Results: MatrixExample1.sas

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

The CORR Procedure

The CORR Procedure

Variables Information

3 Variables: W1 W2 Y

Covariance Matrix

Covariance Matrix, DF = 150
  W1 W2 Y
W1 1.93667204 1.10443268 0.76668496
W2 1.10443268 1.90607023 0.79486165
Y 0.76668496 0.79486165 10.32742126

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Take a look at SigmaHat

The PRINT Procedure

Data Set WORK.SIGMAHAT

Obs _TYPE_ _NAME_ W1 W2 Y
1 COV W1 1.937 1.104 0.767
2 COV W2 1.104 1.906 0.795
3 COV Y 0.767 0.795 10.327
4 MEAN   9.809 10.056 13.103
5 STD   1.392 1.381 3.214
6 N   150.000 150.000 150.000

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Matrix input

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.SIGMAHAT
N Obs 150
Model Type LINEQS
Analysis Covariances

Optimization

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Matrix input

The CALIS Procedure

Covariance Structure Analysis: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Optimization Problem

Parameter Estimates 5
Functions (Observations) 6

Iteration Start

Optimization Start
Active Constraints 0 Objective Function 0.0001339463
Max Abs Gradient Element 0.0075344463 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   0.0000471 0.000087 0.000023 0 1.006
2   0 6 0   0.0000471 2.069E-9 1.953E-7 0 0.997

Iteration Stop

Optimization Results
Iterations 2 Function Calls 9
Jacobian Calls 4 Active Constraints 0
Objective Function 0.0000470521 Max Abs Gradient Element 1.9528194E-7
Lambda 0 Actual Over Pred Change 0.9966016311
Radius 0.0001346614    
Convergence criterion (ABSGCONV=0.00001) satisfied.

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Matrix input

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Chi-Square 0.0071
Chi-Square DF 1
Pr > Chi-Square 0.9330

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Matrix input

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
Y =   0.7072 (**) F + 1.0000   epsilon
W1 =   1.0000   F + 1.0000   e1
W2 =   1.0000   F + 1.0000   e2

Linear Effects

Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
Y F beta1 0.70719 0.28961 2.4419 0.0146
W1 F   1.00000      
W2 F   1.00000      

Variance Parms

Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent F phi 1.10448 0.18095 6.1038 <.0001
Error epsilon psi 9.77505 1.15255 8.4813 <.0001
  e1 omega1 0.83437 0.15848 5.2648 <.0001
  e2 omega2 0.79951 0.15607 5.1228 <.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable Error Variance Total Variance R-Square
Y 9.77505 10.32742 0.0535
W1 0.83437 1.93885 0.5697
W2 0.79951 1.90399 0.5801

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Raw data input

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.BABY
N Records Read 150
N Records Used 150
N Obs 150
Model Type LINEQS
Analysis Covariances

Optimization

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Raw data input

The CALIS Procedure

Covariance Structure Analysis: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Optimization Problem

Parameter Estimates 5
Functions (Observations) 6

Iteration Start

Optimization Start
Active Constraints 0 Objective Function 0.0001339463
Max Abs Gradient Element 0.0075344463 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   0.0000471 0.000087 0.000023 0 1.006
2   0 6 0   0.0000471 2.069E-9 1.953E-7 0 0.997

Iteration Stop

Optimization Results
Iterations 2 Function Calls 9
Jacobian Calls 4 Active Constraints 0
Objective Function 0.0000470521 Max Abs Gradient Element 1.9528194E-7
Lambda 0 Actual Over Pred Change 0.996602059
Radius 0.0001346614    
Convergence criterion (ABSGCONV=0.00001) satisfied.

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Raw data input

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Chi-Square 0.0071
Chi-Square DF 1
Pr > Chi-Square 0.9330

Illustrate matrix input to proc calis

Jerry Brunner: Student Number 999999999

Raw data input

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
Y =   0.7072 (**) F + 1.0000   epsilon
W1 =   1.0000   F + 1.0000   e1
W2 =   1.0000   F + 1.0000   e2

Linear Effects

Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
Y F beta1 0.70719 0.28961 2.4419 0.0146
W1 F   1.00000      
W2 F   1.00000      

Variance Parms

Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent F phi 1.10448 0.18095 6.1038 <.0001
Error epsilon psi 9.77505 1.15255 8.4813 <.0001
  e1 omega1 0.83437 0.15848 5.2648 <.0001
  e2 omega2 0.79951 0.15607 5.1228 <.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable Error Variance Total Variance R-Square
Y 9.77505 10.32742 0.0535
W1 0.83437 1.93885 0.5697
W2 0.79951 1.90399 0.5801