DATE: 11/ 5/2007 TIME: 15:39 L I S R E L 8.80 BY Karl G. J”reskog & Dag S”rbom This program is published exclusively by Scientific Software International, Inc. 7383 N. Lincoln Avenue, Suite 100 Lincolnwood, IL 60712, U.S.A. Phone: (800)247-6113, (847)675-0720, Fax: (847)675-2140 Copyright by Scientific Software International, Inc., 1981-2006 Use of this program is subject to the terms specified in the Universal Copyright Convention. Website: www.ssicentral.com The following lines were read from file D:\Saved\Projects\INTERACT\kjexampl.ls8: Set up Kenny-Judd (1984) example model in LISREL 8 DA NI=9 NO=500 MA=CM ! 9 observed variables, 500 sample size, analyze covar. matrix ! Must analyze covariance matrix when modeling interaction LA x1 x2 z1 z2 x1_z1 x1_z2 x2_z1 x2_z2 y ! labels for observed variables, same order as in covar. matrix CM FI=KJEXAMPL.CM ! covariance matrix from Kenny and Judd (1984) SE 9 1 2 3 4 5 6 7 8 ! re-order observed variables so that "y" variables come first MO NY=1 NE=1 NX=8 NK=7 PS=SY TE=FI PH=SY,FI TD=SY,FI GA=FI ! Main parameter matrices, most parameters fixed LE ETA_Y ! Label for Eta construct LK KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 Z_TD2 ! Labels for Ksi constructs--main effects are X and Z FR GA(1,1) GA(1,2) GA(1,3) ! paths from main effects and interaction to dependent VA 1.0 LY(1,1) VA 1.0 LX(1,1) LX(3,2) ! set reference variables for Y, X and Z FR LX(2,1) LX(4,2) PH(1,1) PH(2,2) PH(2,1) TD(1,1) TD(2,2) TD(3,3) TD(4,4) ! Other "free" parameters for the main effects constructs ! Here come the constrained interaction parameters VA 1.0 LX(5,3) CO LX(6,3) = LX(4,2) CO LX(7,3) = LX(2,1) CO LX(8,3) = LX(2,1) * LX(4,2) CO TD(5,5) = TD(1,1) * TD(3,3) CO TD(6,6) = TD(1,1) * TD(4,4) CO TD(7,7) = TD(2,2) * TD(3,3) CO TD(8,8) = TD(2,2) * TD(4,4) CO PH(3,3) = PH(1,1) * PH(2,2) + PH(2,1)^2 VA 1.0 LX(5,4) CO LX(7,4) = LX(2,1) CO PH(4,4) = PH(1,1) * TD(3,3) VA 1.0 LX(6,5) CO LX(8,5) = LX(2,1) CO PH(5,5) = PH(1,1) * TD(4,4) VA 1.0 LX(5,6) CO LX(6,6) = LX(4,2) CO PH(6,6) = PH(2,2) * TD(1,1) VA 1.0 LX(7,7) CO LX(8,7) = LX(4,2) CO PH(7,7) = PH(2,2) * TD(2,2) ! Starting values are important to help LISREL deal with ! this very nonstandard model ST -.15 GA(1,1) ST .35 GA(1,2) ST .70 GA(1,3) ST 0.16 PS(1,1) ST .20 PH(2,1) ST 2.15 PH(1,1) ST 1.60 PH(2,2) ST 0.36 TD(1,1) ST 0.81 TD(2,2) ST 0.49 TD(3,3) ST 0.64 TD(4,4) ST 0.60 LX(2,1) ST 0.70 LX(4,2) ! Output line--usual keywords OU AD=OFF RS MI Set up Kenny-Judd (1984) example model in LISREL 8 Number of Input Variables 9 Number of Y - Variables 1 Number of X - Variables 8 Number of ETA - Variables 1 Number of KSI - Variables 7 Number of Observations 500 Set up