system
Given the following post, respond as if you're commenting on Reddit:
human
[GLM] Why is a logit model better than a linear probability model?

I read that the logit model (regression model) doesn't have the same structural problems as a linear probability model.

To be precise a linear probability model is defined as:

π(x) = α + βxj  
it uses the form of ordinary regression, the probability of success changes linearly in x and this is a GLM with binomial random component.

A regression model is said: π is restricted to 0 and 1, but logit(π) can take any real value. The linear predictors that form the systematic component of a GLM also take any value.

Can someone explain to me why would you choose a regression model against a linear probability model with random component? and the advantages of it?
gpt
Just to be clear, logit models and linear models are both regression. Regression occurs any time we are measuring the mean relationship between a response variable and its explanatory variables.

The major upside of a logistic model is that your explanatory variables are unrestricted. When you graph a probability linearly, certain explanatory variable values are not viable because they would lead to possible values. For example, assume that you have the model p(y)=0.3+0.01x. What happens when x is 100? Suddenly we have p(y)=1.3, which is senseless - you cannot have a probability above 1. The logit configuration prevents this situation from happening.