The SAS System

PROC NLP: Nonlinear Maximization


Gradient is computed using analytic formulas.


Hessian is computed using analytic formulas.

The SAS System

PROC NLP: Nonlinear Maximization

Optimization Start
Parameter Estimates
N Parameter Estimate Gradient
Objective
Function
1 a 2.373153 111.514229
2 b_black -0.134660 0.083162
3 b_othrace -0.046020 3.321411
4 b_female -0.483197 15.070609
5 b_age 0.006174 5470.871964
6 b_educ 0.016718 1914.743787
7 b_edlths -0.319932 -0.870915
8 b_edjc 0.138664 5.194659
9 b_edcoll 0.153112 35.775201
10 b_edgrad 0.235061 55.426665
11 b_prestige 0.016475 6658.810981
12 sigma 0.860106 191.352738


Value of Objective Function = -20566.44031


The SAS System

PROC NLP: Nonlinear Maximization


Newton-Raphson Ridge Optimization


Without Parameter Scaling

Parameter Estimates 12
Functions (Observations) 7084

Optimization Start
Active Constraints 0 Objective Function -20566.44031
Max Abs Gradient Element 6658.8109807    

Iteration   Restarts Function
Calls		 Active
Constraints		   Objective
Function		 Objective
Function
Change		 Max Abs
Gradient
Element		 Ridge Ratio
Between
Actual
and
Predicted
Change
1   0 2 0   -20563 3.8909 167.2 0 1.024
2   0 3 0   -20563 0.00621 0.2846 0 1.001
3   0 4 0   -20563 3.028E-8 1.163E-6 0 0.996

Optimization Results
Iterations 3 Function Calls 5
Hessian Calls 4 Active Constraints 0
Objective Function -20562.54324 Max Abs Gradient Element 1.1627082E-6
Ridge 0 Actual Over Pred Change 0.9963065743

GCONV convergence criterion satisfied.


The SAS System

PROC NLP: Nonlinear Maximization

Optimization Results
Parameter Estimates
N Parameter Estimate Approx
Std Err		 t Value Approx
Pr > |t|		 Gradient
Objective
Function
1 a 2.331575 0.114488 20.365315 1.217193E-89 1.9530439E-8
2 b_black -0.140946 0.030493 -4.622211 0.000003864 7.843948E-11
3 b_othrace -0.051844 0.041377 -1.252988 0.210251 6.021532E-10
4 b_female -0.501066 0.021004 -23.855800 4.81657E-121 2.8263067E-9
5 b_age 0.006564 0.000825 7.950957 2.139257E-15 0.000000951
6 b_educ 0.018596 0.008159 2.279177 0.022686 0.000000335
7 b_edlths -0.318422 0.045358 -7.020127 2.422753E-12 -4.40403E-11
8 b_edjc 0.136311 0.040444 3.370355 0.000755 8.738634E-10
9 b_edcoll 0.157421 0.041049 3.834967 0.000127 5.9947971E-9
10 b_edgrad 0.274054 0.061264 4.473365 0.000007820 9.8582569E-9
11 b_prestige 0.016866 0.000902 18.700975 3.275149E-76 0.000001163
12 sigma 0.871562 0.007795 111.811903 0 0.000000152


Value of Objective Function = -20562.54324