Results: ClassicalPathExperiment.sas

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Ordinary double measurement for comparison

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.DOUBLE
N Records Read 114
N Records Used 114
N Obs 114
Model Type LINEQS
Analysis Covariances

Optimization

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Ordinary double measurement for comparison

The CALIS Procedure

Covariance Structure Analysis: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Optimization Problem

Parameter Estimates 9
Functions (Observations) 10
Lower Bounds 6
Upper Bounds 0

Iteration Start

Optimization Start
Active Constraints 0 Objective Function 0.7781996469
Max Abs Gradient Element 1.0721944648 Radius 2.4066041055

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   0.09293 0.6853 0.0163 0 1.617
2   0 6 0   0.0007994 0.0921 0.00161 0 1.344
3   0 8 0   0.0007636 0.000036 0.000101 0 0.998
4   0 10 0   0.0007636 2.136E-8 3.942E-6 0 0.988

Iteration Stop

Optimization Results
Iterations 4 Function Calls 13
Jacobian Calls 6 Active Constraints 0
Objective Function 0.0007636029 Max Abs Gradient Element 3.9417928E-6
Lambda 0 Actual Over Pred Change 0.9883266467
Radius 0.0017056951    
Convergence criterion (ABSGCONV=0.00001) satisfied.

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Ordinary double measurement for comparison

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Chi-Square 0.0871
Chi-Square DF 1
Pr > Chi-Square 0.7680

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Ordinary double measurement for comparison

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
Fbirths =   0.7567 (**) Fbreeders + 1.0000   epsilon
W1 =   1.0000   Fbreeders + 1.0000   e1
V1 =   1.0000   Fbirths + 1.0000   e2
W2 =   1.0000   Fbreeders + 1.0000   e3
V2 =   1.0000   Fbirths + 1.0000   e4

Linear Effects

Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
Fbirths Fbreeders beta1 0.75667 0.05387 14.0472 <.0001
W1 Fbreeders   1.00000      
V1 Fbirths   1.00000      
W2 Fbreeders   1.00000      
V2 Fbirths   1.00000      

Variance Parms

Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent Fbreeders phi 357.14465 64.93594 5.5000 <.0001
Disturbance epsilon psi 33.63389 10.86056 3.0969 0.0020
Error e1 omega11 330.68357 67.11362 4.9272 <.0001
  e2 omega22 321.25427 54.16001 5.9316 <.0001
  e3 omega33 416.33416 80.76314 5.1550 <.0001
  e4 omega44 93.00057 35.56645 2.6148 0.0089

Covariance Parms

Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate Standard
Error		 t Value Pr > |t|
e1 e2 omega12 308.53831 57.24861 5.3894 <.0001
e3 e4 omega34 101.40561 45.51337 2.2280 0.0259

Sq. Mult. Correlations

Squared Multiple Correlations
Variable Error Variance Total Variance R-Square
Fbirths 33.63389 238.11722 0.8588
W1 330.68357 687.82822 0.5192
V1 321.25427 559.37148 0.4257
W2 416.33416 773.47881 0.4617
V2 93.00057 331.11778 0.7191

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Ordinary double measurement for comparison

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Standardized Results

Equations

Standardized Results for Linear Equations
Fbirths =   0.9267 (**) Fbreeders + 1.0000   epsilon
W1 =   0.7206 (**) Fbreeders + 1.0000   e1
V1 =   0.6524 (**) Fbirths + 1.0000   e2
W2 =   0.6795 (**) Fbreeders + 1.0000   e3
V2 =   0.8480 (**) Fbirths + 1.0000   e4

Linear Effects

Standardized Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
Fbirths Fbreeders beta1 0.92669 0.02648 34.9896 <.0001
W1 Fbreeders   0.72058 0.04851 14.8538 <.0001
V1 Fbirths   0.65245 0.04598 14.1901 <.0001
W2 Fbreeders   0.67951 0.05140 13.2208 <.0001
V2 Fbirths   0.84802 0.05943 14.2680 <.0001

Variance Parms

Standardized Results for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent Fbreeders phi 1.00000      
Disturbance epsilon psi 0.14125 0.04909 2.8776 0.0040
Error e1 omega11 0.48076 0.06991 6.8766 <.0001
  e2 omega22 0.57431 0.06000 9.5723 <.0001
  e3 omega33 0.53826 0.06985 7.7059 <.0001
  e4 omega44 0.28087 0.10080 2.7863 0.0053

Covariance Parms

Standardized Results for Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate Standard
Error		 t Value Pr > |t|
e1 e2 omega12 0.49742 0.06054 8.2158 <.0001
e3 e4 omega34 0.20038 0.08207 2.4416 0.0146

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Ordinary reduced model for H0: beta1=0

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

The CALIS Procedure

Fit

Fit Summary

Fit Summary
Chi-Square 44.5280
Chi-Square DF 2
Pr > Chi-Square <.0001

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Standardized Latent 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.DOUBLE
N Records Read 114
N Records Used 114
N Obs 114
Model Type LINEQS
Analysis Covariances

Optimization

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Standardized Latent Model

The CALIS Procedure

Covariance Structure Analysis: Optimization

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Optimization Problem

Parameter Estimates 9
Functions (Observations) 10
Lower Bounds 5
Upper Bounds 1

Iteration Start

Optimization Start
Active Constraints 0 Objective Function 28.823376572
Max Abs Gradient Element 8.616629831 Radius 7.3847990349

