# Validation of linear logistic regression for binned binomial data

I am looking at how pavement thickness variation parameters(absolute thickness, variance, slopes, critical points) relate to distress occurrence.

After some research, I have settled on the linear logistic model for regression testing. In order to get distress rates (pHat), I bin my binary data data using MATLAB's binning algorithm and then use the following function to fit a logistic linear model:

function[pihat] = fitRegression(X,Y)
%X = [n x 1] array of predictor variable
%Y = [n x 1] logical array of distress occurrence

[N,edges,bin] = histcounts(X); %use MATLAB automatic binning algorithm
X = (edges(1:end-1) + edges(2:end))/2; % get mean bin values for regression fitting.
bin = bin(bin~=0); %remove 0 data
for i = 1:length(N)
pihat(i) = sum(Y(bin==i))./N(i); % calculate pihat for each bin
end

Y = pihat;

• Why do you bin the data ? If I understand your code (I don't know mathlab) you have an explanatory variable $X$ and a dependent variable $Y$ where $Y$ is binary, so you can do logistic regression without binning ? or is $X$ categorical ? if $X$ is categorical, then binning should make no difference compared to using the binary $Y$ as an dependent.