The SAS System 08:54 Wednesday, August 8, 2001 1 The CALIS Procedure Covariance Structure Analysis: Pattern and Initial Values Automatic Variable Selection, the Following Manifest Variables are not Used in the Model read1 read2 read3 read4 gen homecog id Using the VAR statement for variable selection could save memory and computing time. LINEQS Model Statement Matrix Rows Columns ------Matrix Type------- Term 1 1 _SEL_ 5 13 SELECTION 2 _BETA_ 13 13 EQSBETA IMINUSINV 3 _GAMMA_ 13 7 EQSGAMMA 4 _PHI_ 7 7 SYMMETRIC The 6 Endogenous Variables Manifest anti1 anti2 anti3 anti4 Latent f1 f2 The 7 Exogenous Variables Manifest Intercept Latent Error e1 e2 e3 e4 d1 d2 The SAS System 08:54 Wednesday, August 8, 2001 2 The CALIS Procedure Covariance Structure Analysis: Pattern and Initial Values Manifest Variable Equations with Initial Estimates anti1 = 1.0000 f1 + 1.0000 e1 anti2 = 1.0000 f1 + 1.0000 f2 + 1.0000 e2 anti3 = 1.0000 f1 + 2.0000 f2 + 1.0000 e3 anti4 = 1.0000 f1 + 3.0000 f2 + 1.0000 e4 The SAS System 08:54 Wednesday, August 8, 2001 3 The CALIS Procedure Covariance Structure Analysis: Pattern and Initial Values Latent Variable Equations with Initial Estimates f1 = .*Intercept + 1.0000 d1 al1 f2 = .*Intercept + 1.0000 d2 al2 Variances of Exogenous Variables Variable Parameter Estimate Intercept . e1 th . e2 th . e3 th . e4 th . d1 ph11 . d2 ph22 . Covariances Among Exogenous Variables Var1 Var2 Parameter Estimate d1 d2 ph21 . The SAS System 08:54 Wednesday, August 8, 2001 4 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Observations 221 Model Terms 1 Variables 5 Model Matrices 4 Informations 15 Parameters 6 Variable Mean Unc StD anti1 1.49321 2.14688 anti2 1.83710 2.56905 anti3 1.87783 2.60506 anti4 2.06787 2.93954 Intercept 1.00000 1.00227 Set Covariances of Exogenous Manifest Variables Intercept NOTE: Some initial estimates computed by two-stage LS method. The SAS System 08:54 Wednesday, August 8, 2001 5 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Vector of Initial Estimates Parameter Estimate Type 1 al1 1.47808 Matrix Entry: _GAMMA_[5:1] 2 al2 0.32705 Matrix Entry: _GAMMA_[6:1] 3 th 1.45060 Matrix Entry: _PHI_[2:2] _PHI_[3:3] _PHI_[4:4] _PHI_[5:5] 4 ph11 1.32348 Matrix Entry: _PHI_[6:6] 5 ph21 -0.13121 Matrix Entry: _PHI_[7:6] 6 ph22 0.07174 Matrix Entry: _PHI_[7:7] The SAS System 08:54 Wednesday, August 8, 2001 6 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Levenberg-Marquardt Optimization Scaling Update of More (1978) Parameter Estimates 6 Functions (Observations) 15 Optimization Start Active Constraints 0 Objective Function 0.3183156234 Max Abs Gradient Element 3.2995045531 Radius 16.481359084 Ratio Between Actual Objective Max Abs and Function Active Objective Function Gradient Predicted Iter Restarts Calls Constraints Function Change Element Lambda Change 1 0 2 0 0.02679 0.2915 0.1363 0 0.686 2 0 3 0 0.02527 0.00152 6.87E-16 0 1.038 Optimization Results Iterations 2 Function Calls 4 Jacobian Calls 3 Active Constraints 0 Objective Function 0.025270035 Max Abs Gradient Element 6.869505E-16 Lambda 0 Actual Over Pred Change 