I am new to categorical data analysis and I would like to ask for a simple explanation of the difference between linear predictions and predicted probabilities in a logit model.


1 Answer 1


I assume by the Logit model, you are talking about the logistic model. In the logistic regression model, the linear prediction is the weighted sum of feature values of the sample. It is assumed in logistic regression that the log-odd of $y=1$ is equal to this summation. See the equation below.

$log(\frac{p}{1-p})=\sum_{j=1}^{m}x_m\beta_m$. Here p is the predicted probabilities.

Let's denote the weighted sum by LP(linear prediction). After reversing the equation we have:


So predicted probability is the predicted probability that a sample has label 1. The linear prediction is just the output of an intermedia step.


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