Question

I am running Logit Regression in Stata.

1. How can I know the explanatory power of the regression (in OLS, I look at R^2)?

2. Is there a meaningful approach in expanding the regression with other independent variables (in OLS, I manually keep on adding the independent variables and look for adjusted R^2; my guess is Stata should have simplified this manual process)?

Answer 1

I’m worried that you are getting the fundamentals of modelling wrong here:

1. The explanatory power of a regression model is theoretically determined by your interpretation of the coefficients, not by the R-squared. The R^2 represents the amount of variance that your linear model predicts, which might be an appropriate benchmark to your model, or not.

2. Identically, the presence or absence of an independent variable in your model requires substantive justification. If you want to have a look at how the R-squared changes when adding or subtracting parts of your model, see help nestreg for help on nested regression.

To summarize: the explanatory power of your model and its variable composition cannot be determined just by crunching the numbers. You first need an adequate theory to build your model onto.

Now, if you are running logit:

• Read Long and Freese (Ch. 3) to understand how log likelihood converges (or not) in your model.
• Do not expect to find something as straightforward as the R-squared for logit.
• Use logit diagnostics on your model, just like you should be after running OLS.

You might also want to read the likelihood ratio Chi-squared test or run additional lrtest commands as explained by Eric.