Results: CarCalisReg.sas

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Proc reg for comparison

The REG Procedure

Model: MODEL1

Dependent Variable: lper100k

The REG Procedure

MODEL1

Fit

lper100k

Number of Observations

Number of Observations Read	100
Number of Observations Used	100

Analysis of Variance

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	2	757.27066	378.63533	116.36	<.0001
Error	97	315.64094	3.25403
Corrected Total	99	1072.91160

Fit Statistics

Root MSE	1.80389	R-Square	0.7058
Dependent Mean	12.27800	Adj R-Sq	0.6997
Coeff Var	14.69208

Parameter Estimates

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	1	-3.61747	2.95847	-1.22	0.2244
weight	1	0.00495	0.00155	3.20	0.0018
length	1	1.83563	1.01735	1.80	0.0743

Metric Cars 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.AUTO
N Records Read	100
N Records Used	100
N Obs	100
Model Type	LINEQS
Analysis	Means and Covariances

Metric Cars 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

Covariances

Covariance Matrix (DF = 100)
	lper100k	weight	length
lper100k	10.72912	984.08962	1.47215
weight	984.08962	129698.99	186.41747
length	1.47215	186.41747	0.29938

Determinant	12871	Ln	9.462730

Means

Means
lper100k	weight	length
12.27800	1413.2100	4.84920

Optimization

Metric Cars 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	0
Max Abs Gradient Element	1.782968E-16	Radius	1

Iteration Stop

Optimization Results
Iterations	0	Function Calls	4
Jacobian Calls	1	Active Constraints	0
Objective Function	0	Max Abs Gradient Element	1.782968E-16
Lambda	0	Actual Over Pred Change	0
Radius	1

Convergence criterion (ABSGCONV=0.00001) satisfied.

Note:The Moore-Penrose inverse is used in computing the covariance matrix for parameter estimates.

Note:Covariance matrix for the estimates is not full rank.

Note:The variance of some parameter estimates is zero or some parameter estimates are linearly related to other parameter estimates as shown in the following equations:

Linear Dependence

phi11	=	129584	+	383.259241	*	phi22
mu1	=	1460.676413	-	9.788504	*	mu2

Metric Cars 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	100
	Number of Variables	3
	Number of Moments	9
	Number of Parameters	9
	Number of Active Constraints	0
	Baseline Model Function Value	3.4772
	Baseline Model Chi-Square	347.7159
	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	50.4465
	Schwarz Bayesian Criterion	41.4465
	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

Metric Cars 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

Predicted Covariances

Predicted Covariances
	lper100k	weight	length
lper100k	10.72912	984.08962	1.47215
weight	984.08962	129698.99	186.41747
length	1.47215	186.41747	0.29938

Determinant	12871	Ln	9.462730

Predicted Means

Predicted Means
lper100k	weight	length
12.27800	1413.2100	4.84920

Metric Cars 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
lper100k	=		-3.6175	(ns)	Intercept	+	0.00495	(**)	weight	+	1.8356	(ns)	length	+	1.0000		epsilon

Linear Effects

Effects in Linear Equations
Variable	Predictor	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
lper100k	Intercept	beta0	-3.61747	2.91376	-1.2415	0.2144
lper100k	weight	beta1	0.00495	0.00152	3.2511	0.0011
lper100k	length	beta2	1.83563	1.00197	1.8320	0.0669

Variance Parms

Estimates for Variances of Exogenous Variables
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	weight	phi11	129699	0.00918	14131102	<.0001
	length	phi22	0.29938	0.01889	15.8509	<.0001
Error	epsilon	psi	3.15641	0.44638	7.0711	<.0001

Covariance Parms

Covariances Among Exogenous Variables
Var1	Var2	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
weight	length	phi12	186.41747	6.38570	29.1930	<.0001

Mean Parms

Mean Parameters
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	weight	mu1	1413	36.01375	39.2409	<.0001
	length	mu2	4.84920	0.05472	88.6256	<.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable	Error Variance	Total Variance	R-Square
lper100k	3.15641	10.72912	0.7058

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Weight re-scaled

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.AUTO2
N Records Read	100
N Records Used	100
N Obs	100
Model Type	LINEQS
Analysis	Means and Covariances

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Weight re-scaled

The CALIS Procedure

Mean and Covariance Structures: Descriptive Statistics

Descriptive Statistics

Covariances

Covariance Matrix (DF = 100)
	lper100k	weight	length
lper100k	10.72912	9.84090	1.47215
weight	9.84090	12.96990	1.86417
length	1.47215	1.86417	0.29938

Determinant	1.287098	Ln	0.252390

Means

Means
lper100k	weight	length
12.27800	14.13210	4.84920

Optimization

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Weight re-scaled

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	0
Max Abs Gradient Element	1.624159E-14	Radius	1

Iteration Stop

Optimization Results
Iterations	0	Function Calls	4
Jacobian Calls	1	Active Constraints	0
Objective Function	0	Max Abs Gradient Element	1.624159E-14
Lambda	0	Actual Over Pred Change	0
Radius	1

Convergence criterion (ABSGCONV=0.00001) satisfied.

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Weight re-scaled

The CALIS Procedure

Mean and Covariance Structures: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Modeling Info	Number of Observations	100
	Number of Variables	3
	Number of Moments	9
	Number of Parameters	9
	Number of Active Constraints	0
	Baseline Model Function Value	3.4772
	Baseline Model Chi-Square	347.7159
	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	50.4465
	Schwarz Bayesian Criterion	41.4465
	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

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Weight re-scaled

The CALIS Procedure

Mean and Covariance Structures: Maximum Likelihood Estimation

Predicted Covariances

Predicted Covariances
	lper100k	weight	length
lper100k	10.72912	9.84090	1.47215
weight	9.84090	12.96990	1.86417
length	1.47215	1.86417	0.29938

Determinant	1.287098	Ln	0.252390

Predicted Means

Predicted Means
lper100k	weight	length
12.27800	14.13210	4.84920

Metric Cars Data: Fit a regression model with proc calis

Jerry Brunner: Student Number 999999999

Weight re-scaled

The CALIS Procedure

Mean and Covariance Structures: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
lper100k	=		-3.6175	(ns)	Intercept	+	0.4949	(**)	weight	+	1.8356	(ns)	length	+	1.0000		epsilon

Linear Effects

Effects in Linear Equations
Variable	Predictor	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
lper100k	Intercept	beta0	-3.61747	2.91376	-1.2415	0.2144
lper100k	weight	beta1	0.49491	0.15223	3.2511	0.0011
lper100k	length	beta2	1.83563	1.00197	1.8320	0.0669

Variance Parms

Estimates for Variances of Exogenous Variables
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	weight	phi11	12.96990	1.83422	7.0711	<.0001
	length	phi22	0.29938	0.04234	7.0711	<.0001
Error	epsilon	psi	3.15641	0.44638	7.0711	<.0001

Covariance Parms

Covariances Among Exogenous Variables
Var1	Var2	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
weight	length	phi12	1.86417	0.27126	6.8723	<.0001

Mean Parms

Mean Parameters
Variable Type	Variable	Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Observed	weight	mu1	14.13210	0.36014	39.2409	<.0001
	length	mu2	4.84920	0.05472	88.6256	<.0001

Sq. Mult. Correlations

Squared Multiple Correlations
Variable	Error Variance	Total Variance	R-Square
lper100k	3.15641	10.72912	0.7058