Programming and Numerical Analysis: Programming with LIMDEP and NLOGIT

Command Language

LIMDEP and NLOGIT’s command language may be used to write routines and programs for:

  • New estimators
  • Test statistics
  • Manipulate model results
  • Standardize groups of calculations
  • Simulate model and estimator behavior

Features of the Programming Language

The programming language includes:

  • All model estimation commands
  • Computational tools
    • Matrix algebra - subscripting in matrices
    • Scalar scientific calculator
    • Variable transformations and creating new variables
  • Control statements and looping
  • Procedures with adjustable parameters (subroutines)
    • PROCEDURE (argument, ..., ...)
    • EXECUTE procedure
    • Bootstrapping
    • Repeated execution of procedures
    • Libraries of procedures

Numerical Analysis Tools

Numerical analysis tools are provided for analyzing functions of a variable and functions of the data:

  • Function evaluation
  • Function plotting
  • Compute derivatives and save as gradient vector
  • Integration by quadrature
  • Integration by trapezoids
  • Integration by simulation
  • Matrix algebra
    • Characteristic roots
    • Roots of dynamic equations
    • Character vectors
    • Singular value decomposition
  • Scientific calculator: dozens of functions
  • Values of and asymptotic variances for nonlinear functions

Example: Poisson Model with a Fixed Value Restriction

The following is an iterative procedure to fit a Poisson regression while constraining one of the parameters to equal one (used when the ‘exposure’ period differs by observation).

?=====================================================================
? Set up the matrix procedure.  We strip off the last element of 
? b to obtain the vector beta. delta is the update vector, 
? initialized at 0, so the first iteration uses the starting values.
?=====================================================================
NAMELIST	; x = one,a,c,d,e,c67,c72,c77,p77 $
POISSON	; Lhs = num ; Rhs = x,logmth $
MATRIX	; beta = B(1:9) ; delta = [9|0] $   
CALC	; conv = 1  $
?=====================================================================
? 1.  Update beta.
? 2.  Compute expected values and residuals, imposing constraint 
?     on slope on log(months)=1.
? 3.  Iterate using Newton's method
? Exit rule, conv must be initialized above because it is checked 
? at entry to the iteration, not at exit.  
?=====================================================================
PROCEDURE
MATRIX	; beta = beta - delta 	$ update coefficient vector
CREATE	; ey = Exp(x'beta + logmth) 
  	; uy = ey - num $
MATRIX	; g = x'uy 		? first derivatives vector
	; h =   			? negative of 2nd derivatives
	; delta = h * g 		$ update vector
CALC	; List ; conv = g'delta	$ convergence measure
ENDPROCEDURE
?=====================================================================
? Execute procedure until convergence, then display final results. 
?=====================================================================
EXECUTE ; until conv < .00001 $ 
MATRIX  ; Stat(beta,h,X) $

This program produces the following listing prior to the statistical output:

    CONV    =  .84415590973720680D+03
    CONV    =  .16345624762698120D+03
    CONV    =  .12305922124358570D+02
    CONV    =  .11423883549203680D+00
    CONV    =  .13468418817524850D-04
    CONV    =  .25224428518082010D-12
    CONV < .00001