%% this subroutine calculates the gradient
%% of the logit log likelikood
%% inputs are y,x,beta and the function
%% returns a (kx1) vector of 1st derivatives
function [grad]=logitgrad(y,x,beta)

nk1=size(x);  %% get dimensions of x
k=nk1(2);   %% parameters
xbeta=x*beta;
exp_xbeta=exp(xbeta);
prob=exp_xbeta./(1+exp_xbeta);
constant=y-prob;
itt=ones(1,k);
derb=kron(itt,constant).*x;
grad=sum(derb)';
end