Speaking Stata: Some notes on quadratic fits

Quadratic fits are often used in regression and other modeling projects as either the whole of a model or part of a larger model. In this column, I discuss various small Stata devices that may help, including the twoway qfit command, calculation of the turning point position from coefficient estimates, and plotting the fitted curve over a wider range. The main principles carry over from regression to various more complicated models such as generalized linear models. A specific example is the model known in statistical ecology as Gaussian logit, which is just a logit regression fitting a unimodal bell-like curve to a proportion as a quadratic function of some controlling variable. The column includes commentary on wider historical, scientific, and statistical aspects of quadratic fits, with some remarks on their limitations and alternatives.