Statistical Methods for Comparing Regression Coefficients Between Models

TLDR

Statistical methods for comparing regression coefficients between nested models are developed, addressing situations where two linear model explanations of a phenomenon are compared. The study recommends a fundamental shift in model comparison strategies and result presentation in social research. Researchers can evaluate coefficient changes by computing standard errors and related statistics from routine regression outputs when adding covariates. The approach extends to generalized linear models, yielding results for logistic and log-linear models.

Abstract

Statistical methods are developed for comparing regression coefficients between models in the setting where one of the models is nested in the other. Comparisons of this kind are of interest whenever two explanations of a given phenomenon are specified as linear models. In this case, researchers should ask whether the coefficients associated with a given set of predictors change in a significant way when other predictors or covariates are added as controls. Simple calculations based on quantities provided by routines for regression analysis can be used to obtain the standard errors and other statistics that are required. Results are also given for the class of generalized linear models (e.g., logistic regression, log-linear models, etc.). We recommend fundamental change in strategies for model comparison in social research as well as modifications in the presentation of results from regression or regression-type models.