATTITUDE . 875*I 8. 124 . 161 I 5. 424 I I I E 5 -ATTITUDE . 576*I . 115 I I ATTITUDE=V 6 = 1. 269*F 1 + 1. 000 E 6 5. 023 I I . 127 E 6 -ATTITUDE . 360*I . 132 I 10. 005 2. 729 I I INTENTIO=F 2 = 1. 311*F 1 + 1. 000 D 2 . 214 6. 116 35

. . . adding parameters ? LAGRANGE MULTIPLIER TEST (FOR ADDING PARAMETERS) ORDERED UNIVARIATE TEST STATISTICS: NO CODE PARAMETER CHI-SQUARE PROBABILITY PARAMETER CHANGE ---------- --------------- 1 2 12 V 2, F 1 1. 427 0. 232 0. 410 2 2 12 V 1, F 1 1. 427 0. 232 -0. 404 3 2 20 V 4, F 2 0. 720 0. 396 0. 080 4 2 20 V 5, F 2 0. 289 0. 591 -0. 045 5 2 20 V 6, F 2 0. 059 0. 808 -0. 025 6 2 20 V 3, F 2 0. 000 1. 000 0. 000 7 2 0 F 1, F 1 0. 000 1. 000 0. 000 8 2 0 F 2, D 2 0. 000 1. 000 0. 000 9 2 0 V 1, F 2 0. 000 1. 000 0. 000 36

Hopkins and Hopkins (1997): “Strategic planningfinancial performance relationships in banks: a causal examination”. Strategic Management Journal, Vol 18 (8), pp. (635 -652) 37

Data to be analyzed • Sample: 112 comercial bancs • Data obtained by survey • Dependent variable: • Intensity of strategic plannification • Finance results • Independent variables: • Directive factors • Contour factors • Organizative factors 38

39

40

41

42

43

44

Covariance matrix: : 0. 48 0. 76 0. 60 0. 51 0. 46 0. 54 -0. 06 -0. 09 0. 01 0. 31 -0. 17 -0. 21 -0. 16 0. 04 0. 44 -0. 26 -0. 06 -0. 16 -0. 19 0. 16 0. 27 0. 52 0. 32 0. 44 0. 66 0. 23 0. 07 -0. 24 0. 52 0. 40 0. 51 0. 76 0. 26 0. 19 -0. 15 0. 76 0. 49 0. 27 0. 43 0. 64 0. 17 0. 10 -0. 21 0. 77 0. 81 0. 12 0. 16 0. 09 0. 28 0. 18 0. 24 0. 07 0. 36 0. 41 0. 35 0. 34 0. 27 0. 64 0. 31 0. 23 -0. 01 0. 56 0. 67 0. 57 0. 45 0. 23 0. 08 0. 16 0. 07 0. 09 0. 16 -0. 01 0. 28 0. 30 0. 27 0. 29 0. 30 0. 03 0. 02 0. 04 -0. 07 -0. 05 -0. 03 -0. 05 0. 06 -0. 06 0. 03 0. 01 -0. 07 0. 03 0. 20 0. 32 0. 22 0. 09 -0. 24 -0. 33 0. 05 -0. 02 -0. 07 -0. 08 0. 02 0. 05 -0. 23 -0. 03 0. 15 0. 06 0. 11 -0. 03 0. 10 0. 13 0. 16 0. 13 0. 07 0. 06 0. 19 0. 21 0. 13 0. 16 Means: 34. 30 12. 75 3. 50 6. 70 7. 10 7. 00 7. 05 7. 20 7. 30 7. 45 21. 50 3. 54 2. 35 S. D. : 58. 58 4. 10 1. 61 1. 95 1. 62 1. 55 1. 52 1. 64 1. 96 1. 88 1. 78 1. 54 12. 87 0. 56 0. 67 45