Results: aware5.sas

Doughnut Shop Brand Awareness Study: Model 5

Put latent variable model back in

The CALIS Procedure

Covariance Structure Analysis: Model and Initial Values

The CALIS Procedure

Modeling Specification

Modeling Info

Modeling Information
Maximum Likelihood Estimation
Data Set WORK.TORUS
N Records Read 200
N Records Used 200
N Obs 200
Model Type LINEQS
Analysis Covariances

Doughnut Shop Brand Awareness Study: Model 5

Put latent variable model back in

The CALIS Procedure

Covariance Structure Analysis: Descriptive Statistics

Descriptive Statistics

Covariances

Covariance Matrix (DF = 200)
  w1 w2 w3 w4 w5 w6 v1 v2 v3 v4
w1 Brand Awareness 1 24.24078 10.13520 12.32448 6.63708 13.06048 15.04750 16.12528 11.86898 7.79903 8.12188
w2 Brand Awareness 2 10.13520 18.32360 6.62180 2.87860 7.58980 7.73000 8.30620 5.85280 4.65120 4.20000
w3 Ad Awareness 1 12.32448 6.62180 22.94778 8.64118 10.57178 12.70250 14.81498 11.28328 5.63372 6.85938
w4 Ad Awareness 2 6.63708 2.87860 8.64118 18.09298 6.50418 7.36250 7.52558 6.32968 3.71932 2.78938
w5 Interest 1 13.06048 7.58980 10.57178 6.50418 21.18578 16.32750 16.35098 10.82728 6.11473 6.25938
w6 Interest 2 15.04750 7.73000 12.70250 7.36250 16.32750 23.93000 16.80750 11.19750 7.61250 7.65250
v1 Purchase Intention 1 16.12528 8.30620 14.81498 7.52558 16.35098 16.80750 29.44978 14.94948 9.53852 10.06938
v2 Purchase Intention 2 11.86898 5.85280 11.28328 6.32968 10.82728 11.19750 14.94948 20.87877 6.96323 6.69688
v3 Purchase Behaviour 1 7.79903 4.65120 5.63372 3.71932 6.11473 7.61250 9.53852 6.96323 21.59478 17.65813
v4 Purchase Behaviour 2 8.12188 4.20000 6.85938 2.78938 6.25938 7.65250 10.06938 6.69688 17.65813 22.16938
Determinant 191909745153 Ln 25.980291

Optimization

Doughnut Shop Brand Awareness Study: Model 5

Put latent variable model back in

The CALIS Procedure

Covariance Structure Analysis: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Optimization Problem

Parameter Estimates 28
Functions (Observations) 55
Lower Bounds 15
Upper Bounds 0

Iteration Start

Optimization Start
Active Constraints 0 Objective Function 0.1016760046
Max Abs Gradient Element 0.0313316908 Radius 1

Iteration History

Iteration   Restarts Function
Calls		 Active
Constraints		   Objective
Function		 Objective
Function
Change		 Max Abs
Gradient
Element		 Lambda Ratio
Between
Actual
and
Predicted
Change
1   0 4 0   0.09503 0.00665 0.00853 0 0.928
2   0 6 0   0.09482 0.000210 0.000876 0 0.932
3   0 8 0   0.09481 3.935E-6 0.000242 0 0.795
4   0 10 0   0.09481 2.198E-7 0.000052 0 0.752
5   0 12 0   0.09481 1.484E-8 0.000014 0 0.737
6   0 14 0   0.09481 1.062E-9 3.543E-6 0 0.732

Iteration Stop

Optimization Results
Iterations 6 Function Calls 17
Jacobian Calls 8 Active Constraints 0
Objective Function 0.0948118648 Max Abs Gradient Element 3.5432106E-6
Lambda 0 Actual Over Pred Change 0.7317077247
Radius 0.000356371    
Convergence criterion (ABSGCONV=0.00001) satisfied.

