DATE: 11/12/2007 TIME: 13:55 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 E:\Class Files\kjmc.ls8: Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach DA NI=9 NO=500 MA=CM ! reading in covariance matrix--must analyze covariances for interactions CM FI=KJEXAMPL.CM ME 0 0 0 0 0 0 0 0 5.0 ! labels for measures of 4 factors: X and Z (main), XZ (interaction), ! Y (dependent) LA x1 x2 z1 z2 x1_z1 x1_z2 x2_z1 x2_z2 y ! selecting the product of the "1" measures ! and the product of the "2" measures SE y x1 x2 z1 z2 x1_z1 x2_z2 / MO NY=1 NE=1 NX=6 NK=3 PS=SY PH=SY GA=FU,FR C LX=FU,FI LY=FU,FI TD=SY TE=SY,FI KA=FI AL=FR TY=FI ! construct labels LE Y LK X Z XZ ! Here's the main effects measurement model VA 1.0 LY(1,1) LX(1,1) LX(3,2) FR LX(2,1) LX(4,2) ! Here are the constraints on PHI FI PH(3,1) PH(3,2) ! after mean centering and with normality, interaction factor should be ! orthogonal CO PH(3,3) = PH(1,1) * PH(2,2) + PH(2,1)^2 ! Here is Marsh et al's value for the mean of the interaction construct CO KA(3) = PH(2,1) ! Here are the loadings for the interaction measures VA 1.0 LX(5,3) CO LX(6,3) = LX(2,1) * LX(4,2) ! Here are the constraints on the measurement error variances for the interaction measures. CO TD(5,5) = PH(1,1) * TD(3,3) + PH(2,2) * TD(1,1) + TD(1,1) * TD(3,3) CO TD(6,6) = PH(1,1) * TD(4,4) * LX(2,1)^2 + PH(2,2) * TD(2,2) * LX(4,2)^2 C + TD(2,2) * TD(4,4) OU AD=OFF RS MI Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach Number of Input Variables 9 Number of Y - Variables 1 Number of X - Variables 6 Number of ETA - Variables 1 Number of KSI - Variables 3 Number of Observations 500 Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach 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 x2_z2 0.97 -0.05 -0.04 0.04 -0.04 1.34 Covariance Matrix x2_z2 -------- x2_z2 1.96 Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- 5.00 - - - - - - - - - - Means x2_z2 -------- - - Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach Parameter Specifications LAMBDA-X X Z XZ -------- -------- -------- x1 0 0 0 x2 1 0 0 z1 0 0 0 z2 0 2 0 x1_z1 0 0 0 x2_z2 0 0 Constr'd GAMMA X Z XZ -------- -------- -------- Y 3 4 5 PHI X Z XZ -------- -------- -------- X 6 Z 7 8 XZ 0 0 Constr'd PSI Y -------- 9 THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 10 11 12 13 Constr'd Constr'd ALPHA Y -------- 14 KAPPA X Z XZ -------- -------- -------- 0 0 Constr'd Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach Number of Iterations = 14 LISREL Estimates (Maximum Likelihood) LAMBDA-Y Y -------- y 1.00 LAMBDA-X X Z XZ -------- -------- -------- x1 1.00 - - - - x2 0.58 - - - - (0.06) 9.89 z1 - - 1.00 - - z2 - - 0.71 - - (0.06) 10.89 x1_z1 - - - - 1.00 x2_z2 - - - - 0.41 (0.03) 14.87 GAMMA X Z XZ -------- -------- -------- Y -0.16 0.33 0.70 (0.03) (0.04) (0.04) -4.99 8.29 16.83 Covariance Matrix of ETA and KSI Y X Z XZ -------- -------- -------- -------- Y 2.17 X -0.27 2.16 Z 0.50 0.21 1.61 XZ 2.48 - - - - 3.52 Mean Vector of Eta-Variables Y -------- 5.10 PHI X Z XZ -------- -------- -------- X 2.16 (0.25) 8.77 Z 0.21 1.61 (0.07) (0.17) 3.04 9.24 XZ - - - - 3.52 (0.30) 11.76 PSI Y -------- 0.21 (0.09) 2.29 Squared Multiple Correlations for Y - Variables y -------- 1.00 THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 0.32 0.79 0.56 0.54 1.91 1.45 (0.20) (0.08) (0.14) (0.08) (0.20) (0.07) 1.58 9.98 3.97 7.16 9.58 19.79 Squared Multiple Correlations for X - Variables x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 0.87 0.48 0.74 0.60 0.65 0.29 ALPHA Y -------- 4.95 (0.04) 114.89 KAPPA X Z XZ -------- -------- -------- - - - - 0.21 (0.07) 3.04 Goodness of Fit Statistics Degrees of Freedom = 21 Minimum Fit Function Chi-Square = 25.40 (P = 0.23) Normal Theory Weighted Least Squares Chi-Square = 25.03 (P = 0.25) Estimated Non-centrality Parameter (NCP) = 4.03 90 Percent Confidence Interval for NCP = (0.0 ; 20.80) Minimum Fit Function Value = 0.051 Population Discrepancy Function Value (F0) = 0.0081 90 Percent Confidence Interval for F0 = (0.0 ; 0.042) Root Mean Square Error of Approximation (RMSEA) = 0.020 90 Percent Confidence Interval for RMSEA = (0.0 ; 0.045) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.98 Expected Cross-Validation Index (ECVI) = 0.13 90 Percent Confidence Interval for ECVI = (0.094 ; 0.14) ECVI for Saturated Model = 0.11 ECVI for Independence Model = 2.01 Chi-Square for Independence Model with 21 Degrees of Freedom = 988.70 Independence AIC = 1002.70 Model AIC = 63.03 Saturated AIC = 56.00 Independence CAIC = 1039.20 Model CAIC = 162.11 