1 WHAT IS STRUCTURAL EQUATION MODELING (SEM)?. 2 LINEAR STRUCTURAL RELATIONS.

Presentation on theme: "1 WHAT IS STRUCTURAL EQUATION MODELING (SEM)?. 2 LINEAR STRUCTURAL RELATIONS."— Presentation transcript:

1 1 WHAT IS STRUCTURAL EQUATION MODELING (SEM)?

2 2 LINEAR STRUCTURAL RELATIONS

3 3 Terminología LINEAR LATENT VARIABLE MODELS T.W. Anderson (1989), Journal of Econometrics MULTIVARIATE LINEAR RELATIONS T.W. Anderson (1987), 2nd 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)

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

5 5 Computer programs SEM software: –EQS http://www.mvsoft.comhttp://www.mvsoft.com –LISREL http://www.ssicentral.comhttp://www.ssicentral.com –MPLUShttp://www.statmodel.com/index2.htmlhttp://www.statmodel.com/index2.html –AMOShttp://smallwaters.com/amos/http://smallwaters.com/amos/ –Mx http://www.vipbg.vcu.edu/~vipbg/dr/MNEALE.shtml http://www.vipbg.vcu.edu/~vipbg/dr/MNEALE.shtml

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

7 7... 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.

8 8 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

9 9... web sites SEM webs: –http://www.gsu.edu/~mkteer/semfaq.html –http://www.ssicentral.com/lisrel/ref.htmhttp://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 squareshttp://www.psyc.abdn.ac.uk/homedir/jcrawf ord/psychom.htm

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

11 11 Moment Structure  =  (  ) S sample covariance matrix  population covariance matrix

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

13 13 Type of variables Manifest Variables: Y i, X i Measurement Model: 22 X3X3 X4X4 32 42 Measurement error, disturbances:  i,  i 33 44

14 14 The form of structural equation models Latent constructs: - Endogenous  i - Exogenous  i Structural Model: - Regression of  1 on  2   12 - Regression of  1 on  2 :  12 Structural Error:  i

15 15 LISREL model:  (m x 1) =  (m x m)  (m x 1) +  (m x n)  (n x 1) +  (m x 1) y (p x 1) =  y(p x m)  (m x 1) +  (p x 1) x (q x 1) =  x(q x n)  (n x 1) +  (q x 1)

16 16... path diagram (LISREL) X1X1 X2X2 X3X3 X4X4 X5X5 11 22 11 22 33 Y6Y6 Y7Y7 Y1Y1 Y2Y2 Y3Y3 Y4Y4 Y5Y5  11  22  31  32 11 22 33  21 11 22 33 44 55 11 22 33 66 77 44 55

17 17 SEM : i=1,2,...., n g, donde: z i : vector de variables observables,  i : vector de variables endógenas  i : vector de variables exógenas v i = (  i ’,  i ’)’: vector de variables observables y latentes, U (g) : matriz de selección completamente especificada, B,  y  = E(  i  i ’): matrices de parámetros del modelo

18 18 El modelo general: donde:   var 

19 19... path diagram (EQS) V1V1 V2V2 V3V3 V4V4 V5V5 F1F1 F2F2 F3F3 F4F4 F5F5 V 11 V 12 V6V6 V7V7 V8V8 V9V9 V 10     D3D3 D5D5 D4D4  11 22 33 44 55     11  12   

20 20 Main virtues of SEM (ctd.) Flexibility on the type of data: –Continuous and ordinal variables – multiple sample –Informative missingness (MCA, MAR) –Finite mixture distributions –Multilevel models –Samples with complex design –General longitudinal type of data –...

21 21 RESEARCH DESINGS

22 22 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

23 23.. data collection designs Longitudinal –a) Retrospective –b) Prospective –c) Repeated measures –d) panel –e) Rotating panel Experimental, quasi-experimental data Observational or non-experimental

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

25 25 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.