Doughnut Shop Brand Awareness Study: Model 5

Put latent variable model back in

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Modeling Info Number of Observations 200
  Number of Variables 10
  Number of Moments 55
  Number of Parameters 28
  Number of Active Constraints 0
  Baseline Model Function Value 4.9657
  Baseline Model Chi-Square 993.1450
  Baseline Model Chi-Square DF 45
  Pr > Baseline Model Chi-Square <.0001
Absolute Index Fit Function 0.0948
  Chi-Square 18.9624
  Chi-Square DF 27
  Pr > Chi-Square 0.8714
  Z-Test of Wilson & Hilferty -1.1341
  Hoelter Critical N 423
  Root Mean Square Residual (RMR) 0.4193
  Standardized RMR (SRMR) 0.0195
  Goodness of Fit Index (GFI) 0.9822
Parsimony Index Adjusted GFI (AGFI) 0.9638
  Parsimonious GFI 0.5893
  RMSEA Estimate 0.0000
  RMSEA Lower 90% Confidence Limit 0.0000
  RMSEA Upper 90% Confidence Limit 0.0290
  Probability of Close Fit 0.9938
  ECVI Estimate 0.3911
  ECVI Lower 90% Confidence Limit 0.4392
  ECVI Upper 90% Confidence Limit 0.4544
  Akaike Information Criterion 74.9624
  Bozdogan CAIC 195.3153
  Schwarz Bayesian Criterion 167.3153
  McDonald Centrality 1.0203
Incremental Index Bentler Comparative Fit Index 1.0000
  Bentler-Bonett NFI 0.9809
  Bentler-Bonett Non-normed Index 1.0141
  Bollen Normed Index Rho1 0.9682
  Bollen Non-normed Index Delta2 1.0083
  James et al. Parsimonious NFI 0.5885

Doughnut Shop Brand Awareness Study: Model 5

Put latent variable model back in

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Covariances

Predicted Covariances
  w1 w2 w3 w4 w5 w6 v1 v2 v3 v4
w1 Brand Awareness 1 24.24078 10.13520 12.30054 6.68066 13.47964 14.71619 16.39709 11.59177 7.20706 7.49349
w2 Brand Awareness 2 10.13520 18.32360 6.49308 3.52652 7.11549 7.76823 8.65552 6.11894 3.80438 3.95558
w3 Ad Awareness 1 12.30054 6.49308 22.94778 8.64117 11.31213 12.34985 14.94592 10.56588 6.69515 6.96124
w4 Ad Awareness 2 6.68066 3.52652 8.64117 18.09297 6.14384 6.70745 8.11743 5.73854 3.63627 3.78079
w5 Interest 1 13.47964 7.11549 11.31213 6.14384 21.18578 16.33386 15.53965 10.98561 6.54764 6.80786
w6 Interest 2 14.71619 7.76823 12.34985 6.70745 16.33386 23.93000 16.96518 11.99338 7.14828 7.43238
v1 Purchase Intention 1 16.39709 8.65552 14.94592 8.11743 15.53965 16.96518 29.44977 14.96565 9.54550 9.92488
v2 Purchase Intention 2 11.59177 6.11894 10.56588 5.73854 10.98561 11.99338 14.96565 20.87877 6.74811 7.01630
v3 Purchase Behaviour 1 7.20706 3.80438 6.69515 3.63627 6.54764 7.14828 9.54550 6.74811 21.59478 17.65813
v4 Purchase Behaviour 2 7.49349 3.95558 6.96124 3.78079 6.80786 7.43238 9.92488 7.01630 17.65813 22.16938
Determinant 210995551389 Ln 26.075103

Doughnut Shop Brand Awareness Study: Model 5

Put latent variable model back in

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
F_PI =   0.2295 (ns) F_BrAw + 0.3687 (**) F_AdAw + 0.5531 (**) F_Inter + 1.0000   epsilon1
F_PBeh =   -0.1292 (ns) F_Inter + 0.5458 (**) F_PI + 1.0000   epsilon2        
w1 =   1.0000   F_BrAw + 1.0000   e1                
w2 =   0.5279 (**) F_BrAw + 1.0000   e2                
w3 =   1.0000   F_AdAw + 1.0000   e3                
w4 =   0.5431 (**) F_AdAw + 1.0000   e4                
w5 =   1.0000   F_Inter + 1.0000   e5                
w6 =   1.0917 (**) F_Inter + 1.0000   e6                
v1 =   1.0000   F_PI + 1.0000   e7                
v2 =   0.7069 (**) F_PI + 1.0000   e8                
v3 =   1.0000   F_PBeh + 1.0000   e9                
v4 =   1.0397 (**) F_PBeh + 1.0000   e10                

