DATE: 11/12/2007 TIME: 13:53 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\kjmgapi.ls8: Set up Kenny-Judd (1984) interaction example--Marsh GAPI approach DA NI=9 NO=500 MA=CM LA x1 x2 z1 z2 x1_z1 x1_z2 x2_z1 x2_z2 y CM FI=KJEXAMPL.CM ME 0 0 0 0 0 0 0 0 5.0 SE y x1 x2 z1 z2 x1_z1 x2_z2 / ! selecting the product of the first measures ! and the product of the second measures 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 LE ETA_Y LK X Z XZ ! Here's the main effects measurement model VA 1.0 LY(1,1) VA 1.0 LX(1,1) LX(3,2) FR LX(2,1) LX(4,2) ! The GAPI approach is to let PHI be free !FI PH(3,1) PH(3,2) !CO PH(3,3) = PH(1,1) * PH(2,2) + PH(2,1)^2 ! Here is Marsh's specification for Kappa 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) interaction example--Marsh GAPI 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) interaction example--Marsh GAPI 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) interaction example--Marsh GAPI 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 -------- -------- -------- ETA_Y 3 4 5 PHI X Z XZ -------- -------- -------- X 6 Z 7 8 XZ 9 10 11 PSI ETA_Y -------- 12 THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 13 14 15 16 Constr'd Constr'd ALPHA ETA_Y -------- 17 KAPPA X Z XZ -------- -------- -------- 0 0 Constr'd Set up Kenny-Judd (1984) interaction example--Marsh GAPI approach Number of Iterations = 18 LISREL Estimates (Maximum Likelihood) LAMBDA-Y ETA_Y -------- y 1.00 LAMBDA-X X Z XZ -------- -------- -------- x1 1.00 - - - - x2 0.57 - - - - (0.06) 9.83 z1 - - 1.00 - - z2 - - 0.72 - - (0.07) 10.79 x1_z1 - - - - 1.00 x2_z2 - - - - 0.41 (0.03) 14.80 GAMMA X Z XZ -------- -------- -------- ETA_Y -0.13 0.34 0.69 (0.03) (0.05) (0.04) -3.75 7.61 15.88 Covariance Matrix of ETA and KSI ETA_Y X Z XZ -------- -------- -------- -------- ETA_Y 2.20 X -0.41 2.16 Z 0.43 0.21 1.55 XZ 2.55 -0.30 -0.11 3.70 Mean Vector of Eta-Variables ETA_Y -------- 5.10 PHI X Z XZ -------- -------- -------- X 2.16 (0.26) 8.27 Z 0.21 1.55 (0.07) (0.18) 3.01 8.51 XZ -0.30 -0.11 3.70 (0.16) (0.14) (0.38) -1.88 -0.77 9.63 PSI ETA_Y -------- 0.24 (0.09) 2.53 Squared Multiple Correlations for Y - Variables y -------- 1.00 THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 0.28 0.81 0.58 0.53 1.85 1.44 (0.21) (0.08) (0.14) (0.08) (0.20) (0.08) 1.34 10.42 4.25 7.04 9.13 18.96 Squared Multiple Correlations for X - Variables x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- 0.89 0.46 0.73 0.60 0.67 0.30 ALPHA ETA_Y -------- 4.96 (0.04) 114.87 KAPPA X Z XZ -------- -------- -------- - - - - 0.21 (0.07) 3.01 Goodness of Fit Statistics Degrees of Freedom = 18 Minimum Fit Function Chi-Square = 21.04 (P = 0.28) Normal Theory Weighted Least Squares Chi-Square = 20.63 (P = 0.30) Estimated Non-centrality Parameter (NCP) = 2.63 90 Percent Confidence Interval for NCP = (0.0 ; 18.11) Minimum Fit Function Value = 0.042 Population Discrepancy Function Value (F0) = 0.0053 90 Percent Confidence Interval for F0 = (0.0 ; 0.036) Root Mean Square Error of Approximation (RMSEA) = 0.017 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 = (0.098 ; 0.13) 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 = 62.63 Saturated AIC = 56.00 Independence CAIC = 1039.20 Model CAIC = 172.14 Saturated CAIC = 202.01 Normed Fit Index (NFI) = 0.98 Non-Normed Fit Index (NNFI) = 1.00 Parsimony Normed Fit Index (PNFI) = 0.84 Comparative Fit Index (CFI) = 1.00 Incremental Fit Index (IFI) = 1.00 Relative Fit Index (RFI) = 0.98 Critical N (CN) = 842.81 Root Mean Square Residual (RMR) = 0.079 Standardized RMR = 0.033 Goodness of Fit Index (GFI) = 0.99 Adjusted Goodness of Fit Index (AGFI) = 0.99 Parsimony Goodness of Fit Index (PGFI) = 0.64 Set up Kenny-Judd (1984) interaction example--Marsh GAPI approach Fitted