1.0376339641 Radius 0.2136888506 ABSGCONV convergence criterion satisfied. The SAS System 08:54 Wednesday, August 8, 2001 7 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Fit Function 0.0253 Goodness of Fit Index (GFI) 0.9897 GFI Adjusted for Degrees of Freedom (AGFI) 0.9806 Root Mean Square Residual (RMR) 0.2567 Parsimonious GFI (Mulaik, 1989) 0.7917 Chi-Square 5.5594 Chi-Square DF 8 Pr > Chi-Square 0.6964 Independence Model Chi-Square 874.11 Independence Model Chi-Square DF 10 RMSEA Estimate 0.0000 RMSEA 90% Lower Confidence Limit . RMSEA 90% Upper Confidence Limit 0.0609 ECVI Estimate 0.0813 ECVI 90% Lower Confidence Limit . ECVI 90% Upper Confidence Limit 0.1273 Probability of Close Fit 0.9074 Bentler's Comparative Fit Index 1.0000 Normal Theory Reweighted LS Chi-Square 5.7396 Akaike's Information Criterion -10.4406 Bozdogan's (1987) CAIC -45.6259 Schwarz's Bayesian Criterion -37.6259 McDonald's (1989) Centrality 1.0055 Bentler & Bonett's (1980) Non-normed Index 1.0035 Bentler & Bonett's (1980) NFI 0.9936 James, Mulaik, & Brett (1982) Parsimonious NFI 0.7949 Z-Test of Wilson & Hilferty (1931) -0.5188 Bollen (1986) Normed Index Rho1 0.9920 Bollen (1988) Non-normed Index Delta2 1.0028 Hoelter's (1983) Critical N 615 The SAS System 08:54 Wednesday, August 8, 2001 8 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Manifest Variable Equations with Estimates anti1 = 1.0000 f1 + 1.0000 e1 anti2 = 1.0000 f1 + 1.0000 f2 + 1.0000 e2 anti3 = 1.0000 f1 + 2.0000 f2 + 1.0000 e3 anti4 = 1.0000 f1 + 3.0000 f2 + 1.0000 e4 The SAS System 08:54 Wednesday, August 8, 2001 9 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Latent Variable Equations with Estimates f1 = 1.5543*Intercept + 1.0000 d1 Std Err 0.0962 al1 t Value 16.1635 f2 = 0.1765*Intercept + 1.0000 d2 Std Err 0.0428 al2 t Value 4.1279 Variances of Exogenous Variables Standard Variable Parameter Estimate Error t Value Intercept 1.00455 e1 th 1.53591 0.10355 14.83 e2 th 1.53591 0.10355 14.83 e3 th 1.53591 0.10355 14.83 e4 th 1.53591 0.10355 14.83 d1 ph11 0.96845 0.20789 4.66 d2 ph22 0.09672 0.04373 2.21 Covariances Among Exogenous Variables Standard Var1 Var2 Parameter Estimate Error t Value d1 d2 ph21 0.15110 0.07178 2.10 The SAS System 08:54 Wednesday, August 8, 2001 10 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Manifest Variable Equations with Standardized Estimates anti1 = 0.8298 f1 + 0.5581 e1 anti2 = 0.7578 f1 + 0.1471 f2 + 0.5097 e2 anti3 = 0.6891 f1 + 0.2676 f2 + 0.4635 e3 anti4 = 0.6268 f1 + 0.3651 f2 + 0.4216 e4 The SAS System 08:54 Wednesday, August 8, 2001 11 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Latent Variable Equations with Standardized Estimates f1 = 0.8454*Intercept + 0.5341 d1 al1 f2 = 0.4944*Intercept + 0.8693 d2 al2 Squared Multiple Correlations Error Total Variable Variance Variance R-Square 1 anti1 1.53591 4.93118 0.6885 2 anti2 1.53591 5.91245 0.7402 3 anti3 1.53591 7.14973 0.7852 4 anti4 1.53591 8.64300 0.8223 5 f1 0.96845 3.39527 0.7148 6 f2 0.09672 0.12800 0.2444 Correlations Among Exogenous Variables Var1 Var2 Parameter Estimate d1 d2 ph21 0.49372