ENH: comparing params or effects across nested nonlinear models, Logit, ...

[josef-pkt]

I browsed several articles on this topic but just to get a basic overview

An omitted variable inside a nonlinear mean or inverse link function adds extra noise, so that variance of the true linear predictor increases. The additional noise shifts the mean (Jensen's inequality), similar to issue with control functions.

In binary models like Logit or Probit, the coefficients/params are scaled, i.e. scale dependent. In nested models, extra terms will capture additional random fluctuation, change the underlying scale (variance of linear term), which then implies a different scaling of the parameters.

Several articles show methods to work around this.
The main alternative is to look at "margins", marginal or partial effects instead of looking directly at params.

Two references, but AFAIR I skimmed some more

Williams, Richard, and Abigail Jorgensen. “Comparing Logit & Probit Coefficients between Nested Models.” Social Science Research 109 (January 1, 2023): 102802. https://doi.org/10.1016/j.ssresearch.2022.102802.

Mize, Trenton D., Long Doan, and J. Scott Long. “A General Framework for Comparing Predictions and Marginal Effects across Models.” Sociological Methodology 49, no. 1 (August 1, 2019): 152–89. https://doi.org/10.1177/0081175019852763.

(aside we don't have a generic "post-estimation" label, the main related label is diagnostic.)