The SAS System 08:54 Wednesday, August 8, 2001 12 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 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_ 7 15 SELECTION 2 _BETA_ 15 15 EQSBETA IMINUSINV 3 _GAMMA_ 15 9 EQSGAMMA 4 _PHI_ 9 9 SYMMETRIC The 6 Endogenous Variables Manifest anti1 anti2 anti3 anti4 Latent f1 f2 The 9 Exogenous Variables Manifest gen homecog Intercept Latent Error e1 e2 e3 e4 d1 d2 The SAS System 08:54 Wednesday, August 8, 2001 13 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 14 The CALIS Procedure Covariance Structure Analysis: Pattern and Initial Values Latent Variable Equations with Initial Estimates f1 = .*gen + .*homecog + .*Intercept + 1.0000 d1 gamma1 gamma2 al1 f2 = .*gen + .*homecog + .*Intercept + 1.0000 d2 gamma3 gamma4 al2 Variances of Exogenous Variables Variable Parameter Estimate gen . homecog . Intercept . e1 th . e2 th . e3 th . e4 th . d1 ph11 . d2 ph22 . Covariances Among Exogenous Variables Var1 Var2 Parameter Estimate gen homecog . gen Intercept . homecog Intercept . d1 d2 ph21 . The SAS System 08:54 Wednesday, August 8, 2001 15 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Observations 221 Model Terms 1 Variables 7 Model Matrices 4 Informations 28 Parameters 10 Variable Mean Unc StD anti1 1.49321 2.14688 anti2 1.83710 2.56905 anti3 1.87783 2.60506 anti4 2.06787 2.93954 gen 0.52489 0.72614 homecog 9.09955 9.44482 Intercept 1.00000 1.00227 Set Covariances of Exogenous Manifest Variables gen homecog Intercept NOTE: Some initial estimates computed by two-stage LS method. The SAS System 08:54 Wednesday, August 8, 2001 16 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Vector of Initial Estimates Parameter Estimate Type 1 gamma1 0.55942 Matrix Entry: _GAMMA_[5:1] 2 gamma2 -0.10195 Matrix Entry: _GAMMA_[5:2] 3 al1 2.11217 Matrix Entry: _GAMMA_[5:3] 4 gamma3 0.12302 Matrix Entry: _GAMMA_[6:1] 5 gamma4 -0.02764 Matrix Entry: _GAMMA_[6:2] 6 al2 0.51399 Matrix Entry: _GAMMA_[6:3] 7 th 1.45060 Matrix Entry: _PHI_[4:4] _PHI_[5:5] _PHI_[6:6] _PHI_[7:7] 8 ph11 1.18164 Matrix Entry: _PHI_[8:8] 9 ph21 -0.16563 Matrix Entry: _PHI_[9:8] 10 ph22 0.06329 Matrix Entry: _PHI_[9:9] The SAS System 08:54 Wednesday, August 8, 2001 17 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Levenberg-Marquardt Optimization Scaling Update of More (1978) Parameter Estimates 10 Functions (Observations) 28 Optimization Start Active Constraints 0 Objective Function 0.4407912197 Max Abs Gradient Element 12.973946857 Radius 400.98130045 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 0.04148 0.3993 0.1615 0 0.632 2 0 3 0 0.03951 0.00196 5.89E-15 0 1.043 Optimization Results Iterations 2 Function Calls 4 Jacobian Calls 3 Active Constraints 0 Objective Function 0.0395144349 Max Abs Gradient Element 5.887651E-15 Lambda 0 Actual Over Pred Change 1.0427410403 Radius 0.2905137569 ABSGCONV convergence criterion satisfied. The SAS System 08:54 Wednesday, August 8, 2001 18 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Fit Function 0.0395 Goodness of Fit Index (GFI) 0.9886 GFI Adjusted for Degrees of Freedom (AGFI) 0.9733 Root Mean Square Residual (RMR) 0.2406 Parsimonious GFI (Mulaik, 1989) 0.5649 Chi-Square 8.6932 Chi-Square DF 12 Pr > Chi-Square 0.7289 Independence Model Chi-Square 1662.2 Independence Model Chi-Square DF 21 RMSEA Estimate 0.0000 RMSEA 90% Lower Confidence Limit . RMSEA 90% Upper Confidence Limit 0.0511 ECVI Estimate 0.1339 ECVI 90% Lower Confidence Limit . ECVI 90% Upper Confidence Limit 0.2090 Probability of Close Fit 0.9461 Bentler's Comparative Fit Index 1.0000 Normal Theory Reweighted LS Chi-Square 8.9145 Akaike's Information Criterion -15.3068 Bozdogan's (1987) CAIC -68.0848 Schwarz's Bayesian Criterion -56.0848 McDonald's (1989) Centrality 1.0075 Bentler & Bonett's (1980) Non-normed Index 1.0035 Bentler & Bonett's (1980) NFI 0.9948 James, Mulaik, & Brett (1982) Parsimonious NFI 0.5684 Z-Test of Wilson & Hilferty (1931) -0.6126 Bollen (1986) Normed Index Rho1 0.9908 Bollen (1988) Non-normed Index Delta2 1.0020 Hoelter's (1983) Critical N 534 The SAS System 08:54 Wednesday, August 8, 2001 19 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 20 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Latent Variable Equations with Estimates f1 = 0.5716*gen + -0.0626*homecog + 1.8240*Intercept + 1.0000 d1 Std Err 0.1875 gamma1 0.0382 gamma2 0.3740 al1 t Value 3.0486 -1.6378 4.8773 f2 = 0.0791*gen + -0.0452*homecog + 0.5465*Intercept + 1.0000 d2 Std Err 0.0841 gamma3 0.0172 gamma4 0.1678 al2 t Value 0.9403 -2.6370 3.2573 Variances of Exogenous Variables Standard Variable Parameter Estimate Error t Value gen 0.52727 homecog 89.20455 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 0.86246 0.19845 4.35 d2 ph22 0.08277 0.04256 1.94 Covariances Among Exogenous Variables Standard Var1 Var2 Parameter Estimate Error t Value gen homecog 4.79091 gen Intercept 0.52727 homecog Intercept 9.14091 d1 d2 ph21 0.12249 0.07014 1.75 The SAS System 08:54 Wednesday, August 8, 2001 21 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 22 The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Latent Variable Equations with Standardized Estimates f1 = 0.2253*gen + -0.3209*homecog + 0.9921*Intercept + 0.5040 d1 gamma1 gamma2 al1 f2 = 0.1605*gen + -1.1939*homecog + 1.5309*Intercept + 0.8042 d2 gamma3 gamma4 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 0.86246 3.39527 0.7460 6 f2 0.08277 0.12800 0.3533 Correlations Among Exogenous Variables Var1 Var2 Parameter Estimate gen homecog 0.69856 gen Intercept 0.72449 homecog Intercept 0.96563 d1 d2 ph21 0.45846