Kenny-Judd (1984) example model in LISREL 8 Covariance Matrix y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 2.17 x1 -0.37 2.40 x2 -0.18 1.25 1.54 z1 0.40 0.45 0.20 2.10 z2 0.28 0.23 0.12 1.14 1.37 x1_z1 2.56 -0.37 -0.07 -0.15 -0.13 5.67 x1_z2 1.58 -0.30 -0.04 -0.13 -0.12 2.87 x2_z1 1.62 -0.08 -0.05 0.04 0.04 2.99 x2_z2 0.97 -0.05 -0.04 0.04 -0.04 1.34 Covariance Matrix x1_z2 x2_z1 x2_z2 -------- -------- -------- x1_z2 3.08 x2_z1 1.35 3.41 x2_z2 1.39 1.72 1.96 Set up Kenny-Judd (1984) example model in LISREL 8 Parameter Specifications LAMBDA-X KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- x1 0 0 0 0 0 0 x2 1 0 0 0 0 0 z1 0 0 0 0 0 0 z2 0 2 0 0 0 0 x1_z1 0 0 0 0 0 0 x1_z2 0 0 Constr'd 0 0 Constr'd x2_z1 0 0 Constr'd Constr'd 0 0 x2_z2 0 0 Constr'd 0 Constr'd 0 LAMBDA-X Z_TD2 -------- x1 0 x2 0 z1 0 z2 0 x1_z1 0 x1_z2 0 x2_z1 0 x2_z2 Constr'd GAMMA KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- ETA_Y 3 4 5 0 0 0 GAMMA Z_TD2 -------- ETA_Y 0 PHI KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- KSI_X 6 KSI_Z 7 8 KSI_XZ 0 0 Constr'd X_TD3 0 0 0 Constr'd X_TD4 0 0 0 0 Constr'd Z_TD1 0 0 0 0 0 Constr'd Z_TD2 0 0 0 0 0 0 PHI Z_TD2 -------- Z_TD2 Constr'd PSI ETA_Y -------- 9 THETA-DELTA x1 x2 z1 z2 x1_z1 x1_z2 -------- -------- -------- -------- -------- -------- 10 11 12 13 Constr'd Constr'd THETA-DELTA x2_z1 x2_z2 -------- -------- Constr'd Constr'd Set up Kenny-Judd (1984) example model in LISREL 8 Number of Iterations = 7 LISREL Estimates (Maximum Likelihood) LAMBDA-Y ETA_Y -------- y 1.00 LAMBDA-X KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- x1 1.00 - - - - - - - - - - x2 0.64 - - - - - - - - - - (0.03) 23.37 z1 - - 1.00 - - - - - - - - z2 - - 0.69 - - - - - - - - (0.03) 26.50 x1_z1 - - - - 1.00 1.00 - - 1.00 x1_z2 - - - - 0.69 - - 1.00 0.69 (0.03) (0.03) 26.50 26.50 x2_z1 - - - - 0.64 0.64 - - - - (0.03) (0.03) 23.37 23.37 x2_z2 - - - - 0.44 - - 0.64 - - (0.03) (0.03) 17.53 23.37 LAMBDA-X Z_TD2 -------- x1 - - x2 - - z1 - - z2 - - x1_z1 - - x1_z2 - - x2_z1 1.00 x2_z2 0.69 (0.03) 26.50 GAMMA KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- ETA_Y -0.17 0.32 0.71 - - - - - - (0.03) (0.03) (0.04) -5.25 9.20 19.50 GAMMA Z_TD2 -------- ETA_Y - - Covariance Matrix of ETA and KSI ETA_Y KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 -------- -------- -------- -------- -------- -------- ETA_Y 2.16 KSI_X -0.20 1.94 KSI_Z 0.48 0.40 1.70 KSI_XZ 2.45 - - - - 3.46 X_TD3 - - - - - - - - 0.87 X_TD4 - - - - - - - - - - 1.10 Z_TD1 - - - - - - - - - - - - Z_TD2 - - - - - - - - - - - - Covariance Matrix of ETA and KSI Z_TD1 Z_TD2 -------- -------- Z_TD1 0.78 Z_TD2 - - 1.27 PHI KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- KSI_X 1.94 (0.12) 16.47 KSI_Z 0.40 1.70 (0.09) (0.10) 4.51 17.00 KSI_XZ - - - - 3.46 (0.26) 13.24 X_TD3 - - - - - - 0.87 (0.11) 7.58 X_TD4 - - - - - - - - 1.10 (0.08) 13.05 Z_TD1 - - - - - - - - - - 0.78 (0.12) 6.20 Z_TD2 - - - - - - - - - - - - PHI Z_TD2 -------- Z_TD2 1.27 (0.09) 13.96 PSI ETA_Y -------- 0.24 (0.08) 3.13 Squared Multiple Correlations for Y - Variables y -------- 1.00 THETA-DELTA x1 x2 z1 z2 x1_z1 x1_z2 -------- -------- -------- -------- -------- -------- 0.46 0.74 0.45 0.57 0.20 0.26 (0.07) (0.04) (0.06) (0.03) (0.04) (0.04) 6.44 17.56 8.08 16.31 5.14 6.17 THETA-DELTA x2_z1 x2_z2 -------- -------- 0.33 0.42 (0.04) (0.03) 7.68 13.59 Squared Multiple Correlations for X - Variables x1 x2 z1 z2 x1_z1 x1_z2 -------- -------- -------- -------- -------- -------- 0.81 0.51 0.79 0.59 0.96 0.92 Squared Multiple Correlations for X - Variables x2_z1 x2_z2 -------- -------- 0.90 0.80 Goodness of Fit Statistics Degrees of Freedom = 32 Minimum Fit Function Chi-Square = 44.79 (P = 0.066) Normal Theory Weighted Least Squares Chi-Square = 45.28 (P = 0.060) Estimated Non-centrality Parameter (NCP) = 13.28 90 Percent Confidence Interval for NCP = (0.0 ; 35.19) Minimum Fit Function Value = 0.090 Population Discrepancy Function Value (F0) = 0.027 90 Percent Confidence Interval for F0 = (0.0 ; 0.071) Root Mean Square Error of Approximation (RMSEA) = 0.029 90 Percent Confidence Interval for RMSEA = (0.0 ; 0.047) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.98 Expected Cross-Validation Index (ECVI) = 0.21 90 Percent Confidence Interval for ECVI = (0.15 ; 0.22) ECVI for Saturated Model = 0.18 ECVI for Independence Model = 4.64 Chi-Square for Independence Model with 36 Degrees of Freedom = 2295.19 Independence AIC = 2313.19 Model AIC = 103.28 Saturated AIC = 90.00 Independence CAIC = 2360.12 Model CAIC = 254.50 Saturated CAIC = 324.66 Normed Fit Index (NFI) = 0.98 Non-Normed Fit Index (NNFI) = 0.99 Parsimony Normed Fit Index (PNFI) = 0.87 Comparative Fit Index (CFI) = 0.99 Incremental Fit Index (IFI) = 0.99 Relative Fit Index (RFI) = 0.98 Critical N (CN) = 590.53 Root Mean Square Residual (RMR) = 0.14 Standardized RMR = 0.048 Goodness of Fit Index (GFI) = 0.98 Adjusted Goodness of Fit Index (AGFI) = 0.97 Parsimony Goodness of Fit Index (PGFI) = 0.70 Set up Kenny-Judd (1984) example model in LISREL 8 Fitted Covariance Matrix y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 2.16 x1 -0.20 2.39 x2 -0.13 1.23 1.53 z1 0.48 0.40 0.26 2.15 z2 0.33 0.28 0.18 1.17 1.38 x1_z1 2.45 - - - - - - - - 5.31 x1_z2 1.69 - - - - - - - - 2.92 x2_z1 1.56 - - - - - - - - 2.76 x2_z2 1.07 - - - - - - - - 1.52 Fitted