Date:         Fri, 10 Aug 2001 14:26:16 -0500
Reply-To:     seymour.d.douglas@ACCENTURE.COM
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Seymour Douglas <seymour.d.douglas@ACCENTURE.COM>
Subject:      Logit model in IML
Content-type: text/plain; charset=iso-8859-1

1.   DoubleMatrix2D x;
2.   x = new DenseDoubleMatrix2D(T,K);
3.   System.out.println(x);
4.   DoubleMatrix2D y;
5.   y = new DenseDoubleMatrix2D(T,1);
6.   System.out.println(x);
7.   'x= transpose(DenseDoubleMatrix2D x)
8.   x'x=mult( DenseDoubleMatrix2D  x, DenseDoubleMatrix2D  'x)
9.   invxx=inverse(DenseDoubleMatrix2D  x'x)
10.  'y=transpose(DenseDoubleMatrix2D y)
11.  x'y =mult( DenseDoubleMatrix2D  x, DenseDoubleMatrix2D  'y)
12.  bhat= mult(DenseDoubleMatrix2D  invxx,  DenseDoubleMatrix2D  x'y)
13.  Set initial log-likelihood l0
14.  Count rows to get sample size t=nrow(x)
15.  Count columns in x to get  number of regressors k=ncol(x)
16.  Count the number of ones in y, ysum-sum(y)
17.  Define x*x= matrix multiplication of x, if x*x is a square matrix,
inv(x*x) is the generalized inverse.
18.  Define  element by element  matrix multiplication #
19.  Generate the starting values  for the regression b-hat=inv(x*x)*x'y
20.  Declare a storage matrix (for results)
21.  BEGIN ITERATION LOOP do it=1 to 25 while crit >1.0e-8)
22.  Define z =x*b-hat
23.  Define logistic probability distribution function pdf=exp(-z)/(1+exp
(-z)
24.  Define cumulative logistic distribution function cdf=1/(1+exp(-z)
25.  Define the elements of the gradient vector grad=(y#(1-cdf)-(1-y)#cdf)
#x
26.  Define gradient vector grad =grad[+,]'
27.  Let d =pdf
28.  Define the information matrix inf=(x#d)'x
29.  Define the inverse of the information matrix invinf=inv(inf)
30.  Define current log-likehood loglhood= sum(y#log(cdf)+(1-y)
#log*(1-cdf))
31.  Define the step towards maximum delta =invinf*grad
32.  Let // Define vertical concatenation //
33.  Let Max define the maximum element of a collection of elements
34.  Define the convergence criteria
a.   The change in the log-likelihood Crit1=abs(loglhood-l0)
b.   The gradient length, Crit2 = ssq(grad)
c.   Step length, Crit 3 =ssq(delta)
d.   Concatentate criteria



35.  Define All criteria -Critall=Crit1//Crit2//Crit3
36.  Select maximum of all criteria crit=max(critall)
37.  Update log-likelihood function b-hat=b-hat+delta
38.  Print up results
39.  end
40.  Define logit covariance matrix cov= invinf
41.  Let  vecdiag be an operation that extracts the diagonal elements of a
matrix.
42.  Calculate the standard errors  stderr=sqrt(vecdiag(cov))
43.  Calculate t-stat , t-stat= bhat/stderr
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