Results: 431s17SATcalisReg.sas

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Proc reg for comparison

The REG Procedure

Model: MODEL1

Dependent Variable: gpa

The REG Procedure

MODEL1

Fit

gpa

Number of Observations

Number of Observations Read 200
Number of Observations Used 200

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 7.77445 3.88723 12.93 <.0001
Error 197 59.23635 0.30069    
Corrected Total 199 67.01080      

Fit Statistics

Root MSE 0.54835 R-Square 0.1160
Dependent Mean 2.63010 Adj R-Sq 0.1070
Coeff Var 20.84917    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 0.60807 0.44131 1.38 0.1698
verbal 1 0.00231 0.00055213 4.18 <.0001
math 1 0.00099736 0.00060947 1.64 0.1033

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Surface regression with proc calis

The CALIS Procedure

Mean and Covariance Structures: Model and Initial Values

The CALIS Procedure

Modeling Specification

Modeling Info

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

Variables

Variables in the Model
Number of Endogenous Variables = 1
Number of Exogenous Variables = 3
Endogenous Manifest gpa
  Latent  
Exogenous Manifest math verbal
  Latent  
  Error epsilon

Equations

Initial Estimates for Linear Equations
gpa =   beta0 (.) Intercept + beta1 (.) verbal + beta2 (.) math +   1 epsilon

Variance Parms

Initial Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate
Observed verbal phi11 .
  math phi22 .
Error epsilon sigmasq .

Covariance Parms

Initial Estimates for Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate
verbal math phi12 .

Mean Parms

Initial Estimates for Mean Parameters
Variable
Type		 Variable Parameter Estimate
Observed verbal mu1 .
  math mu2 .

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Surface regression with proc calis

The CALIS Procedure

Mean and Covariance Structures: Descriptive Statistics

Descriptive Statistics

Simple Statistics

Simple Statistics
Variable Mean Std Dev
verbal 595.66500 73.04494
math 649.54000 66.17309
gpa 2.63010 0.57884

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Surface regression with proc calis

The CALIS Procedure

Mean and Covariance Structures: Optimization

Optimization

Init Est Methods

Initial Estimation Methods
1 Observed Moments of Variables
2 McDonald Method
3 Two-Stage Least Squares

Initial Estimates

Optimization Start
Parameter Estimates
N Parameter Estimate Gradient
Value of Objective Function = 1.0298662E-7
1 beta0 0.60636 0
2 beta1 0.00231 0.02370
3 beta2 0.00100 0.07804
4 phi11 5336 5.1052E-25
5 phi22 4379 3.3087E-24
6 sigmasq 0.29618 4.7542E-17
7 phi12 1330 0
8 mu1 595.66500 0
9 mu2 649.54000 0

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Surface regression with proc calis

The CALIS Procedure

Mean and Covariance Structures: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Optimization Problem

Parameter Estimates 9
Functions (Observations) 9

Iteration Start

Optimization Start
Active Constraints 0 Objective Function 1.0298662E-7
Max Abs Gradient Element 0.0780409714 Radius 137.4668888

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 1.03E-7 3.477E-7 0 1.000

Iteration Stop

Optimization Results
Iterations 1 Function Calls 7
Jacobian Calls 3 Active Constraints 0
Objective Function 0 Max Abs Gradient Element 3.4771422E-7
Lambda 0 Actual Over Pred Change 1.00000008
Radius 0.0126327759    
Convergence criterion (GCONV2=0) satisfied.

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Surface regression with proc calis

The CALIS Procedure

Mean and Covariance Structures: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Modeling Info Number of Observations 200
  Number of Variables 3
  Number of Moments 9
  Number of Parameters 9
  Number of Active Constraints 0
  Baseline Model Function Value 0.2020
  Baseline Model Chi-Square 40.4036
  Baseline Model Chi-Square DF 3
  Pr > Baseline Model Chi-Square <.0001
Absolute Index Fit Function 0.0000
  Chi-Square 0.0000
  Chi-Square DF 0
  Pr > Chi-Square .
  Z-Test of Wilson & Hilferty .
  Hoelter Critical N .
  Root Mean Square Residual (RMR) 0.0000
  Standardized RMR (SRMR) 0.0000
  Goodness of Fit Index (GFI) 1.0000
Parsimony Index Adjusted GFI (AGFI) .
  Parsimonious GFI 0.0000
  RMSEA Estimate .
  Probability of Close Fit .
  Akaike Information Criterion 18.0000
  Bozdogan CAIC 56.6849
  Schwarz Bayesian Criterion 47.6849
  McDonald Centrality 1.0000
Incremental Index Bentler Comparative Fit Index 1.0000
  Bentler-Bonett NFI 1.0000
  Bentler-Bonett Non-normed Index .
  Bollen Normed Index Rho1 .
  Bollen Non-normed Index Delta2 1.0000
  James et al. Parsimonious NFI 0.0000

Open SAT Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Surface regression with proc calis

The CALIS Procedure

Mean and Covariance Structures: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
gpa =   0.6081 (ns) Intercept + 0.00231 (**) verbal + 0.000997 (ns) math + 1.0000   epsilon

Linear Effects

Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
gpa Intercept beta0 0.60807 0.43799 1.3883 0.1650
gpa verbal beta1 0.00231 0.0005480 4.2100 <.0001
gpa math beta2 0.0009974 0.0006049 1.6488 0.0992

Variance Parms

Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Observed verbal phi11 5336 533.55628 10.0000 <.0001
  math phi22 4379 437.88784 10.0000 <.0001
Error epsilon sigmasq 0.29618 0.02962 10.0000 <.0001

Covariance Parms

Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate Standard
Error		 t Value Pr > |t|
verbal math phi12 1330 354.48558 3.7512 0.0002

Mean Parms

Mean Parameters
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Observed verbal mu1 595.66500 5.16506 115.3 <.0001
  math mu2 649.54000 4.67914 138.8 <.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable Error Variance Total Variance R-Square
gpa 0.29618 0.33505 0.1160