DATE: 10/29/2007 TIME: 15:34 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\mackenz1.spl: Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Observed Variables: ATT_AD1 ATT_AD2 ATT_AD3 POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 BUY_INT2 BUY_INT3 Sample Size: 200 Correlation Matrix from file macklow.km Standard Deviations from file macklow.sd Means from file macklow.me Latent Variables: ATT_AD POSCOGNI NEGCOGNI BRANDATT BUYINTEN Relationships: ATT_AD1 = Const + 1*ATT_AD ATT_AD2 ATT_AD3 = Const + ATT_AD POS_COG1 = Const + 1*POSCOGNI NEG_COG1 = Const + 1*NEGCOGNI BRANDAT1 = Const + 1*BRANDATT BRANDAT2 BRANDAT3 = Const + BRANDATT BUY_INT1 = Const + 1*BUYINTEN BUY_INT2 BUY_INT3 = Const + BUYINTEN POSCOGNI = ATT_AD NEGCOGNI = ATT_AD BRANDATT = ATT_AD + POSCOGNI + NEGCOGNI BUYINTEN = BRANDATT Set the error variance for POS_COG1 to 0 Set the error variance for NEG_COG1 to 0 Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Sample Size: 160 Correlation Matrix from file mackhigh.km Standard Deviations from file mackhigh.sd Means from file mackhigh.me Relationships: POSCOGNI = Const + ATT_AD NEGCOGNI = Const + ATT_AD BRANDATT = Const + ATT_AD + POSCOGNI + NEGCOGNI BUYINTEN = Const + BRANDATT ATT_AD = Const Set the variance of ATT_AD free Set the error variance of POSCOGNI free Set the error variance of NEGCOGNI free Set the error variance of BRANDATT free Set the error variance of BUYINTEN free Set the error variances for ATT_AD1 - ATT_AD3 free Set the error variances for BRANDAT1 - BUY_INT3 free LISREL OUTPUT: RS MI End of Problem Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Covariance Matrix POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 0.66 NEG_COG1 -0.05 0.61 BRANDAT1 0.26 -0.23 1.42 BRANDAT2 0.10 -0.23 0.91 1.66 BRANDAT3 0.29 -0.32 1.23 0.99 1.64 BUY_INT1 0.18 -0.13 0.66 0.22 0.73 1.77 BUY_INT2 0.14 -0.13 0.65 0.31 0.81 1.67 BUY_INT3 0.30 -0.27 0.89 0.58 0.96 1.39 ATT_AD1 0.31 -0.19 1.00 0.68 1.02 0.72 ATT_AD2 0.17 -0.17 0.85 0.81 0.92 0.42 ATT_AD3 0.31 -0.25 1.03 0.81 1.08 0.50 Covariance Matrix BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 2.04 BUY_INT3 1.50 2.76 ATT_AD1 0.74 0.90 1.51 ATT_AD2 0.41 0.62 0.90 1.30 ATT_AD3 0.45 0.67 1.21 1.05 1.59 Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.56 0.58 4.69 4.53 4.66 2.16 Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- 2.32 3.55 4.27 5.02 4.48 Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Covariance Matrix POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 1.00 NEG_COG1 -0.02 0.85 BRANDAT1 0.33 -0.22 1.21 BRANDAT2 0.18 -0.16 0.48 1.17 BRANDAT3 0.36 -0.31 0.92 0.56 1.32 BUY_INT1 0.28 -0.35 0.59 0.51 0.68 1.80 BUY_INT2 0.41 -0.29 0.55 0.49 0.70 1.55 BUY_INT3 0.43 -0.11 0.40 0.56 0.63 1.38 ATT_AD1 0.27 -0.19 0.70 0.43 0.77 0.60 ATT_AD2 0.21 -0.12 0.60 0.42 0.61 0.49 ATT_AD3 0.30 -0.06 0.75 0.51 0.83 0.56 Covariance Matrix BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 2.43 BUY_INT3 1.22 2.76 ATT_AD1 0.54 0.58 1.54 ATT_AD2 0.48 0.49 1.05 1.39 ATT_AD3 0.52 0.64 1.13 1.05 1.44 Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.59 0.78 4.86 4.71 4.74 2.19 Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- 2.50 3.59 4.35 4.93 4.59 Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Parameter Specifications LAMBDA-Y EQUALS LAMBDA-Y IN THE FOLLOWING GROUP LAMBDA-X EQUALS LAMBDA-X IN THE FOLLOWING GROUP BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI 0 0 0 0 NEGCOGNI 0 0 0 0 BRANDATT 7 8 0 0 BUYINTEN 0 