Results: Babydouble.sas

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

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

Variables

Variables in the Model
Number of Endogenous Variables = 3
Number of Exogenous Variables = 4
Endogenous Manifest W1 W2 Y
  Latent  
Exogenous Manifest  
  Latent F
  Error e1 e2 epsilon

Equations

Initial Estimates for Linear Equations
Y =   beta1 (.) F +   1 epsilon
W1 =     1 F +   1 e1
W2 =     1 F +   1 e2

Variance Parms

Initial Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate
Latent F phi .
Error epsilon psi .
  e1 omega1 .
  e2 omega2 .

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

The CALIS Procedure

Covariance Structure Analysis: Descriptive Statistics

Descriptive Statistics

Simple Statistics

Simple Statistics
Variable Mean Std Dev
W1 9.80860 1.39164
W2 10.05620 1.38061
Y 13.10307 3.21363

Covariances

Covariance Matrix (DF = 150)
  W1 W2 Y
W1 1.93667 1.10443 0.76668
W2 1.10443 1.90607 0.79486
Y 0.76668 0.79486 10.32742
Determinant 24.527991 Ln 3.199815

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

The CALIS Procedure

Covariance Structure Analysis: Optimization

Optimization

Init Est Methods

Initial Estimation Methods
1 Instrumental Variables Method
2 McDonald Method

Initial Estimates

Optimization Start
Parameter Estimates
N Parameter Estimate Gradient
Value of Objective Function = 0.0001339463
1 beta1 0.71970 0.00132
2 phi 1.09447 -0.00195
3 psi 9.76052 -0.0000846
4 omega1 0.84220 0.00564
5 omega2 0.81160 0.00753

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

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.

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Modeling Info Number of Observations 150
  Number of Variables 3
  Number of Moments 6
  Number of Parameters 5
  Number of Active Constraints 0
  Baseline Model Function Value 0.4410
  Baseline Model Chi-Square 66.1504
  Baseline Model Chi-Square DF 3
  Pr > Baseline Model Chi-Square <.0001
Absolute Index Fit Function 0.0000
  Chi-Square 0.0071
  Chi-Square DF 1
  Pr > Chi-Square 0.9330
  Z-Test of Wilson & Hilferty -1.2430
  Hoelter Critical N 81642
  Root Mean Square Residual (RMR) 0.0082
  Standardized RMR (SRMR) 0.0019
  Goodness of Fit Index (GFI) 1.0000
Parsimony Index Adjusted GFI (AGFI) 0.9998
  Parsimonious GFI 0.3333
  RMSEA Estimate 0.0000
  RMSEA Lower 90% Confidence Limit 0.0000
  RMSEA Upper 90% Confidence Limit 0.0625
  Probability of Close Fit 0.9445
  ECVI Estimate 0.0685
  ECVI Lower 90% Confidence Limit 0.0753
  ECVI Upper 90% Confidence Limit 0.0792
  Akaike Information Criterion 10.0071
  Bozdogan CAIC 30.0602
  Schwarz Bayesian Criterion 25.0602
  McDonald Centrality 1.0033
Incremental Index Bentler Comparative Fit Index 1.0000
  Bentler-Bonett NFI 0.9999
  Bentler-Bonett Non-normed Index 1.0472
  Bollen Normed Index Rho1 0.9997
  Bollen Non-normed Index Delta2 1.0152
  James et al. Parsimonious NFI 0.3333

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Covariances

Predicted Covariances
  W1 W2 Y
W1 1.93885 1.10448 0.78107
W2 1.10448 1.90399 0.78107
Y 0.78107 0.78107 10.32742
Determinant 24.529145 Ln 3.199862

Simple double measurement with proc calis

Jerry Brunner: Student Number 999999999

Fit the centered model

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