A0732
Title: An ANOVA-like decomposition of logistic regression parameters
Authors: Monia Lupparelli - University of Florence (Italy) [presenting]
Luca La Rocca - University of Modena and Reggio Emilia (Italy)
Alberto Roverato - University of Padova (Italy)
Abstract: A logistic regression setting is considered to study the effect of a focal variable (treatment, risk factor) on a binary outcome given a set of explanatory variables. This effect, measured on the odds-ratio scale, is expected to be heterogenous in multiple models defined by different sets of explanatory variables. Studying this heterogeneity represents a fundamental research question rising in many contexts, i.e., to study distortion of effects, to verify parametric collapsibility with application in precision medicine and mediation analysis. Despite the large interest in this issue, comparing logistic regression coefficients in multiple models, even not nested, is still not a trivial task. Based on a log-hybrid parameterization, an ANOVA-like expansion of the regression coefficient related to the focal variable is provided, where the elements of this expansion are associated with all subsets of the selected variables and are invariant across models. Exploiting this expansion, an exact formula linking the focal regression coefficients in different models has been derived to test hypotheses by answering specific questions simultaneously without fitting multiple logistic models. The resulting class of models has an interesting representation in terms of two-block regression. Results are illustrated for the case of binary variables, but they can also be generalized to the non-binary case.
