The SAS System 10:15 Wednesday, April 17, 2013 56 The CALIS Procedure Covariance Structure Analysis: Model and Initial Values Modeling Information Data Set WORK.MXTEST N Records Read 500 N Records Used 500 N Obs 500 Model Type PATH Analysis Covariances Variables in the Model Endogenous Manifest x1 x2 x3 x4 x5 Latent Exogenous Manifest Latent G Number of Endogenous Variables = 5 Number of Exogenous Variables = 1 Initial Estimates for PATH List --------Path-------- Parameter Estimate x1 <--- G theta1 . x2 <--- G theta2 . x3 <--- G theta3 . x4 <--- G theta4 . x5 <--- G theta5 . Initial Estimates for Variance Parameters Variance Type Variable Parameter Estimate Exogenous G 1.00000 Error x1 _Add1 . x2 _Add2 . x3 _Add3 . x4 _Add4 . x5 _Add5 . NOTE: Parameters with prefix '_Add' are added by PROC CALIS. The SAS System 10:15 Wednesday, April 17, 2013 57 The CALIS Procedure Covariance Structure Analysis: Descriptive Statistics Simple Statistics Variable Mean Std Dev x1 -0.04008 0.44558 x2 -0.04584 0.54009 x3 -0.05588 0.61158 x4 -0.05581 0.73026 x5 -0.07555 0.81872 The SAS System 10:15 Wednesday, April 17, 2013 58 The CALIS Procedure Covariance Structure Analysis: Optimization Initial Estimation Methods 1 Instrumental Variables Method 2 McDonald Method Optimization Start Parameter Estimates N Parameter Estimate Gradient 1 theta1 0.39740 0.00640 2 theta2 0.50392 0.00638 3 theta3 0.57828 0.02828 4 theta4 0.70237 -0.01173 5 theta5 0.79532 -0.01747 6 _Add1 0.04062 -0.06164 7 _Add2 0.03776 -0.08340 8 _Add3 0.03962 -0.41069 9 _Add4 0.03995 0.20929 10 _Add5 0.03777 0.37227 Value of Objective Function = 0.0154252561 The SAS System 10:15 Wednesday, April 17, 2013 59 The CALIS Procedure Covariance Structure Analysis: Optimization Levenberg-Marquardt Optimization Scaling Update of More (1978) Parameter Estimates 10 Functions (Observations) 15 Optimization Start Active Constraints 0 Objective Function 0.0154252561 Max Abs Gradient Element 0.4106912295 Radius 11.702964841 Ratio Between Actual Objective Max Abs and Function Active Objective Function Gradient Predicted Iter Restarts Calls Constraints Function Change Element Lambda Change 1 0 4 0 0.01480 0.000623 0.0310 0 1.084 2 0 6 0 0.01480 4.278E-6 0.00261 0 1.085 3 0 8 0 0.01480 3.022E-8 0.000212 0 1.084 4 0 10 0 0.01480 2.14E-10 0.000019 0 1.084 5 0 12 0 0.01480 1.51E-12 1.47E-6 0 1.085 Optimization Results Iterations 5 Function Calls 15 Jacobian Calls 7 Active Constraints 0 Objective Function 0.014797598 Max Abs Gradient Element 1.470204E-6 Lambda 0 Actual Over Pred Change 1.0847636926 Radius 3.5490254E-6 Convergence criterion (GCONV=1E-8) satisfied. The SAS System 10:15 Wednesday, April 17, 2013 60 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Fit Summary Modeling Info N Observations 500 N Variables 5 N Moments 15 N Parameters 10 N Active Constraints 0 Baseline Model Function Value 7.4650 Baseline Model Chi-Square 3725.0597 Baseline Model Chi-Square DF 10 Pr > Baseline Model Chi-Square <.0001 Absolute Index Fit Function 0.0148 Chi-Square 7.3840 Chi-Square DF 5 Pr > Chi-Square 0.1936 Z-Test of Wilson & Hilferty 0.8691 Hoelter Critical N 749 Root Mean Square Residual (RMSR) 0.0012 Standardized RMSR (SRMSR) 0.0032 Goodness of Fit Index (GFI) 0.9943 Parsimony Index Adjusted GFI (AGFI) 0.9828 Parsimonious GFI 0.4971 RMSEA Estimate 0.0309 RMSEA Lower 90% Confidence Limit 0.0000 RMSEA Upper 90% Confidence Limit 0.0746 Probability of Close Fit 0.7136 ECVI Estimate 0.0554 ECVI Lower 90% Confidence Limit 0.0507 ECVI Upper 90% Confidence Limit 0.0785 Akaike Information Criterion 27.3840 Bozdogan CAIC 79.5301 Schwarz Bayesian Criterion 69.5301 McDonald Centrality 0.9976 Incremental Index Bentler Comparative Fit Index 0.9994 Bentler-Bonett NFI 0.9980 Bentler-Bonett Non-normed Index 0.9987 Bollen Normed Index Rho1 0.9960 Bollen Non-normed Index Delta2 0.9994 James et al. Parsimonious NFI 0.4990 The SAS System 10:15 Wednesday, April 17, 2013 61 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation PATH List Standard --------Path-------- Parameter Estimate Error t Value x1 <--- G theta1 0.39715 0.01555 25.54167 x2 <--- G theta2 0.50366 0.01823 27.62504 x3 <--- G theta3 0.57724 0.02045 28.23283 x4 <--- G theta4 0.70277 0.02401 29.26646 x5 <--- G theta5 0.79625 0.02667 29.85591 Variance Parameters Variance Standard Type Variable Parameter Estimate Error t Value Exogenous G 1.00000 Error x1 _Add1 0.04081 0.00281 14.52088 x2 _Add2 0.03802 0.00280 13.56466 x3 _Add3 0.04083 0.00313 13.04612 x4 _Add4 0.03939 0.00343 11.48228 x5 _Add5 0.03629 0.00368 9.84847 Squared Multiple Correlations Error Total Variable Variance Variance R-Square x1 0.04081 0.19854 0.7944 x2 0.03802 0.29169 0.8697 x3 0.04083 0.37404 0.8908 x4 0.03939 0.53328 0.9261 x5 0.03629 0.67030 0.9459 The SAS System 10:15 Wednesday, April 17, 2013 62 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Standardized Results for PATH List Standard --------Path-------- Parameter Estimate Error t Value x1 <--- G theta1 0.89131 0.00972 91.71064 x2 <--- G theta2 0.93255 0.00640 145.61568 x3 <--- G theta3 0.94385 0.00549 171.97748 x4 <--- G theta4 0.96236 0.00402 239.10944 x5 <--- G theta5 0.97256 0.00328 296.56341 Standardized Results for Variance Parameters Variance Standard Type Variable Parameter Estimate Error t Value Exogenous G 1.00000 Error x1 _Add1 0.20557 0.01732 11.86551 x2 _Add2 0.13034 0.01194 10.91221 x3 _Add3 0.10915 0.01036 10.53599 x4 _Add4 0.07386 0.00775 9.53429 x5 _Add5 0.05414 0.00638 8.48673