Log-mean and log-mean linear regression models for multiple binary responses
Year: 2014
Type: preprint
Abstract: In regression models for categorical data a linear model is typically related to the response variables via a transformation of probabilities called the link function. We introduce an approach based on two link functions for binary data named log-mean (LM) and log-mean linear (LML), respectively. The choice of the link function plays a key role for the interpretation of the model, and our approach is especially appealing in terms of interpretation of the eects of covariates on the interactions of responses. Similarly to Poisson regression, the LM and LML regression coecients of single outcomes are logrelative risks, and we show that the relative risk interpretation is maintained also in the regressions of the interactions of responses. Furthermore, certain collections of zero LML regression coecients imply that the relative risks for joint responses factorize with respect to the corresponding relative risks for marginal responses. This work is motivated by the analysis of a dataset obtained from a case-control study aimed to investigate the eect of HIV-infection on multimorbidity, that is simultaneous presence of two or more noninfectious commorbidities in one patient.
Source: arXiv (Cornell University)
Authors: Monia Lupparelli, Alberto Roverato
Institution: University of Bologna
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2170432012