3
$\begingroup$

Suppose I am fitting a logistic regression with intercept only, which is equivalent tho using the count to estimate the outcome probability and make prediction.

Can I say following?

We are using prior only to make the prediction.

I think some persons from CV corrected me, that the word prior has close relationship with Bayesian statistics, and the statement is not correct.

If it is not accurate, what should I say if we only use the counts to estimate the outcome probability?

$\endgroup$
3
  • 1
    $\begingroup$ Try: We are using "counts" only to make the prediction" $\endgroup$
    – Jon
    Aug 15, 2016 at 18:28
  • 3
    $\begingroup$ Unless you're doing Bayesian Logistic regression, don't use the word prior. $\endgroup$
    – Jon
    Aug 15, 2016 at 18:29
  • $\begingroup$ If I read that, it would sound like a tautology. Of course in any Bayesian estimation a prior is used to make the posterior which is the prediction! Just don't use the word prior if it's not Bayesian. $\endgroup$ Aug 15, 2016 at 18:36

2 Answers 2

1
$\begingroup$

I say it's fine.

Logistic regression estimates $P(Y = 1\vert X = x)$.

$$ P(Y = 1\vert X = x) = \dfrac{ P(X = x\vert Y = 1)P(Y = 1) }{ P(X = x) } $$

$P(Y = 1)$ is the prior probability that $Y = 1$.

If we only use an intercept in our model, no matter what features we have, then the probability predicted by the logistic regression model is the proportion of $Y$-values with $Y = 1$. This is $P(Y = 1)$, so the prior probability that $Y = 1$.

$\endgroup$
-1
$\begingroup$

Answered in comments by Jon:

Try: We are using "counts" only to make the prediction". Unless you're doing Bayesian Logistic regression, don't use the word prior.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.