Linear Effects

Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
F_PI F_BrAw gamma1 0.22946 0.14512 1.5811 0.1138
F_PI F_AdAw gamma2 0.36871 0.16133 2.2855 0.0223
F_PI F_Inter gamma3 0.55314 0.17006 3.2527 0.0011
F_PBeh F_Inter gamma4 -0.12922 0.25729 -0.5022 0.6155
F_PBeh F_PI beta 0.54576 0.22389 2.4376 0.0148
w1 F_BrAw   1.00000      
w2 F_BrAw lambda2 0.52787 0.07693 6.8614 <.0001
w3 F_AdAw   1.00000      
w4 F_AdAw lambda4 0.54312 0.09032 6.0130 <.0001
w5 F_Inter   1.00000      
w6 F_Inter lambda6 1.09174 0.08070 13.5275 <.0001
v1 F_PI   1.00000      
v2 F_PI lambda8 0.70694 0.06580 10.7445 <.0001
v3 F_PBeh   1.00000      
v4 F_PBeh lambda10 1.03974 0.10995 9.4567 <.0001

Variance Parms

Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent F_BrAw phi11 19.20021 3.11005 6.1736 <.0001
  F_AdAw phi22 15.91026 3.03264 5.2463 <.0001
  F_Inter phi33 14.96137 2.15291 6.9494 <.0001
Disturbance epsilon1 psi1 3.30084 1.34000 2.4633 0.0138
  epsilon2 psi2 12.61968 2.09657 6.0192 <.0001
Error e1 omega01 5.04057 2.07471 2.4295 0.0151
  e2 omega02 12.97354 1.41337 9.1792 <.0001
  e3 omega03 7.03752 2.21843 3.1723 0.0015
  e4 omega04 13.39978 1.47671 9.0741 <.0001
  e5 omega05 6.22440 0.95995 6.4841 <.0001
  e6 omega06 6.09775 1.06321 5.7352 <.0001
  e7 omega07 8.28018 1.47918 5.5978 <.0001
  e8 omega08 10.29895 1.21486 8.4775 <.0001
  e9 omega09 4.61162 1.68175 2.7422 0.0061
  e10 omega10 3.80945 1.78941 2.1289 0.0333

Covariance Parms

Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate Standard
Error		 t Value Pr > |t|
F_BrAw F_AdAw phi12 12.30054 1.86420 6.5983 <.0001
F_BrAw F_Inter phi13 13.47964 1.83140 7.3603 <.0001
F_AdAw F_Inter phi23 11.31213 1.69375 6.6788 <.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable Error Variance Total Variance R-Square
F_PI 3.30084 21.16960 0.8441
F_PBeh 12.61968 16.98315 0.2569
w1 5.04057 24.24078 0.7921
w2 12.97354 18.32360 0.2920
w3 7.03752 22.94778 0.6933
w4 13.39978 18.09297 0.2594
w5 6.22440 21.18578 0.7062
w6 6.09775 23.93000 0.7452
v1 8.28018 29.44977 0.7188
v2 10.29895 20.87877 0.5067
v3 4.61162 21.59478 0.7864
v4 3.80945 22.16938 0.8282

Simultaneous Tests

Simultaneous Tests
Simultaneous
Test		 Parametric
Function		 Function
Value		 DF Chi-Square p Value
not_one     5 84.50711 <.0001
  d2 -0.47213 1 37.66095 <.0001
  d4 -0.45688 1 25.58534 <.0001
  d6 0.09174 1 1.29204 0.2557
  d8 -0.29306 1 19.83888 <.0001
  d10 0.03974 1 0.13067 0.7177