0 9 0 GAMMA ATT_AD -------- POSCOGNI 10 NEGCOGNI 11 BRANDATT 12 BUYINTEN 0 PHI ATT_AD -------- 13 PSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 14 15 16 17 THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0 0 18 19 20 21 THETA-EPS BUY_INT2 BUY_INT3 -------- -------- 22 23 THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 24 25 26 TAU-Y EQUALS TAU-Y IN THE FOLLOWING GROUP TAU-X EQUALS TAU-X IN THE FOLLOWING GROUP Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Parameter Specifications LAMBDA-Y POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POS_COG1 0 0 0 0 NEG_COG1 0 0 0 0 BRANDAT1 0 0 0 0 BRANDAT2 0 0 1 0 BRANDAT3 0 0 2 0 BUY_INT1 0 0 0 0 BUY_INT2 0 0 0 3 BUY_INT3 0 0 0 4 LAMBDA-X ATT_AD -------- ATT_AD1 0 ATT_AD2 5 ATT_AD3 6 BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI 0 0 0 0 NEGCOGNI 0 0 0 0 BRANDATT 38 39 0 0 BUYINTEN 0 0 40 0 GAMMA ATT_AD -------- POSCOGNI 41 NEGCOGNI 42 BRANDATT 43 BUYINTEN 0 PHI ATT_AD -------- 44 PSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 45 46 47 48 THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0 0 49 50 51 52 THETA-EPS BUY_INT2 BUY_INT3 -------- -------- 53 54 THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 55 56 57 TAU-Y POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 27 28 29 30 31 32 TAU-Y BUY_INT2 BUY_INT3 -------- -------- 33 34 TAU-X ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 35 36 37 ALPHA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 58 59 60 61 KAPPA ATT_AD -------- 62 Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Number of Iterations = 7 LISREL Estimates (Maximum Likelihood) LAMBDA-Y EQUALS LAMBDA-Y IN THE FOLLOWING GROUP LAMBDA-X EQUALS LAMBDA-X IN THE FOLLOWING GROUP BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - - - - - - - NEGCOGNI - - - - - - - - BRANDATT 0.03 -0.15 - - - - (0.07) (0.07) 0.50 -2.20 BUYINTEN - - - - 0.58 - - (0.08) 6.99 GAMMA ATT_AD -------- POSCOGNI 0.25 (0.06) 4.45 NEGCOGNI -0.19 (0.05) -3.51 BRANDATT 0.83 (0.07) 12.74 BUYINTEN - - Covariance Matrix of ETA and KSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN ATT_AD -------- -------- -------- -------- -------- POSCOGNI 0.66 NEGCOGNI -0.05 0.61 BRANDATT 0.26 -0.27 1.15 BUYINTEN 0.15 -0.15 0.66 1.61 ATT_AD 0.27 -0.21 0.96 0.56 1.11 PHI ATT_AD -------- 1.11 (0.14) 7.87 PSI Note: This matrix is diagonal. POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.59 0.57 0.30 1.22 (0.06) (0.06) (0.05) (0.15) 9.85 9.90 5.54 8.36 Squared Multiple Correlations for Structural Equations POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.10 0.07 0.74 0.24 NOTE: Rý for Structural Equations are Hayduk's (2006) Blocked-Error Rý Squared Multiple Correlations for Reduced Form POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.10 0.07 0.73 0.17 Reduced Form ATT_AD -------- POSCOGNI 0.25 (0.06) 4.45 NEGCOGNI -0.19 (0.05) -3.51 BRANDATT 0.87 (0.06) 13.89 BUYINTEN 0.50 (0.08) 6.55 THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - 0.27 0.97 0.30 0.18 (0.04) (0.10) (0.05) (0.06) 6.05 9.45 5.76 3.13 THETA-EPS BUY_INT2 BUY_INT3 -------- -------- 0.29 1.49 (0.07) (0.16) 4.31 9.44 W_A_R_N_I_N_G: THETA-EPS is not positive definite Squared Multiple Correlations for Y - Variables POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 1.00 1.00 0.81 0.39 0.82 0.90 Squared Multiple Correlations for Y - Variables BUY_INT2 BUY_INT3 -------- -------- 0.86 0.45 THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.41 