# Which measure of model fit to report when performing likelihood based regression: AIC, BIC, Pseudo R-square?

I'd like to hear your opinions on the following:

• What parameters would you report when estimating different likelihood based regression? AIC, BIC, Pseudo $R^2$?
• What is the standard to report?

It should be a parameter which answers the question of how good the specified model is.

• Probably depends heavily on the field and journal you are interested in. – Sacha Epskamp Jun 7 '11 at 19:55
• See stats.stackexchange.com/q/577/159 for some discussion. – Rob Hyndman Jun 8 '11 at 4:41
• Nice link, @RobHyndman, here's a nice discussion on pseudo $R^2$, : stats.stackexchange.com/questions/3559/… – gung Nov 14 '11 at 4:49
• None of the measures mentioned is a measure of goodness of fit. They are mainly measures of predictive discrimination. I tend to report pseudo $R^2$ and Somers' $D_{xy}$ rank correlation between predicted and observed $Y$, which is a simple translation of $c$-index (ROC area) when $Y$ is binary. – Frank Harrell Dec 15 '11 at 14:05

## 2 Answers

Which is "standard" must depend on field. Like @EpiGrad , I often see none reported.

But in model building, I usually find that the various measures agree; when they do not, it is worth thinking about the models. Indeed, it is always worth thinking about the models - hopefully with a subject matter expert.

A model which makes no substantive sense is a bad model, regardless of any statistical measure; a model which leads to insight is a good model.

• You might consider using either italics or bold face to set off particular words of emphasis. ALL CAPS just doesn't look pleasant (to my eyes, at least). – cardinal Nov 14 '11 at 0:42
• I have gone ahead and made the edits. I hope you don't mind. Cheers. :) – cardinal Nov 14 '11 at 21:41

Frankly, in my field, I never see measures of model fit reported. They tend to get used as internal diagnostics, with the assumption that by the time you've reached the point where you're trying to report model results, you've properly tuned your model.

In essence, we're interested in estimates of effect - if your model fits terribly, why are you (hypothetical you, not @author) trying to publish it?