# 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 - Reinstate Monica 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