# Predicted Probabilities for Logit Models

Last month I asked this question here.

After thinking about it recently, I was wondering if it makes sense to think about logit probabilities in that regards. Since the predictor of a coefficient shows the log odds change in the response variable independent of all other predictors, we would expect that plotting bid vs pr(outcome), with the curve representing a different predictor is simply not useful. So if the coefficient for variable x is 0.5, that would be the log odds change regardless of the values for y, z, or f. Therefore, I'm wondering if it makes sense to make such a graph.

1. Am I thinking about logistic regression correctly? Since logit coefficients are independent of the other predictors, wouldn't a plot like that be largely "useless."

2. If that is the case, what should be the main use for predicted probabilities when using logit models?

Just some sample code if you wish:

df=data.frame(income=c(5,5,3,3,6,5),
won=c(0,0,1,1,1,0),
age=c(18,18,23,50,19,39),
home=c(0,0,1,0,0,1))
str(df)

md1 = glm(factor(won) ~ income + age + home,
data=df, family=binomial(link="logit"))


Thanks!

• It might help to change how you think about chances a little. Rather than thinking in terms of probabilities, which are numbers between $0$ and $1$, logistic regression invites (nay, forces) you to think in terms of log odds (which can be any real number). When you do that, logistic regression looks remarkably like OLS multivariate regression. Perhaps then your present question almost answers itself from this viewpoint?
– whuber
Commented Aug 13, 2012 at 22:06
• Ah, sorry, I was not clear in my post. Right, the coefficient are in log-odds. But those values aren't too information, so I thought people use odds ratios or predicted prob's. I'm specifically talking about the probabilities. Commented Aug 13, 2012 at 23:20

## 1 Answer

I think you are confusing independent with marginal here. The beta gives you the marginal effect , that is, the change in log-odds due to a unit change in the predictor, if all other predictors are the same. You can also think of this as the difference in log-odds for two observations with the same values for all predictors except for one, where they differ by one unit.

The effects are generally not independent though, as what usually happens is that when one predictor changes, the others also change. The plot you suggest is one way of taking into account the multivariate relationships between your predictors. It won't be a "smooth" plot in general if there are two or more predictors.

As a simple example suppose that you had one continuous predictor, income, and a categorical predictor, sex. A plot of predicted probability against income will show two lines- the male line and the female line.