' MLOGIT1.PRG (1.0 - 6/29/98)
' revised for version 4.0 (10/27/2000 h)
' example program for EViews LogL object
'
' multinomial logit with three choices
' with two individual specific regressors
'
' for a discussion, see Section 19.7 of Greene, William H. (1997) 
' Econometric Analysis, 3rd edition, Prentice-Hall

'change path to program path
%path = @runpath
cd "{%path}"

' load artificial data
load mlogit

' declare parameter vector
coef(3) b2
coef(3) b3
' true values are
' b2(1) -0.4 b2(2) 1 b2(3) -0.2
' b3(1) -0.4 b3(2) 0.3 b3(3) 0.5


' setup the loglikelihood
logl mlogit
mlogit.append @logl logl1

' define index for each choice
mlogit.append xb2 = b2(1)+b2(2)*x1+b2(3)*x2
mlogit.append xb3 = b3(1)+b3(2)*x1+b3(3)*x2

' define prob for each choice
mlogit.append denom = 1+exp(xb2)+exp(xb3)
mlogit.append pr1 = 1/denom
mlogit.append pr2 = exp(xb2)/denom
mlogit.append pr3 = exp(xb3)/denom

' specify likelihood
mlogit.append logl1 = (1-dd2-dd3)*log(pr1)+dd2*log(pr2)+dd3*log(pr3)

' specify analytic derivatives
for !i=2 to 3	
	mlogit.append @deriv b{!i}(1) grad{!i}1 b{!i}(2) grad{!i}2 b{!i}(3) grad{!i}3
	mlogit.append grad{!i}1 = dd{!i}-pr{!i}
	mlogit.append grad{!i}2 = grad{!i}1*x1
	mlogit.append grad{!i}3 = grad{!i}1*x2
next

' get starting values from binomial logit

equation eq2.binary(d=l) dd2 c x1 x2
b2 = eq2.@coefs

equation eq3.binary(d=l) dd3 c x1 x2
b3 = eq3.@coefs

' check analytic derivatives at starting values
freeze(tab1) mlogit.checkderiv
show tab1

' do MLE and display results
mlogit.ml(showopts,m=1000,c=1e-5)
show mlogit.output

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