0.49 0.29 (0.06) (0.06) (0.05) 7.43 8.33 5.85 Squared Multiple Correlations for X - Variables ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.73 0.64 0.81 TAU-Y EQUALS TAU-Y IN THE FOLLOWING GROUP TAU-X EQUALS TAU-X IN THE FOLLOWING GROUP Group Goodness of Fit Statistics Contribution to Chi-Square = 96.48 Percentage Contribution to Chi-Square = 63.96 Root Mean Square Residual (RMR) = 0.11 Standardized RMR = 0.063 Goodness of Fit Index (GFI) = 0.92 Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Fitted Covariance Matrix POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 0.66 NEG_COG1 -0.05 0.61 BRANDAT1 0.26 -0.27 1.42 BRANDAT2 0.19 -0.19 0.84 1.58 BRANDAT3 0.28 -0.29 1.25 0.91 1.66 BUY_INT1 0.15 -0.15 0.66 0.48 0.72 1.79 BUY_INT2 0.15 -0.16 0.69 0.50 0.75 1.67 BUY_INT3 0.13 -0.14 0.58 0.43 0.64 1.41 ATT_AD1 0.27 -0.21 0.96 0.70 1.05 0.56 ATT_AD2 0.24 -0.19 0.85 0.62 0.92 0.49 ATT_AD3 0.29 -0.23 1.03 0.75 1.12 0.60 Fitted Covariance Matrix BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 2.01 BUY_INT3 1.46 2.74 ATT_AD1 0.58 0.49 1.52 ATT_AD2 0.51 0.43 0.98 1.35 ATT_AD3 0.62 0.52 1.18 1.05 1.56 Fitted Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.56 0.58 4.71 4.57 4.64 2.15 Fitted Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- 2.34 3.54 4.28 4.96 4.50 Fitted Residuals POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 0.00 NEG_COG1 0.00 0.00 BRANDAT1 0.00 0.03 0.00 BRANDAT2 -0.08 -0.04 0.07 0.09 BRANDAT3 0.01 -0.03 -0.02 0.08 -0.02 BUY_INT1 0.03 0.02 0.00 -0.26 0.01 -0.02 BUY_INT2 -0.01 0.03 -0.04 -0.19 0.05 0.01 BUY_INT3 0.17 -0.14 0.30 0.15 0.32 -0.02 ATT_AD1 0.04 0.02 0.04 -0.02 -0.02 0.16 ATT_AD2 -0.07 0.02 0.01 0.19 0.00 -0.06 ATT_AD3 0.01 -0.02 0.01 0.06 -0.04 -0.09 Fitted Residuals BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 0.03 BUY_INT3 0.03 0.02 ATT_AD1 0.16 0.41 0.00 ATT_AD2 -0.10 0.19 -0.08 -0.04 ATT_AD3 -0.17 0.15 0.02 0.00 0.03 Fitted Residuals for Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.00 0.00 -0.02 -0.04 0.02 0.01 Fitted Residuals for Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- -0.02 0.01 -0.01 0.06 -0.02 Standardized Residuals for Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - -0.91 -0.92 1.39 1.31 Standardized Residuals for Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- -1.51 0.13 -0.37 2.10 -1.32 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.26 Median Fitted Residual = 0.01 Largest Fitted Residual = 0.41 Stemleaf Plot - 2|6 - 1|9740 - 0|988764444322222221000000000 0|111111222223333334456789 1|5566799 2| 3|02 4|1 Standardized Residuals POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 - - NEG_COG1 0.03 - - BRANDAT1 0.15 1.68 -0.10 BRANDAT2 -1.55 -0.73 1.35 1.39 BRANDAT3 0.45 -1.37 -1.66 1.42 -0.75 BUY_INT1 0.54 0.32 -0.01 -3.07 0.18 -1.26 BUY_INT2 -0.22 0.40 -0.89 -2.04 1.12 0.68 BUY_INT3 1.90 -1.63 3.10 1.22 3.02 -0.35 ATT_AD1 1.20 0.63 0.89 -0.23 -0.57 2.32 ATT_AD2 -2.16 0.49 0.14 2.70 -0.07 -0.90 ATT_AD3 0.64 -0.98 0.18 0.97 -1.26 -1.43 Standardized Residuals BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 1.15 BUY_INT3 0.42 0.18 ATT_AD1 2.13 3.55 -0.10 ATT_AD2 -1.30 1.73 -1.96 -0.85 ATT_AD3 -2.31 1.28 0.98 0.05 0.81 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -3.07 Median Standardized Residual = 0.16 Largest Standardized Residual = 3.55 Stemleaf Plot - 3|1 - 2|3200 - 1|765443330 - 0|9997764221110000 0|11122234445566789 1|0012223444779 2|137 3|016 Largest Negative Standardized Residuals Residual