# Hosmer-Lemeshow GOF test in Matlab

I am trying to calculate the Hosmer-Lemeshow Goodness-of-Fit (GOF) test, following the steps presented in the book "Logistic Regression. A Self- Learning Text" by David Kleinbaum and M. Klein.

The following function calculates all the steps, gives as outputs the chi-squared, degrees of freedom and the p-value, as well as some interesting plots described in the manual, which look fine to me.

However, I get a completely different result when I run this test in R (holsem.test, from ResourceSelection package).

I was surprised I could not find any code online, so maybe this becomes useful in the future. Neither could I see what I am doing wrong. Maybe R uses a very different method?

If you are also keen to find out and see this work, please feel free to join.

Thank you a lot,

EDIT: one thing that I find intriguing is the fixed lenght or size of the deciles. My data, for example, has 5479 observations, which cannot be nicely divided by 10. This may lead to some discrepancies bewteen methods. However, I believe 5479 is a long enough series and ignoring a maximum of 9 observations should not be of great harm.

 % This function performs the Hoslem-Lemeshow Goodness-of-Fit test
% 06-January-2017 [email protected]
%
% Inputs
%       Q: The number of groups or quantiles (normally Q=10).
%       y: 1D array of observations. Must be a series of {0,1}.
%       fit: 1D array of the model's fitted values.
% Outputs
%       chi2: The Hosmer-Lemeshow chi-square statistics.
%       df: Degrees-of-freedom.
%       p: p-value

function [chi2,df,p]=hoslem(fit,y,Q)
[ordems,I]=sort(fit,'descend'); % Sorts the fitted values
% Calculates the length of each decile.
% Note that the division of length/10 may not be exact. Therefore, the
% considered series may differ from original inputs in up to 10
% observations, at most. This error shold be to non-significant for very
% long series.
qlen=round(length(y)/Q)-1;
qlens=zeros(Q+1,1);
for i=1:Q+1
qlens(i,1)=1+(i-1)*qlen;    % Determines the thresholds of deciles
end
qlims=zeros(Q+1,1);             % Positions of thresholds
for i=1:Q+1
qlims(i,1)=ordems(qlens(i,1));
end
plot(1:Q+1,qlims,'o')
% Couts Observed Cases por Decile (Ocq)
ocq=zeros(Q,1); t=1; count=0;
for i=1:max(qlens)-1
if count==qlen
t=t+1; count=0;
end
ocq(t,1)=ocq(t,1)+(y(I(i)));
count=count+1;
end
% Couts Non-Observed Cases por Decile (Oncq)
oncq=zeros(Q,1); t=1; count=0;
for i=1:max(qlens)-1
if count==qlen
t=t+1; count=0;
end
if (y(I(i)))==0
oncq(t,1)=oncq(t,1)+1;
end
count=count+1;
end
figure(1)
plot(ocq); hold on; plot(oncq)
legend('Observed cases','Non-observed cases'); hold off
% Expected cases (Ecq) e noncases (Encq) per Decile
ecq=zeros(Q,1);
t=1; count=0;
for i=1:max(qlens)-1
if count==qlen
t=t+1; count=0;
end
ecq(t,1)=ecq(t,1)+ordems(i);
count=count+1;
end
figure(2)
plot(ecq,ocq,'-o'); hold on;
xlabel('Expected cases'); ylabel('Oobserved cases');
encq=qlen-ecq;
% Calculates HL statistics
chi2= sum(sum(((ocq-ecq).^2)/ecq)) + sum(sum(((oncq-encq).^2)/encq));
df=Q-2;
p=1-chi2cdf(chi2,Q-2);
end