0
$\begingroup$

How do you find the coefficients for logistic regression?

Is it a case of just transforming the samples from the dependent variable and preceding to fit it like a linear regression?

$\endgroup$
0

1 Answer 1

-1
$\begingroup$

No, it is not just transforming the outcome variable and performing linear regression. There is a difference between using a link function, and transforming the outcome. For example, using a log link, you are estimating $\log( E(Y|X) )$, but if you log transform the outcome variable and use linear regression, you are estimating $E( \log(Y) | X )$, which is totally different (see Jensen's inequality, for example).

To fit a logistic regression model you perform maximum likelihood. The data is assumed to follow a Bernoulli distribution, conditional on the covariates. The success probability is equal to the inverse logit of $X \beta$, i.e., $1/(1+\exp(-X \beta))$, and you can form the likelihood out of that. Optimize that as a function of $\beta$ and you have the MLE, which is what you get when you get when you fit a logistic regression model.

$\endgroup$

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