for BUY_INT1 and BRANDAT2 -3.07 Largest Positive Standardized Residuals Residual for BUY_INT3 and BRANDAT1 3.10 Residual for BUY_INT3 and BRANDAT3 3.02 Residual for ATT_AD1 and BUY_INT3 3.55 Residual for ATT_AD2 and BRANDAT2 2.70 Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Qplot of Standardized Residuals 3.5.......................................................................... . .. . . . . . . . . . . . . . . . . . . . . . . . x . . . . . x . . . x . . . x . . . x x . N . . xx . o . . * x . r . . xxx . m . . x* . a . . xx* . l . . *x . . . ** . Q . .* xx . u . .xx . a . .x*x . n . . *x . t . * x x . i . *x. . l . * x. . e . *x . . s . xx . . . x x . . . x . . . x . . . x . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . -3.5.......................................................................... -3.5 3.5 Standardized Residuals Group 1: Low Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Modification Indices and Expected Change Modification Indices for LAMBDA-Y POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POS_COG1 - - 0.00 0.00 0.16 NEG_COG1 0.00 - - 0.00 0.04 BRANDAT1 0.03 2.84 0.01 0.01 BRANDAT2 2.41 0.54 1.94 6.12 BRANDAT3 0.23 1.90 0.56 1.55 BUY_INT1 0.56 0.25 1.03 1.59 BUY_INT2 2.41 0.37 0.48 1.33 BUY_INT3 4.61 5.01 11.36 0.03 Expected Change for LAMBDA-Y POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POS_COG1 - - 0.00 -0.02 0.02 NEG_COG1 0.00 - - 0.07 0.01 BRANDAT1 0.01 0.11 -0.01 0.00 BRANDAT2 -0.14 -0.07 0.06 -0.16 BRANDAT3 0.03 -0.10 -0.02 0.06 BUY_INT1 0.04 0.03 -0.06 -0.12 BUY_INT2 -0.09 0.04 -0.04 0.03 BUY_INT3 0.24 -0.26 0.32 0.01 Modification Indices for LAMBDA-X ATT_AD -------- ATT_AD1 0.01 ATT_AD2 0.73 ATT_AD3 0.66 Expected Change for LAMBDA-X ATT_AD -------- ATT_AD1 -0.01 ATT_AD2 -0.03 ATT_AD3 0.03 Modification Indices for BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - 0.00 0.00 0.17 NEGCOGNI 0.00 - - 0.00 0.04 BRANDATT - - - - - - 0.04 BUYINTEN 0.15 0.04 - - - - Expected Change for BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - 0.00 -0.02 0.02 NEGCOGNI 0.00 - - 0.07 0.01 BRANDATT - - - - - - 0.01 BUYINTEN 0.04 0.02 - - - - Modification Indices for GAMMA ATT_AD -------- POSCOGNI - - NEGCOGNI - - BRANDATT - - BUYINTEN 0.03 Expected Change for GAMMA ATT_AD -------- POSCOGNI - - NEGCOGNI - - BRANDATT - - BUYINTEN -0.03 No Non-Zero Modification Indices for PHI Modification Indices for PSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - NEGCOGNI 0.00 - - BRANDATT - - - - - - BUYINTEN 0.17 0.03 0.04 - - Expected Change for PSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - NEGCOGNI 0.00 - - BRANDATT - - - - - - BUYINTEN 0.03 0.01 0.01 - - Modification Indices for THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 - - NEG_COG1 0.00 - - BRANDAT1 0.00 2.85 - - BRANDAT2 3.55 0.22 0.23 - - BRANDAT3 0.53 2.30 1.85 0.65 - - BUY_INT1 0.79 0.05 2.59 8.99 2.28 - - BUY_INT2 1.67 0.25 4.27 0.52 5.97 5.01 BUY_INT3 1.70 1.92 1.00 2.34 0.03 2.80 Modification Indices for THETA-EPS BUY_INT2 BUY_INT3 -------- -------- BUY_INT2 - - BUY_INT3 0.04 - - Expected Change for THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 - - NEG_COG1 0.00 - - BRANDAT1 0.00 0.06 - - BRANDAT2 -0.10 -0.03 0.02 - - BRANDAT3 0.03 -0.06 -0.10 0.04 - - BUY_INT1 0.03 0.01 0.05 -0.13 -0.05 - - BUY_INT2 -0.05 0.02 -0.06 0.03 0.08 0.38 BUY_INT3 0.09 -0.09 0.06 0.14 -0.01 -0.16 Expected Change for THETA-EPS BUY_INT2 BUY_INT3 -------- -------- BUY_INT2 - - BUY_INT3 0.02 - - Modification Indices