📄 f_sempanel.m
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function lik = f_sempanel(rho,eD,W,detval,T)
% PURPOSE: evaluates concentrated log-likelihood for the
% spatial panel error model using sparse matrix algorithms
% ---------------------------------------------------
% USAGE:llike = f_sem(rho,eD,W,detm,T)
% where: rho = spatial error parameter
% eD = begls residuals
% W = spatial weight matrix
% detm = matrix with [rho log determinant] values
% computed in sem_panel.m using one of
% Kelley Pace's routines
% T = number of time points
% ---------------------------------------------------
% RETURNS: a scalar equal to minus the log-likelihood
% function value at the parameter rho
% ---------------------------------------------------
% written by: James P. LeSage 1/2000
% University of Toledo
% Department of Economics
% Toledo, OH 43606
% jlesage@spatial-econometrics.com
% partly rewritten by J.P. Elhorst 4/2004 to account for spatial panels
% "Specification and Estimation of Spatial Panel Data Models",
% International Regional Science Review, Vol. 26, pp. 244-268.
n = length(W);
gsize = detval(2,1) - detval(1,1);
i1 = find(detval(:,1) <= rho + gsize);
i2 = find(detval(:,1) <= rho - gsize);
i1 = max(i1);
i2 = max(i2);
index = round((i1+i2)/2);
if isempty(index)
index = 1;
end;
detm = detval(index,2);
B = speye(n) - rho*sparse(W);
Be=zeros(n*T,1);
for t=1:T
t1=1+(t-1)*n;t2=t*n;
Be([t1:t2],1)= B*eD([t1:t2],1);
end
epe = Be'*Be;
%lik = (n*T/2)*log(2*pi*epe) - T*detm;
lik = (n*T/2)*log(epe) - T*detm;
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