partial correlation for logistic regression

Question

I am looking for an equivalent of partial correlation but for logistic regression. I.e., I want to have a measure of an effect a variable have on the outcome, independent of other variables in the model, that is scaled between -1 and 1. References would also be appreciated

Answer 1

One way would be to compute standardized coefficients, standardizing both by the standard deviation of the corresponding predictor and the standard deviation of $y^*$, the latent continuous variable underlying the binary outcome. Standardized coefficients do not have the same interpretation as partial correlations, but they are a scale-free way of describing the relationship between a predictor and the outcome conditional on the other covariates.

Another method would be to use one of the pseudo-$R^2$ measures available for logistic regression and compute the change in the pseudo-$R^2$ corresponding to removing each predictor from the full model while keeping other predictors in the model, which is how the squared semi-partial correlation is computed in linear regression. McKelvey & Zavoina's $R^2$ is a nice choice because it also relies on the continuous latent variable $y^*$.

Answer 2

It is not related with partial correlation, but something you can do to measure the effect a variable has on the outcome of logistic regressions is the Odds Ratio statistic.

It can be interpreted as follow: for a one-unit increase in your continuous predictor variable, the odds of the dependent variable being positive (=1) increase by factor x. If you have a OR of 1.5 if means that a one unit increase in the continuous variable leads to a 50% increase in the odds of the event.

The odds ratio of each variable can be obtained by the exponentiation of the trained model coefficients.