for THETA-DELTA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- ATT_AD1 1.51 0.53 1.07 4.53 0.43 0.08 ATT_AD2 4.40 0.35 0.12 9.46 0.39 0.10 ATT_AD3 0.31 1.31 0.02 0.04 0.86 0.81 Modification Indices for THETA-DELTA-EPS BUY_INT2 BUY_INT3 -------- -------- ATT_AD1 2.64 0.31 ATT_AD2 0.35 0.38 ATT_AD3 4.62 0.48 Expected Change for THETA-DELTA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- ATT_AD1 0.05 0.03 0.04 -0.11 -0.02 0.01 ATT_AD2 -0.09 0.02 -0.01 0.17 0.02 -0.01 ATT_AD3 0.02 -0.05 0.00 0.01 -0.03 0.03 Expected Change for THETA-DELTA-EPS BUY_INT2 BUY_INT3 -------- -------- ATT_AD1 0.06 0.04 ATT_AD2 -0.02 0.04 ATT_AD3 -0.07 -0.04 Modification Indices for THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- ATT_AD1 - - ATT_AD2 5.85 - - ATT_AD3 1.73 1.20 - - Expected Change for THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- ATT_AD1 - - ATT_AD2 -0.11 - - ATT_AD3 0.08 0.05 - - Modification Indices for TAU-Y POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - 0.83 0.84 1.94 1.72 Modification Indices for TAU-Y BUY_INT2 BUY_INT3 -------- -------- 2.27 0.02 Expected Change for TAU-Y POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - -0.02 -0.04 0.02 0.01 Expected Change for TAU-Y BUY_INT2 BUY_INT3 -------- -------- -0.02 0.01 Modification Indices for TAU-X ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.14 4.43 1.74 Expected Change for TAU-X ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -0.01 0.06 -0.02 No Non-Zero Modification Indices for ALPHA No Non-Zero Modification Indices for KAPPA Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Number of Iterations = 7 LISREL Estimates (Maximum Likelihood) LAMBDA-Y POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POS_COG1 1.00 - - - - - - NEG_COG1 - - 1.00 - - - - BRANDAT1 - - - - 1.00 - - BRANDAT2 - - - - 0.73 - - (0.06) 12.36 BRANDAT3 - - - - 1.09 - - (0.05) 21.56 BUY_INT1 - - - - - - 1.00 BUY_INT2 - - - - - - 1.04 (0.05) 22.30 BUY_INT3 - - - - - - 0.88 (0.06) 14.57 LAMBDA-X ATT_AD -------- ATT_AD1 1.00 ATT_AD2 0.88 (0.05) 17.95 ATT_AD3 1.07 (0.05) 21.40 BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - - - - - - - NEGCOGNI - - - - - - - - BRANDATT 0.17 -0.24 - - - - (0.06) (0.06) 2.96 -4.02 BUYINTEN - - - - 0.78 - - (0.11) 7.04 GAMMA ATT_AD -------- POSCOGNI 0.25 (0.08) 3.20 NEGCOGNI -0.09 (0.07) -1.28 BRANDATT 0.57 (0.06) 9.10 BUYINTEN - - Covariance Matrix of ETA and KSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN ATT_AD -------- -------- -------- -------- -------- POSCOGNI 1.00 NEGCOGNI -0.03 0.85 BRANDATT 0.33 -0.27 0.81 BUYINTEN 0.26 -0.21 0.63 1.54 ATT_AD 0.27 -0.10 0.69 0.54 1.08 Mean Vector of Eta-Variables POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.03 0.20 0.13 0.06 PHI ATT_AD -------- 1.08 (0.15) 7.16 PSI Note: This matrix is diagonal. POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.93 0.84 0.29 1.05 (0.11) (0.09) (0.06) (0.15) 8.85 8.91 5.13 6.78 Squared Multiple Correlations for Structural Equations POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.07 0.01 0.64 0.32 NOTE: Rý for Structural Equations are Hayduk's (2006) Blocked-Error Rý Squared Multiple Correlations for Reduced Form POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.07 0.01 0.55 0.17 Reduced Form ATT_AD -------- POSCOGNI 0.25 (0.08) 3.20 NEGCOGNI -0.09 (0.07) -1.28 BRANDATT 0.64 (0.07) 9.65 BUYINTEN 0.50 (0.08) 6.12 THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - 0.41 0.84 0.33 0.22 (0.06) (0.10) (0.06) (0.08) 