function like =  to_llike(b,y,x,a)
% PURPOSE: evaluate tobit log-likelihood
%          for left-censoring case (y <= a is censored)
%-----------------------------------------------------
% USAGE:    like = to_llike(b,y,x,a) 
% where:     b = parameter vector (k x 1)
%            y = dependent variable vector (n x 1)
%            x = explanatory variables matrix (n x m)
%            a = left-censoring point (default = 0)
%-----------------------------------------------------
% NOTE: this function returns a scalar equal to the negative
%       of the log-likelihood function
%       k ~= m because we may have additional parameters
%           in addition to the m bhat's (e.g. sigma)
%-----------------------------------------------------

% written by:
% James P. LeSage, Dept of Economics
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% jlesage@spatial-econometrics.com

% error check
if nargin == 4,
 aterm = a; 
elseif nargin == 3
 aterm = 0;
else
 error('wrong # of arguments to to_llike'); 
end;
   h = .000001;             % avoid sigma = 0
   [m junk] = size(b);
   beta = b(1:m-1);         % pull out bhat
   sigma = max([b(m) h]);   % pull out sigma
   xb = x*beta;
   llf1 = -(y-xb).^2./(2*sigma) - .5*log(2*pi*sigma);  
   xbs = -(aterm-xb)./sqrt(sigma); cdf = .5*(1+erf(xbs./sqrt(2)));
   llf2 = log(h+(1-cdf));
   llf = (y > aterm).*llf1 + (y <= aterm).*llf2;
   like = -sum(llf);% scalar result