USA Output 2

8/6/2019 USA Output 2

1/13


2/13

The SAS System

Full Information Maximum Likelihood

The SYSLIN Procedure

Full-Information Maximum Likelihood Estimation

NOTE: Convergence criterion met at iteration 0.

Model IMPORT

Dependent Variable logimport

Label Logarithm of Import

Parameter Estimates

Variable DFParameter

EstimateStandard

Error t Value Pr > |t|VariableLabel

Intercept 1 12.13109 0.079614 152.37 |t|VariableLabel

Intercept 1 -3.91261 0.889770 -4.40 0.0004 Intercept

logpop 1 0.307802 0.390974 0.79 0.4420 Logarithm of Population

inf1 -0.03355 0.025657 -1.31 0.2084 Inflation

logexported_top10_pjc 1 0.355189 0.080154 4.43 0.0004 Exported Top10 PJC


3/13

The SAS System

Least Squares Estimation

The REG Procedure

Model: MODEL1

Dependent Variable: logimport Logarithm of Import

Number of Observations Read 21

Number of Observations Used 21

Analysis of Variance

Source DFSum of

SquaresMean

Square F Value Pr > F

Model 3 1.18726 0.39575 21.10 |t|

Intercept Intercept 1 12.12578 0.08157 148.65


4/13

The SAS System

Generalized Least Squares

The CALIS Procedure

Mean and Covariance Structures: Model and Initial Values

Modeling Information

Data Set WORK.PJCDEMAND

N Records Read 21

N Complete Records 21

N Incomplete Records 0

N Complete Obs 21

N Incomplete Obs 0

Model Type LINEQS

Analysis Means and Covariances

Variables in the Model

Endogenous Manifest logimport logprice_pjc

Latent

Exogenous Manifest inf logexported_top10_pjc logpop

Latent

Error E1 E2

Number of Endogenous Variables = 2Number of Exogenous Variables = 5

Initial Estimates for Linear Equations

logimport = . * Intercept + . * logprice_pjc + . * logpop + . * inf + 1.0000 E1

betanull betalogprice_pjc betalogpop betainf

logprice_pjc = . * Intercept + . * logpop + . * inf + . * logexported_top10_pjc + 1.0000 E2

alphanull alphalogpop alphainf alphatop10

Initial Estimates for Variances of Exogenous Variables

VariableType Variable Parameter Estimate

Error E1 eps1 .

E2 eps2 .

Observed logpop _Add1 .


5/13

The SAS System


The CALIS Procedure

Mean and Covariance Structures: Model and Initial Values

inf _Add2 .

logexported_top10_pjc _Add3 .

NOTE: Parameters with prefix '_Add' are added by PROCCALIS.

Initial Estimates for Covariances Among ExogenousVariables

Var1 Var2 Parameter Estimate

E1 E2 eps3 .

inf logpop _Add4 .

logexported_top10_pjc logpop _Add5 .

logexported_top10_pjc inf _Add6 .

NOTE: Parameters with prefix '_Add' are added byPROC CALIS.

Initial Estimates for Mean Parameters


Observed logpop _Add7 .

inf _Add8 .

logexported_top10_pjc _Add9 .

NOTE: Parameters with prefix '_Add' are added by PROCCALIS.


6/13

The SAS System


The CALIS Procedure

Mean and Covariance Structures: Descriptive Statistics

Simple Statistics

Variable Mean Std Dev

inf Inflation 2.74457 1.10175

logimport Logarithm of Import 12.36868 0.26781

logpop Logarithm of Population 0.06473 0.15038

logexported_top10_pjc Exported Top10 PJC 10.73071 0.73035

logprice_pjc Logarithm of PJC Price -0.17334 0.26337


7/13

The SAS System


The CALIS Procedure

Mean and Covariance Structures: Optimization

Initial Estimation Methods

1 Observed Moments of Variables

2 McDonald Method

3 Two-Stage Least Squares

Optimization StartParameter Estimates

N Parameter Estimate Gradient Lower Bound Upper Bound

1 betanull 12.13109 1.2051E-15 . .

2 betalogprice_pjc -0.56786 2.4971E-16 . .

3 betalogpop 0.66212 1.054E-16 . .

4 betainf 0.03509 3.2526E-15 . .

5 alphanull -3.91261 -4.248E-14 . .

6 alphalogpop 0.30780 -3.716E-15 . .

7 alphainf -0.03355 -1.147E-13 . .

8 alphatop10 0.35519 -4.585E-13 . .

9 eps1 0.01784 -1.44E-14 0 .

10 eps2 0.01462 -8.866E-16 0 .

11 _Add1 0.02261 -2.31E-28 . .

12 _Add2 1.21386 -1.561E-31 . .

13 _Add3 0.53341 -5.352E-30 . .

14 eps3 0.00867 -5.842E-14 . .

15 _Add4 0.05862 4.0337E-30 . .

16 _Add5 -0.09799 -8.244E-29 . .

17 _Add6 -0.27589 1.1209E-30 . .

18 _Add7 0.06473 -7.154E-29 . .

19 _Add8 2.74457 9.2811E-31 . .

20 _Add9 10.73071 -1.226E-29 . .