6.55 8.34 5.38 2.56 THETA-EPS BUY_INT2 BUY_INT3 -------- -------- 0.94 1.59 (0.14) (0.19) 6.78 8.16 W_A_R_N_I_N_G: THETA-EPS is not positive definite Squared Multiple Correlations for Y - Variables POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 1.00 1.00 0.66 0.34 0.75 0.88 Squared Multiple Correlations for Y - Variables BUY_INT2 BUY_INT3 -------- -------- 0.64 0.43 THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.45 0.49 0.23 (0.07) (0.07) (0.05) 6.69 7.40 4.19 Squared Multiple Correlations for X - Variables ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.71 0.63 0.85 TAU-Y POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.56 0.58 4.71 4.57 4.64 2.15 (0.06) (0.06) (0.08) (0.08) (0.09) (0.09) 9.75 10.49 56.86 60.04 51.65 22.75 TAU-Y BUY_INT2 BUY_INT3 -------- -------- 2.34 3.54 (0.10) (0.10) 23.55 34.15 TAU-X ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 4.28 4.96 4.50 (0.08) (0.08) (0.09) 51.18 64.58 52.03 ALPHA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- 0.02 0.21 0.14 -0.03 (0.09) (0.09) (0.08) (0.13) 0.16 2.27 1.78 -0.27 KAPPA ATT_AD -------- 0.06 (0.12) 0.49 Global Goodness of Fit Statistics Degrees of Freedom = 92 Minimum Fit Function Chi-Square = 150.85 (P = 0.00011) Normal Theory Weighted Least Squares Chi-Square = 149.05 (P = 0.00016) Estimated Non-centrality Parameter (NCP) = 57.05 90 Percent Confidence Interval for NCP = (27.55 ; 94.46) Minimum Fit Function Value = 0.42 Population Discrepancy Function Value (F0) = 0.16 90 Percent Confidence Interval for F0 = (0.077 ; 0.26) Root Mean Square Error of Approximation (RMSEA) = 0.059 90 Percent Confidence Interval for RMSEA = (0.041 ; 0.076) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.19 Expected Cross-Validation Index (ECVI) = 0.76 90 Percent Confidence Interval for ECVI = (0.62 ; 0.81) ECVI for Saturated Model = 0.37 ECVI for Independence Model = 9.94 Chi-Square for Independence Model with 110 Degrees of Freedom = 3538.07 Independence AIC = 3582.07 Model AIC = 273.05 Saturated AIC = 264.00 Independence CAIC = 3689.56 Model CAIC = 575.99 Saturated CAIC = 908.97 Normed Fit Index (NFI) = 0.96 Non-Normed Fit Index (NNFI) = 0.98 Parsimony Normed Fit Index (PNFI) = 0.80 Comparative Fit Index (CFI) = 0.98 Incremental Fit Index (IFI) = 0.98 Relative Fit Index (RFI) = 0.95 Critical N (CN) = 304.74 Group Goodness of Fit Statistics Contribution to Chi-Square = 54.37 Percentage Contribution to Chi-Square = 36.04 Root Mean Square Residual (RMR) = 0.072 Standardized RMR = 0.044 Goodness of Fit Index (GFI) = 0.95 Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Fitted Covariance Matrix POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 1.00 NEG_COG1 -0.03 0.85 BRANDAT1 0.33 -0.27 1.21 BRANDAT2 0.24 -0.19 0.59 1.27 BRANDAT3 0.36 -0.29 0.88 0.64 1.28 BUY_INT1 0.26 -0.21 0.63 0.46 0.69 1.76 BUY_INT2 0.27 -0.22 0.65 0.48 0.71 1.60 BUY_INT3 0.23 -0.18 0.55 0.40 0.60 1.36 ATT_AD1 0.27 -0.10 0.69 0.50 0.75 0.54 ATT_AD2 0.24 -0.09 0.61 0.44 0.66 0.48 ATT_AD3 0.29 -0.11 0.74 0.54 0.81 0.58 Fitted Covariance Matrix BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 2.59 BUY_INT3 1.40 2.78 ATT_AD1 0.56 0.47 1.53 ATT_AD2 0.49 0.42 0.96 1.34 ATT_AD3 0.60 0.51 1.16 1.03 1.47 Fitted Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.59 0.78 4.83 4.66 4.77 2.21 Fitted Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- 2.41 3.60 4.34 5.01 4.57 Fitted Residuals POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 0.00 NEG_COG1 