Covariance Matrix x1_z2 x2_z1 x2_z2 -------- -------- -------- x1_z2 3.37 x2_z1 1.52 3.36 x2_z2 1.75 1.84 2.14 Fitted Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 0.02 x1 -0.17 0.00 x2 -0.05 0.02 0.01 z1 -0.08 0.04 -0.06 -0.05 z2 -0.05 -0.05 -0.06 -0.03 -0.01 x1_z1 0.11 -0.37 -0.07 -0.15 -0.13 0.36 x1_z2 -0.11 -0.30 -0.04 -0.13 -0.12 -0.05 x2_z1 0.06 -0.08 -0.05 0.04 0.04 0.23 x2_z2 -0.10 -0.05 -0.04 0.04 -0.04 -0.18 Fitted Residuals x1_z2 x2_z1 x2_z2 -------- -------- -------- x1_z2 -0.29 x2_z1 -0.17 0.05 x2_z2 -0.35 -0.12 -0.18 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.37 Median Fitted Residual = -0.05 Largest Fitted Residual = 0.36 Stemleaf Plot - 3|750 - 2|9 - 1|88775332210 - 0|887665555555544310 0|122444456 1|1 2|3 3|6 Standardized Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y - - x1 -2.14 0.03 x2 -0.74 0.25 0.16 z1 -1.00 0.81 -0.94 -0.53 z2 -0.74 -0.87 -1.18 -0.44 -0.08 x1_z1 0.79 -2.30 -0.55 -0.98 -1.10 1.08 x1_z2 -0.94 -2.37 -0.40 -1.08 -1.21 -0.21 x2_z1 0.55 -0.64 -0.53 0.32 0.38 1.02 x2_z2 -1.13 -0.46 -0.56 0.41 -0.56 -1.08 Standardized Residuals x1_z2 x2_z1 x2_z2 -------- -------- -------- x1_z2 -1.36 x2_z1 -1.05 0.25 x2_z2 -2.47 -0.83 -1.30 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -2.47 Median Standardized Residual = -0.56 Largest Standardized Residual = 1.08 Stemleaf Plot - 2|5 - 2|431 - 1| - 1|43221111000 - 0|9998776665555 - 0|442100 0|233344 0|688 1|01 Set up Kenny-Judd (1984) example model in LISREL 8 Qplot of Standardized Residuals 3.5.......................................................................... . .. . . . . . . . . . . . . . . . . . . . . . . . . . x . . . . . . x . . . x . . . x . . N . x . . o . * . . r . xx . . m . xxx . . a . x x . . l . x . . . * . . Q . x . . u . *x . . a . xx . . n . x* . . t . * . . i . x . . l . xx . . e . xx . . s . x . . . x . . . x . . . x . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . -3.5.......................................................................... -3.5 3.5 Standardized Residuals Set up Kenny-Judd (1984) example model in LISREL 8 Modification Indices and Expected Change No Non-Zero Modification Indices for LAMBDA-Y Modification Indices for LAMBDA-X KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- x1 0.00 1.23 4.77 0.46 0.90 7.51 x2 - - 1.33 1.10 0.02 0.35 2.49 z1 1.03 0.23 0.01 0.00 0.09 0.10 z2 1.39 - - 0.11 0.00 0.61 0.42 x1_z1 0.66 0.68 1.87 0.35 0.05 0.67 x1_z2 1.20 0.54 1.35 0.32 1.19 5.27 x2_z1 0.06 0.64 1.11 4.13 0.93 4.97 x2_z2 0.38 0.14 - - 1.55 0.39 8.57 Modification Indices for LAMBDA-X Z_TD2 -------- x1 3.36 x2 2.35 z1 0.55 z2 0.03 x1_z1 4.88 x1_z2 9.84 x2_z1 4.06 x2_z2 6.29 Expected Change