Value of Objective Function = 0


8/13

The SAS System


The CALIS Procedure

Mean and Covariance Structures: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Parameter Estimates 20

Functions (Observations) 20

Lower Bounds 2

Upper Bounds 0

Optimization Start

Active Constraints 0 Objective Function 0

Max Abs Gradient Element 4.584738E-13 Radius 1

Optimization Results

Iterations 0 Function Calls 4

Jacobian Calls 1 Active Constraints 0

Objective Function 0 Max Abs Gradient Element 4.584738E-13

Lambda 0 Actual Over Pred Change 0

Radius 1

Convergence criterion (ABSGCONV=0.00001) satisfied.


9/13

The SAS System


The CALIS Procedure

Mean and Covariance Structures: Full Information Maximum Likelihood Estimation

Fit Summary

Modeling Info N Complete Observations 21

N Incomplete Observations 0

N Variables 5

N Moments 20

N Parameters 20

N Active Constraints 0

Saturated Model Estimation FIML

Saturated Model Function Value 0.0000

Saturated Model -2 Log-Likelihood 0.0000

Baseline Model Estimation Converged

Baseline Model Function Value 4.6622

Baseline Model -2 Log-Likelihood 97.9054

Baseline Model Chi-Square 97.9054

Baseline Model Chi-Square DF 10

Pr > Baseline Model Chi-Square Chi-Square .

Z-Test of Wilson & Hilferty .

Hoelter Critical N .

Root Mean Square Residual (RMSR) 0.0000

Standardized RMSR (SRMSR) 0.0000

Goodness of Fit Index (GFI) 1.0000

Parsimony Index Adjusted GFI (AGFI) .

Parsimonious GFI 0.0000

RMSEA Estimate .

Probability of Close Fit .


10/13

The SAS System


The CALIS Procedure


Akaike Information Criterion 40.0000

Bozdogan CAIC 80.8904

Schwarz Bayesian Criterion 60.8904

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


11/13

The SAS System


The CALIS Procedure


Linear Equations

logimport = 12.1311 * Intercept + -0.5679 * logprice_pjc + 0.6621 * logpop

Std Err 0.0796 betanull 0.2493 betalogprice_pjc 0.3665 betalogpop

t Value 152.4 -2.2777 1.8068

logprice_pjc = -3.9126 * Intercept + 0.3078 * logpop + -0.0336 * inf

Std Err 0.8898 alphanull 0.3910 alphalogpop 0.0257 alphainf

t Value -4.3973 0.7873 -1.3078

+ 0.0351 * inf + 1.0000 E1

0.0301 betainf

1.1670

+ 0.3552 * logexported_top10_pjc + 1.0000 E2

0.0802 alphatop10

4.4313

Estimates for Variances of Exogenous Variables


StandardError t Value

Error E1 eps1 0.01784 0.00700 2.54895

E2 eps2 0.01462 0.00451 3.24037

Observed logpop _Add1 0.02261 0.00698 3.24037

inf _Add2 1.21386 0.37461 3.24037

logexported_top10_pjc _Add3 0.53341 0.16461 3.24037

Covariances Among Exogenous Variables

Var1 Var2 Parameter EstimateStandard

Error t Value

E1 E2 eps3 0.00867 0.00541 1.60183

inf logpop _Add4 0.05862 0.03835 1.52842

logexported_top10_pjc logpop _Add5 -0.09799 0.03212 -3.05081

logexported_top10_pjc inf _Add6 -0.27589 0.18563 -1.48629


12/13

The SAS System


The CALIS Procedure


Mean Parameters



Observed logpop _Add7 0.06473 0.03282 1.97268

inf _Add8 2.74457 0.24042 11.41562

logexported_top10_pjc _Add9 10.73071 0.15937 67.33015

Squared Multiple Correlations

VariableError

VarianceTotal

Variance R-Square

logimport 0.01784 0.07172 0.7512

logprice_pjc 0.01462 0.06936 0.7892


13/13

The SAS System


The CALIS Procedure


Standardized Results for Linear Equations

logimport = -0.5584 * logprice_pjc + 0.3718 * logpop + 0.1443 * inf + 1.0000 E1

Std Err 0.2327 betalogprice_pjc 0.2046 betalogpop 0.1252 betainf

t Value -2.3999 1.8169 1.1528

logprice_pjc = 0.1758 * logpop + -0.1404 * inf + 0.9850 * logexported_top10_pjc + 1.0000 E2

Std Err 0.2233 alphalogpop 0.1091 alphainf 0.2016 alphatop10

t Value 0.7871 -1.2867 4.8851

Standardized Results for Variances of Exogenous Variables



Error E1 eps1 0.24877 0.11274 2.20663

E2 eps2 0.21076 0.08172 2.57915

Observed logpop _Add1 1.00000

inf _Add2 1.00000

logexported_top10_pjc _Add3 1.00000

Standardized Results for Covariances Among Exogenous Variables

Var1 Var2 Parameter EstimateStandard

Error t Value

E1 E2 eps3 0.12289 0.08233 1.49266

inf logpop _Add4 0.35379 0.19090 1.85322

logexported_top10_pjc logpop _Add5 -0.89220 0.04451 -20.04374

logexported_top10_pjc inf _Add6 -0.34287 0.19256 -1.78054

USA Output 2

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Transcript of USA Output 2