26 26 Polychorical correlation

27 27 Polyserial correlation

28 28 Threshold model

29 29 Modelling the effect on behaviour Behaviour CognitionAffect Bagozzi and Burnkrant (1979), Attitude organization and the attitude behaviour relationship, Journal Of Personality and Social Psychology, 37, 913-29 Correla =.83.65.23 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 U

30 30 Causal model with reciprocal effects DP U1U1 W IU2U2 + - P = price D = demand I = Income W = Wages

31 31 Examples with Coupon data (Bagozzi, 1994)

32 32 Example: Data of Bagozzi, Baumgartner, and Yi (1992), on “coupon usage” : Sample A: Action oriented women (n = 85) Intentions #14.389 Intentions #23.7924.410 Behavior1.9351.8552.385 Attitudes #11.4541.4530.9891.914 Attitudes #21.0871.3090.8410.9611.480 Attitudes #31.6231.7011.1751.2791.2201.971 Sample B: State oriented women (n = 64) Intentions #13.730 Intentions #23.2083.436 Behavior1.6871.6752.171 Attitudes #10.6210.6160.6051.373 Attitudes #21.0630.8640.4280.6711.397 Attitudes #30.8950.8180.5950.9120.6631.498

33 33 Variables /LABELS V1 = Intentions1; V2 = Intentions2; V3 = Behavior; V4 = Attitudes1; V5 = Attitudes2; V6 = Attitudes3; F1 = Attitudes F2 = Intentions V3 = Behavior

34 34 F1F2 V3 D2 E3 SEM multiple indicators V4 V5 V6 V1 V2 E4 E5 E6 E1 E2 F1 = Attitudes F2 = Intentions V3 = Behavior

35 35 INTENTIO=V1 = 1.000 F2 + 1.000 E1 INTENTIO=V2 = 1.014*F2 + 1.000 E2.088 11.585 BEHAVIOR=V3 =.330*F2 +.492*F1 + 1.000 E3.103.204 3.203 2.411 ATTITUDE=V4 = 1.020*F1 + 1.000 E4.136 7.501 ATTITUDE=V5 =.951*F1 + 1.000 E5.117 8.124 ATTITUDE=V6 = 1.269*F1 + 1.000 E6.127 10.005 INTENTIO=F2 = 1.311*F1 + 1.000 D2.214 6.116 VARIANCES OF INDEPENDENT VARIABLES ---------------------------------- E D --- --- E1 -INTENTIO.649*I D2 -INTENTIO 2.020*I.255 I.437 I 2.542 I 4.619 I I I E2 -INTENTIO.565*I I.257 I I 2.204 I I I I E3 -BEHAVIOR 1.311*I I.213 I I 6.166 I I I I E4 -ATTITUDE.875*I I.161 I I 5.424 I I I I E5 -ATTITUDE.576*I I.115 I I 5.023 I I I I E6 -ATTITUDE.360*I I.132 I I 2.729 I I CHI-SQUARE = 5.426, 7 DEGREES OF FREEDOM PROBABILITY VALUE IS 0.60809

36 36... adding parameters ? LAGRANGE MULTIPLIER TEST (FOR ADDING PARAMETERS) ORDERED UNIVARIATE TEST STATISTICS: NO CODE PARAMETER CHI-SQUARE PROBABILITY PARAMETER CHANGE -- ---- --------- ---------- ----------- ---------------- 1 2 12 V2,F1 1.427 0.232 0.410 2 2 12 V1,F1 1.427 0.232 -0.404 3 2 20 V4,F2 0.720 0.396 0.080 4 2 20 V5,F2 0.289 0.591 -0.045 5 2 20 V6,F2 0.059 0.808 -0.025 6 2 20 V3,F2 0.000 1.000 0.000 7 2 0 F1,F1 0.000 1.000 0.000 8 2 0 F2,D2 0.000 1.000 0.000 9 2 0 V1,F2 0.000 1.000 0.000

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

38 38 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

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45 45 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 0.24 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 0.16 0.19 0.21 0.13 0.16 Means: 34.30 12.75 3.50 6.70 7.10 7.00 7.10 7.00 7.05 7.20 7.20 7.30 7.45 21.50 3.54 2.35 S.D.: 58.58 4.10 1.61 1.95 1.65 1.62 1.55 1.52 1.64 1.96 1.88 1.78 1.54 12.87 0.56 0.67