Covariance Matrix y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y 2.20 x1 -0.41 2.44 x2 -0.23 1.22 1.50 z1 0.43 0.21 0.12 2.13 z2 0.31 0.15 0.09 1.11 1.33 x1_z1 2.55 -0.30 -0.17 -0.11 -0.08 5.54 x2_z2 1.04 -0.12 -0.07 -0.04 -0.03 1.50 Fitted Covariance Matrix x2_z2 -------- x2_z2 2.05 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 0.04 -0.04 x2 0.05 0.03 0.04 z1 -0.03 0.23 0.08 -0.03 z2 -0.03 0.08 0.03 0.03 0.04 x1_z1 0.02 -0.07 0.10 -0.04 -0.05 0.17 x2_z2 -0.06 0.07 0.02 0.08 -0.01 -0.14 Fitted Residuals x2_z2 -------- x2_z2 -0.08 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 -------- -------- -------- -------- -------- -------- -2.01 - - - - - - - - -2.00 Standardized Residuals for Means x2_z2 -------- -1.34 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.14 Median Fitted Residual = 0.03 Largest Fitted Residual = 0.23 Stemleaf Plot - 1|4 - 0|8765 - 0|4433321 0|22333444 0|57888 1|0 1|7 2|3 Standardized Residuals y x1 x2 z1 z2 x1_z1 -------- -------- -------- -------- -------- -------- y -2.78 x1 2.41 -0.85 x2 1.01 1.02 0.87 z1 -0.96 3.13 1.21 -0.75 z2 -0.74 1.28 0.54 1.01 0.89 x1_z1 1.05 -1.56 1.09 -0.64 -0.82 - - x2_z2 -0.78 0.97 0.34 1.13 -0.18 -2.52 Standardized Residuals x2_z2 -------- x2_z2 -0.72 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -2.78 Median Standardized Residual = 0.44 Largest Standardized Residual = 3.13 Stemleaf Plot - 2|85 - 1|60 - 0|888877620 0|3599 1|000001123 2|4 3|1 Largest Negative Standardized Residuals Residual for y and y -2.78 Largest Positive Standardized Residuals Residual for z1 and x1 3.13 Set up Kenny-Judd (1984) interaction example--Marsh GAPI approach Qplot of Standardized Residuals 3.5.......................................................................... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . . . . . . x . . . . N . .x . o . . x . r . . * . m . . x . a . . * . l . . x . . . xx . Q . . x x . u . . x . a . x .x . n . x . . t . * . . i . x. . l . .* . e . .x . s . x . . . . . . x . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -3.5.......................................................................... -3.5 3.5 Standardized Residuals Set up Kenny-Judd (1984) interaction example--Marsh GAPI approach Modification Indices and Expected Change No Non-Zero Modification Indices for LAMBDA-Y Modification Indices for LAMBDA-X X Z XZ -------- -------- -------- x1 2.88 4.40 0.97 x2 - - 0.22 0.89 z1 5.33 2.21 0.17 z2 0.45 - - 0.37 x1_z1 0.97 0.81 1.61 x2_z2 0.97 0.81 1.39 Expected Change for LAMBDA-X X Z XZ -------- -------- -------- x1 -0.13 0.12 -0.04 x2 - - -0.02 0.02 z1 0.09 -0.16 0.01 z2 -0.02 - - -0.01 x1_z1 -0.10 -0.12 0.16 x2_z2 0.04 0.05 -0.04 No Non-Zero Modification Indices for GAMMA No Non-Zero Modification Indices for PHI No Non-Zero Modification Indices for PSI Modification Indices for THETA-DELTA-EPS y -------- x1 0.02 x2 0.02 z1 0.04 z2 0.04 x1_z1 1.39 x2_z2 1.39 Expected Change for THETA-DELTA-EPS y -------- x1 0.01 x2 -0.01 z1 0.02 z2 -0.02 x1_z1 -0.55 x2_z2 0.22 Modification Indices for THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 2.88 - - z1 4.90 0.32 - - z2 0.68 0.05 2.88 - - x1_z1 2.60 1.76 0.23 0.03 - - x2_z2 1.58 0.71 1.74 0.94 2.88 0.00 Expected Change for THETA-DELTA x1 x2 z1 z2 x1_z1 x2_z2 -------- -------- -------- -------- -------- -------- x1 - - x2 0.22 - - z1 0.13 -0.03 - - z2 -0.04 0.01 0.20 - - x1_z1 -0.17 0.09 -0.05 0.01 - - x2_z2 0.08 -0.04 0.08 -0.05 -0.24 0.00 No Non-Zero Modification Indices for TAU-Y No Non-Zero Modification Indices for ALPHA Modification Indices for KAPPA X Z XZ -------- -------- -------- 0.03 0.00 4.45 Expected Change for KAPPA X Z XZ -------- -------- -------- -0.01 0.00 -0.22 Maximum Modification Index is 5.33 for Element ( 3, 1) of LAMBDA-X Time used: 0.020 Seconds