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 1   2.30381 26.5196 0.1494 3.739 0.0862
2   0 6 1   0.73303 1.5708 0.0313 0.0234 1.364
3   0 8 0 ' 0.09003 0.6430 1.1323 0 1.896
4   0 10 0   0.00195 0.0881 0.3291 0 1.218
5   0 12 0   0.0007639 0.00119 0.00180 0 1.032
6   0 14 0   0.0007636 2.616E-7 0.000054 0 1.001
7   0 16 0   0.0007636 2.11E-10 1.166E-6 0 1.001

Iteration Stop

Optimization Results
Iterations 7 Function Calls 19
Jacobian Calls 9 Active Constraints 0
Objective Function 0.0007636028 Max Abs Gradient Element 1.1659764E-6
Lambda 0 Actual Over Pred Change 1.0013197306
Radius 0.000308828    
Convergence criterion (ABSGCONV=0.00001) satisfied.

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Standardized Latent Model

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Fit

Fit Summary

Fit Summary
Chi-Square 0.0871
Chi-Square DF 1
Pr > Chi-Square 0.7680

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Standardized Latent Model

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

ML Estimation

Equations

Linear Equations
Fbirths =   0.9267 (**) Fbreeders + 1.0000   epsilon
W1 =   18.8983 (**) Fbreeders + 1.0000   e1
V1 =   15.4310 (**) Fbirths + 1.0000   e2
W2 =   18.8983 (**) Fbreeders + 1.0000   e3
V2 =   15.4310 (**) Fbirths + 1.0000   e4

Linear Effects

Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
Fbirths Fbreeders beta1 0.92669 0.02648 34.9895 <.0001
W1 Fbreeders lambdaX 18.89827 1.71804 10.9999 <.0001
V1 Fbirths lambdaY 15.43103 1.48869 10.3655 <.0001
W2 Fbreeders lambdaX 18.89827 1.71804 10.9999 <.0001
V2 Fbirths lambdaY 15.43103 1.48869 10.3655 <.0001

Variance Parms

Estimates for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent Fbreeders   1.00000      
Disturbance epsilon psi 0.14125 0.04909 2.8776 0.0040
Error e1 omega11 330.68333 67.11363 4.9272 <.0001
  e2 omega22 321.25513 54.16010 5.9316 <.0001
  e3 omega33 416.33487 80.76320 5.1550 <.0001
  e4 omega44 93.00038 35.56644 2.6148 0.0089

Covariance Parms

Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate Standard
Error		 t Value Pr > |t|
e1 e2 omega12 308.53885 57.24867 5.3895 <.0001
e3 e4 omega34 101.40574 45.51337 2.2280 0.0259

Sq. Mult. Correlations

Squared Multiple Correlations
Variable Error Variance Total Variance R-Square
Fbirths 0.14125 1.00000 0.8587
W1 330.68333 687.82795 0.5192
V1 321.25513 559.37196 0.4257
W2 416.33487 773.47950 0.4617
V2 93.00038 331.11721 0.7191

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Standardized Latent Model

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Standardized Results

Equations

Standardized Results for Linear Equations
Fbirths =   0.9267 (**) Fbreeders + 1.0000   epsilon
W1 =   0.7206 (**) Fbreeders + 1.0000   e1
V1 =   0.6524 (**) Fbirths + 1.0000   e2
W2 =   0.6795 (**) Fbreeders + 1.0000   e3
V2 =   0.8480 (**) Fbirths + 1.0000   e4

Linear Effects

Standardized Effects in Linear Equations
Variable Predictor Parameter Estimate Standard
Error		 t Value Pr > |t|
Fbirths Fbreeders beta1 0.92669 0.02648 34.9895 <.0001
W1 Fbreeders lambdaX 0.72058 0.04851 14.8538 <.0001
V1 Fbirths lambdaY 0.65245 0.04598 14.1901 <.0001
W2 Fbreeders lambdaX 0.67951 0.05140 13.2208 <.0001
V2 Fbirths lambdaY 0.84802 0.05943 14.2680 <.0001

Variance Parms

Standardized Results for Variances of Exogenous Variables
Variable
Type		 Variable Parameter Estimate Standard
Error		 t Value Pr > |t|
Latent Fbreeders   1.00000      
Disturbance epsilon psi 0.14125 0.04909 2.8776 0.0040
Error e1 omega11 0.48076 0.06991 6.8766 <.0001
  e2 omega22 0.57431 0.06000 9.5723 <.0001
  e3 omega33 0.53826 0.06985 7.7059 <.0001
  e4 omega44 0.28087 0.10080 2.7863 0.0053

Covariance Parms

Standardized Results for Covariances Among Exogenous Variables
Var1 Var2 Parameter Estimate Standard
Error		 t Value Pr > |t|
e1 e2 omega12 0.49742 0.06054 8.2158 <.0001
e3 e4 omega34 0.20038 0.08207 2.4416 0.0146

Latent path analysis of simulated Fuller Pig data

Based on STA431s17 HW 7 Check

Standardized Reduced model for testing H0: beta1=0

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

The CALIS Procedure

Fit

Fit Summary

Fit Summary
Chi-Square 44.5278
Chi-Square DF 2
Pr > Chi-Square <.0001