function [beta,std_beta,prop]=logit_mle(t,v)
%LOGIT is based on a logit model:
%  prob(t=1|v)=exp{v'*beta}/(1+exp{v'*beta}.
%  Input: t- N by 1 indicator vector, 1's and 0's
%         v- N by k covariates matrix
%  Output: beta- k by 1 estimated coefficient 
%                using Newton's method
%          std_beta- k by 1 standard errors of beta.
%          prop - estimated probabilities of t=1
%                N by 1 vector

dimv=min(size(v));  
beta=zeros(100,dimv); 
beta_old=zeros(dimv,1); 
c=0.00001; 
for i=1:100 
    Lambda=exp(v*beta_old)./(1+exp(v*beta_old));
    frstder=v'*(t-Lambda);
    scndder=v'*(((Lambda.*(1-Lambda))*ones(1,dimv)).*v);
    beta_new=beta_old+inv(scndder)*frstder;
    if sum(abs(beta_new-beta_old))<c & sum(abs(frstder))<c
	beta=beta_new;
	break
    elseif i==100
	warning='Iterations stop at 100.';
	disp(warning)
	beta=beta_new;
    else
	beta(i,:)=beta_new';
	beta_old=beta_new;
    end
end  

L=exp(v*beta)./(1+exp(v*beta));
Var_beta=inv(v'*(((L.*(1-L))*ones(1,dimv)).*v));
std_beta=sqrt(diag(Var_beta));
prop=exp(v*beta)./(1+exp(v*beta));