Saturated CAIC = 202.01 Normed Fit Index (NFI) = 0.97 Non-Normed Fit Index (NNFI) = 1.00 Parsimony Normed Fit Index (PNFI) = 0.97 Comparative Fit Index (CFI) = 1.00 Incremental Fit Index (IFI) = 1.00 Relative Fit Index (RFI) = 0.97 Critical N (CN) = 777.10 Root Mean Square Residual (RMR) = 0.12 Standardized RMR = 0.040 Goodness of Fit Index (GFI) = 0.99 Adjusted Goodness of Fit Index (AGFI) = 0.98 Parsimony Goodness of Fit Index (PGFI) = 0.74 Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach Fitted Covariance Matrix y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 2.17 x1 -0.27 2.48 x2 -0.16 1.25 1.51 z1 0.50 0.21 0.12 2.17 z2 0.35 0.15 0.09 1.14 1.34 x1_z1 2.48 - - - - - - - - 5.43 x2_z2 1.01 - - - - - - - - 1.44 Fitted Covariance Matrix x2_z2 -------- x2_z2 2.04 Fitted Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- 5.10 - - - - - - - - 0.21 Fitted Means x2_z2 -------- 0.09 Fitted Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 0.02 x1 -0.10 -0.09 x2 -0.02 0.01 0.03 z1 -0.09 0.23 0.08 -0.07 z2 -0.07 0.08 0.03 0.00 0.03 x1_z1 0.10 -0.37 -0.07 -0.15 -0.13 0.28 x2_z2 -0.03 -0.05 -0.04 0.04 -0.04 -0.08 Fitted Residuals x2_z2 -------- x2_z2 -0.07 Fitted Residuals for Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- -0.10 - - - - - - - - -0.21 Fitted Residuals for Means x2_z2 -------- -0.09 Standardized Residuals for Means y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- -2.06 - - - - - - - - -2.03 Standardized Residuals for Means x2_z2 -------- -1.36 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.37 Median Fitted Residual = -0.04 Largest Fitted Residual = 0.28 Stemleaf Plot - 3|7 - 2| - 1|530 - 0|9987777554320 0|12333488 1|0 2|38 Standardized Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y - - x1 -1.19 -0.94 x2 -0.31 0.09 0.56 z1 -1.24 3.00 1.14 -0.92 z2 -1.12 1.26 0.52 0.07 0.55 x1_z1 0.80 -2.23 -0.55 -0.96 -1.10 0.82 x2_z2 -0.39 -0.47 -0.57 0.41 -0.58 -0.49 Standardized Residuals x2_z2 -------- x2_z2 -0.53 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -2.23 Median Standardized Residual = -0.43 Largest Standardized Residual = 3.00 Stemleaf Plot - 2|2 - 1|22110 - 0|99665555430 0|11455688 1|13 2| 3|0 Largest Positive Standardized Residuals Residual for z1 and x1 3.00 Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach Qplot of Standardized Residuals 3.5.......................................................................... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . . . . . x . . . . . N . x. . o . x . . r . x x. . m . x . . a . xx . l . x . . . x x . . Q . * . . u . x . . a . * . . n . x. . t . x x. . i . x . . l . xx. . e . x. . s . x . . . . . . x . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -3.5.......................................................................... -3.5 3.5 Standardized Residuals Set up Kenny-Judd (1984) example model in LISREL 8--"constrained" approach Modification Indices and Expected Change No Non-Zero Modification Indices for LAMBDA-Y Modification Indices for LAMBDA-X X Z XZ -------- -------- -------- x1 2.70 4.41 3.74 x2 - - 0.25 0.65 z1 4.99 2.19 0.01 z2 0.39 - - 0.54 x1_z1 4.25 1.69 1.66 x2_z2 0.19 0.37 1.09 Expected Change for LAMBDA-X X Z XZ -------- -------- -------- x1 -0.10 0.11 -0.06 x2 - - -0.02 0.02 z1 0.09 -0.10 0.00 z2 -0.02 - - -0.02 x1_z1 -0.14 -0.11 0.10 x2_z2 0.02 0.03 -0.04 No Non-Zero Modification Indices for GAMMA Modification Indices for PHI X Z XZ -------- -------- -------- X - - Z - - - - XZ 3.29 0.55 - - Expected Change for PHI X Z XZ -------- -------- -------- X - - Z - - - - XZ -0.28 -0.10 - - No Non-Zero Modification Indices for PSI Modification Indices for THETA-DELTA-EPS y -------- x1 0.00 x2 0.00 z1 0.01 z2 0.01 x1_z1 0.20 x2_z2 0.20 Expected Change for THETA-DELTA-EPS y -------- x1 0.00 x2 0.00 z1 -0.01 z2 0.01 x1_z1 -0.23 x2_z2 0.09 Modification Indices for THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 1.28 - - z1 4.73 0.41 - - z2 0.49 0.04 1.28 - - x1_z1 5.03 1.29 0.44 0.01 - - x2_z2 0.98 0.86 1.66 1.02 1.28 0.01 Expected Change for THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 0.13 - - z1 0.13 -0.03 - - z2 -0.03 0.01 0.12 - - x1_z1 -0.22 0.08 -0.06 -0.01 - - x2_z2 0.07 -0.05 0.08 -0.05 -0.14 -0.01 No Non-Zero Modification Indices for TAU-Y No Non-Zero Modification Indices for ALPHA Modification Indices for KAPPA X Z XZ -------- -------- -------- - - - - 4.62 Expected Change for KAPPA X Z XZ -------- -------- -------- - - - - -0.22 Maximum Modification Index is 5.03 for Element ( 5, 1) of THETA-DELTA Time used: 0.030 Seconds