Mixed-Effects Additive Transformation Models with the R Package tramME

Abstract

Regression models that accommodate correlated observations and potential nonlinear predictor-outcome relationships are fundamental in analyzing experimental and observational data. Unlike traditional parametric approaches, transformation models make weaker assumptions on the conditional response distribution, thus allowing for a more universal applicability to at least ordered univariate outcomes. This flexibility makes transformation models an attractive choice for modeling complex relationships in a wide range of domains. The R package tramME extends the transformation model framework with general random effect structures and penalized smooth terms to adapt to dependent data and nonlinear predictor-outcome relationships. This paper presents the statistical framework and implementation details of tramME, including its integration with other popular R packages for transformation modeling (mlt), mixed-effects (lme4) and additive models (mgcv). The package employs the efficient Template Model Builder framework (TMB) for fully parametric likelihood-based estimation and inference. Two illustrations demonstrate that tramME can readily model complex, dependent data structures under settings where the choice of the outcome distribution type is challenging.