Results: CalisRegSAT.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	73.22824
math	649.54000	66.33915
gpa	2.63010	0.58029

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	5362	1.2427E-24
5	phi22	4401	-3.309E-24
6	sigmasq	0.29767	-7.583E-16
7	phi12	1336	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	137.12644309

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	3.46E-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	3.4597565E-7
Lambda	0	Actual Over Pred Change	1.00000008
Radius	0.0126013178

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	40.2016
	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	0.43909	1.3848	0.1661
gpa	verbal	beta1	0.00231	0.0005494	4.1995	<.0001
gpa	math	beta2	0.0009974	0.0006064	1.6447	0.1000

Variance Parms

Estimates for Variances of Exogenous Variables
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	verbal	phi11	5362	537.58311	9.9750	<.0001
	math	phi22	4401	441.19265	9.9750	<.0001
Error	epsilon	sigmasq	0.29767	0.02984	9.9750	<.0001

Covariance Parms

Covariances Among Exogenous Variables
Var1	Var2	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
verbal	math	phi12	1336	357.16093	3.7418	0.0002

Mean Parms

Mean Parameters
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	verbal	mu1	595.66500	5.19101	114.7	<.0001
	math	mu2	649.54000	4.70266	138.1	<.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable	Error Variance	Total Variance	R-Square
gpa	0.29767	0.33674	0.1160

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

Standardized Results

Equations

Standardized Results for Linear Equations
gpa	=		0.2911	(**)	verbal	+	0.1140	(ns)	math	+	1.0000		epsilon

Linear Effects

Standardized Effects in Linear Equations
Variable	Predictor	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
gpa	verbal	beta1	0.29113	0.06659	4.3718	<.0001
gpa	math	beta2	0.11402	0.06894	1.6538	0.0982

Variance Parms

Standardized Results for Variances of Exogenous Variables
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	verbal	phi11	1.00000
	math	phi22	1.00000
Error	epsilon	sigmasq	0.88398	0.04269	20.7078	<.0001

Covariance Parms

Standardized Results for Covariances Among Exogenous Variables
Var1	Var2	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
verbal	math	phi12	0.27510	0.06552	4.1986	<.0001