0.01 0.00 BRANDAT1 0.00 0.04 0.00 BRANDAT2 -0.06 0.03 -0.11 -0.10 BRANDAT3 0.00 -0.02 0.04 -0.08 0.04 BUY_INT1 0.02 -0.14 -0.04 0.05 -0.01 0.04 BUY_INT2 0.14 -0.07 -0.10 0.02 -0.02 -0.05 BUY_INT3 0.21 0.08 -0.15 0.15 0.03 0.02 ATT_AD1 0.00 -0.09 0.01 -0.07 0.02 0.06 ATT_AD2 -0.03 -0.03 -0.01 -0.03 -0.05 0.01 ATT_AD3 0.01 0.05 0.01 -0.03 0.02 -0.02 Fitted Residuals BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 -0.15 BUY_INT3 -0.19 -0.03 ATT_AD1 -0.02 0.10 0.01 ATT_AD2 -0.02 0.07 0.10 0.06 ATT_AD3 -0.07 0.13 -0.03 0.02 -0.03 Fitted Residuals for Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- 0.00 0.00 0.03 0.05 -0.03 -0.02 Fitted Residuals for Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- 0.09 -0.01 0.01 -0.08 0.02 Standardized Residuals for Means POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - 0.91 0.92 -1.39 -1.31 Standardized Residuals for Means BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- 1.51 -0.13 0.37 -2.10 1.32 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.19 Median Fitted Residual = 0.00 Largest Fitted Residual = 0.21 Stemleaf Plot - 1|955 - 1|4100 - 0|98777655 - 0|433333332222211000000 0|111111222222334444 0|556678 1|0034 1|5 2|1 Standardized Residuals POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 - - NEG_COG1 0.10 - - BRANDAT1 0.03 1.11 -0.05 BRANDAT2 -0.81 0.55 -1.71 -1.53 BRANDAT3 -0.05 -0.55 1.83 -1.33 0.94 BUY_INT1 0.30 -1.83 -0.75 0.53 -0.20 1.34 BUY_INT2 1.31 -0.73 -1.11 0.15 -0.18 -0.99 BUY_INT3 1.75 0.70 -1.39 1.17 0.24 0.26 ATT_AD1 0.04 -2.18 0.10 -0.88 0.31 0.67 ATT_AD2 -0.54 -0.64 -0.23 -0.33 -0.89 0.18 ATT_AD3 0.39 2.37 0.27 -0.41 0.51 -0.23 Standardized Residuals BUY_INT2 BUY_INT3 ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- -------- -------- BUY_INT2 -1.26 BUY_INT3 -1.37 -0.17 ATT_AD1 -0.14 0.74 0.08 ATT_AD2 -0.19 0.55 1.84 0.98 ATT_AD3 -0.66 1.00 -0.95 0.52 -0.90 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -2.18 Median Standardized Residual = 0.00 Largest Standardized Residual = 2.37 Stemleaf Plot - 2|2 - 1|875 - 1|4433100 - 0|9998877655 - 0|432222221110000 0|11122233334 0|555557779 1|001233 1|888 2|4 Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Qplot of Standardized Residuals 3.5.......................................................................... . .. . . . . . . . . . . . . . . . . . . . . . . . x . . . . . x . . . x . . . x . . *. . N . xx . o . x* . r . x* . . m . x . . a . xx* . l . *x. . . xx . Q . xx . u . ** . a . xx . n . xxx . t . ** . i . x* . l . x . e . xxx . s . *. . . * . . x . . x . . x . . . . . x . . . . . . . . . . . . . . . . . . . . . . -3.5.......................................................................... -3.5 3.5 Standardized Residuals Group 2: High Brand Motivation MACKENZIE/SPRENG MAR 92 JCR Modification Indices and Expected Change Modification Indices for LAMBDA-Y POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POS_COG1 - - 0.01 0.01 0.89 NEG_COG1 0.01 - - 0.01 2.70 BRANDAT1 0.01 1.60 0.01 1.24 BRANDAT2 0.62 0.45 2.09 0.28 BRANDAT3 0.00 0.74 0.63 0.03 BUY_INT1 1.85 5.87 0.04 1.59 BUY_INT2 1.59 0.43 0.08 1.34 BUY_INT3 2.78 3.05 0.00 0.03 Expected Change for LAMBDA-Y POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POS_COG1 - - 0.01 -0.04 0.08 NEG_COG1 0.01 - - 0.05 -0.12 BRANDAT1 0.01 0.09 0.01 -0.06 BRANDAT2 -0.06 0.06 -0.10 0.04 BRANDAT3 0.00 -0.06 0.05 -0.01 BUY_INT1 -0.09 -0.17 0.02 0.12 BUY_INT2 0.11 0.06 -0.03 -0.09 BUY_INT3 0.17 0.20 0.01 -0.01 Modification Indices