% This Matlab program illustrates the use of the Newton-Raphson algorithm
% to obtain maximum likelihood estimates of a logistic regression.  The data
% and much of the code are taken from Anders Swensen, "Non-linear regression,"
% www.math.uio.no/avdc/kurs/ST110/materiale/opti_30.ps.
% First, load and transform data:
load 'beetle.dat';                   % load data
m=length(beetle(:,1))                % count the rows in the data matrix
x=[];                                % create empty vectors
y=[];
for j=1:m                            % expand group data into individual data
 x=[x,beetle(j,1)*ones(1,beetle(j,2))];
 y=[y,ones(1,beetle(j,3)),zeros(1,beetle(j,2)-beetle(j,3))];
end
beetle2=[x;y]';
% Next, specify starting points for iteration on parameter values:
beta0 = [0;
         0]
% Finally, call the function NR_logistic and use its output
[betaml,Jbar] = NR_logistic(beetle2,beta0)
covmat = inv(Jbar)
stderr = sqrt(diag(covmat))