A Logistic Regression Interpretation

[Ma Xie Er]

I was trying to find an easy interpretation of the predicted probabilities of a logistic regression model, when one of my coworkers claimed that the logistic regression model is a likelihood.

Now, I know that maximum likelihood estimation is used to estimate the parameters, but I didn't think of the model as a likelihood.

The model is E(Y|X)_hat = exp(XBeta_hat)/(1+exp(XBeta_hat)).

Is the above function a likelihood function?

 

[Ma Xie Er]

I was trying to find an easy interpretation of the predicted probabilities of a logistic regression model, when one of my coworkers claimed that the logistic regression model is a likelihood.

Now, I know that maximum likelihood estimation is used to estimate the parameters, but I didn't think of the model as a likelihood.

The model is E(Y|X)_hat = exp(XBeta_hat)/(1+exp(XBeta_hat)).

Is the above function a likelihood function?

I'm going to answer my own question. No, the predicted probability is not a likelihood.

The likelihood is the probability density function, as a function of the data. That is L(p|y) = f(y|p), for a fixed y. The likelihood is telling you how likely p is for a specific value of p, given the data y.

Since the predicted probability does not include all the data (it doesn't include y), you cannot conclude it is a likelihood.