for LAMBDA-X ATT_AD -------- ATT_AD1 0.01 ATT_AD2 0.80 ATT_AD3 1.24 Expected Change for LAMBDA-X ATT_AD -------- ATT_AD1 0.01 ATT_AD2 0.04 ATT_AD3 -0.03 Modification Indices for BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - 0.01 0.01 0.55 NEGCOGNI 0.01 - - 0.01 2.05 BRANDATT - - - - - - 1.70 BUYINTEN 0.64 2.23 - - - - Expected Change for BETA POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - 0.01 -0.04 0.06 NEGCOGNI 0.01 - - 0.05 -0.12 BRANDATT - - - - - - -0.10 BUYINTEN 0.08 -0.16 - - - - No Non-Zero Modification Indices for GAMMA No Non-Zero Modification Indices for PHI Modification Indices for PSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - NEGCOGNI 0.01 - - BRANDATT - - - - - - BUYINTEN 0.60 2.13 1.70 - - Expected Change for PSI POSCOGNI NEGCOGNI BRANDATT BUYINTEN -------- -------- -------- -------- POSCOGNI - - NEGCOGNI 0.01 - - BRANDATT - - - - - - BUYINTEN 0.07 -0.13 -0.10 - - Modification Indices for THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 - - NEG_COG1 0.01 - - BRANDAT1 0.00 1.43 - - BRANDAT2 0.18 0.03 1.13 - - BRANDAT3 0.06 0.13 5.51 0.45 - - BUY_INT1 1.67 4.54 0.33 0.08 1.25 - - BUY_INT2 2.08 0.05 0.22 0.00 0.32 0.07 BUY_INT3 2.61 2.38 4.32 1.79 0.27 1.46 Modification Indices for THETA-EPS BUY_INT2 BUY_INT3 -------- -------- BUY_INT2 - - BUY_INT3 2.29 - - Expected Change for THETA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- POS_COG1 - - NEG_COG1 0.01 - - BRANDAT1 0.00 0.07 - - BRANDAT2 -0.03 0.01 -0.06 - - BRANDAT3 -0.01 -0.02 0.17 -0.04 - - BUY_INT1 -0.08 -0.12 0.03 0.02 -0.05 - - BUY_INT2 0.11 0.02 -0.03 0.00 0.03 0.05 BUY_INT3 0.16 0.14 -0.16 0.13 0.04 0.15 Expected Change for THETA-EPS BUY_INT2 BUY_INT3 -------- -------- BUY_INT2 - - BUY_INT3 -0.20 - - Modification Indices for THETA-DELTA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- ATT_AD1 0.03 5.15 0.19 0.81 0.01 0.97 ATT_AD2 0.11 1.10 0.05 0.23 3.36 0.06 ATT_AD3 0.01 7.71 0.26 0.40 1.36 0.66 Modification Indices for THETA-DELTA-EPS BUY_INT2 BUY_INT3 -------- -------- ATT_AD1 0.10 0.19 ATT_AD2 0.05 0.06 ATT_AD3 0.13 1.79 Expected Change for THETA-DELTA-EPS POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- ATT_AD1 0.01 -0.12 -0.02 -0.05 0.00 0.05 ATT_AD2 -0.02 -0.06 -0.01 0.03 -0.08 0.01 ATT_AD3 0.01 0.14 0.02 0.03 0.05 -0.03 Expected Change for THETA-DELTA-EPS BUY_INT2 BUY_INT3 -------- -------- ATT_AD1 -0.02 -0.03 ATT_AD2 0.01 -0.02 ATT_AD3 -0.02 0.09 Modification Indices for THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- ATT_AD1 - - ATT_AD2 6.04 - - ATT_AD3 4.88 0.15 - - Expected Change for THETA-DELTA ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- ATT_AD1 - - ATT_AD2 0.14 - - ATT_AD3 -0.17 -0.02 - - Modification Indices for TAU-Y POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - 1.05 0.92 1.84 1.73 Modification Indices for TAU-Y BUY_INT2 BUY_INT3 -------- -------- 2.28 0.02 Expected Change for TAU-Y POS_COG1 NEG_COG1 BRANDAT1 BRANDAT2 BRANDAT3 BUY_INT1 -------- -------- -------- -------- -------- -------- - - - - -0.07 0.04 -0.13 -0.09 Expected Change for TAU-Y BUY_INT2 BUY_INT3 -------- -------- 0.12 -0.01 Modification Indices for TAU-X ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.14 4.47 1.77 Expected Change for TAU-X ATT_AD1 ATT_AD2 ATT_AD3 -------- -------- -------- 0.02 -0.11 0.07 No Non-Zero Modification Indices for ALPHA No Non-Zero Modification Indices for KAPPA Max. Mod. Index is 11.36 for Element ( 8, 3) of LAMBDA-Y in Group 1 Time used: 0.050 Seconds