for LAMBDA-X KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- x1 0.00 0.06 -0.07 -0.06 -0.06 -0.27 x2 - - -0.04 0.03 0.01 0.03 0.12 z1 0.05 -0.02 0.00 0.00 0.02 -0.03 z2 -0.04 - - -0.01 0.00 -0.03 -0.04 x1_z1 -0.04 -0.04 0.05 0.06 0.02 -0.10 x1_z2 -0.04 -0.03 -0.04 0.05 -0.06 0.25 x2_z1 0.01 0.03 0.04 0.19 -0.05 0.20 x2_z2 0.02 0.01 - - -0.08 -0.03 -0.19 Expected Change for LAMBDA-X Z_TD2 -------- x1 0.10 x2 -0.07 z1 0.04 z2 0.01 x1_z1 0.14 x1_z2 -0.16 x2_z1 -0.11 x2_z2 0.12 Modification Indices for GAMMA KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- ETA_Y - - - - - - 0.21 0.21 0.99 Modification Indices for GAMMA Z_TD2 -------- ETA_Y 0.99 Expected Change for GAMMA KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- ETA_Y - - - - - - -0.12 0.06 -0.46 Expected Change for GAMMA Z_TD2 -------- ETA_Y 0.18 Modification Indices for PHI KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- KSI_X - - KSI_Z - - - - KSI_XZ 3.24 0.31 0.14 X_TD3 0.58 0.00 8.79 3.01 X_TD4 0.45 0.16 10.82 0.56 1.72 Z_TD1 3.90 2.18 0.59 2.41 0.81 0.93 Z_TD2 0.53 1.72 0.52 0.71 3.27 0.55 Modification Indices for PHI Z_TD2 -------- Z_TD2 0.01 Expected Change for PHI KSI_X KSI_Z KSI_XZ X_TD3 X_TD4 Z_TD1 -------- -------- -------- -------- -------- -------- KSI_X - - KSI_Z - - - - KSI_XZ -0.26 -0.08 0.26 X_TD3 -0.08 -0.01 0.56 0.27 X_TD4 -0.06 -0.03 -0.51 -0.08 -0.15 Z_TD1 -0.22 -0.16 0.15 0.20 -0.09 0.19 Z_TD2 0.07 0.11 -0.12 0.09 -0.14 -0.08 Expected Change for PHI Z_TD2 -------- Z_TD2 -0.01 No Non-Zero Modification Indices for PSI Modification Indices for THETA-DELTA-EPS y -------- x1 0.02 x2 0.02 z1 0.09 z2 0.09 x1_z1 0.05 x1_z2 0.18 x2_z1 0.15 x2_z2 0.36 Expected Change for THETA-DELTA-EPS y -------- x1 -0.01 x2 0.01 z1 -0.02 z2 0.01 x1_z1 0.02 x1_z2 -0.02 x2_z1 -0.02 x2_z2 0.02 Modification Indices for THETA-DELTA x1 x2 z1 z2 x1_z1 x1_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 0.25 - - z1 2.65 1.08 - - z2 0.91 0.01 0.09 - - x1_z1 0.45 0.07 0.52 2.04 1.73 x1_z2 3.62 1.86 1.34 1.16 2.15 0.08 x2_z1 0.02 0.04 0.94 3.88 9.40 1.39 x2_z2 2.12 1.30 3.12 4.60 2.17 2.15 Modification Indices for THETA-DELTA x2_z1 x2_z2 -------- -------- x2_z1 3.50 x2_z2 0.31 1.06 Expected Change for THETA-DELTA x1 x2 z1 z2 x1_z1 x1_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 0.03 - - z1 0.10 -0.05 - - z2 -0.04 0.00 -0.01 - - x1_z1 -0.04 0.01 0.04 -0.06 -0.14 x1_z2 -0.10 0.06 -0.05 0.04 0.09 0.03 x2_z1 0.01 -0.01 -0.05 0.08 0.19 -0.06 x2_z2 0.06 -0.04 0.07 -0.07 -0.07 -0.06 Expected Change for THETA-DELTA x2_z1 x2_z2 -------- -------- x2_z1 -0.18 x2_z2 0.02 0.05 Maximum Modification Index is 10.82 for Element ( 5, 3) of PHI Time used: 0.020 Seconds