A latent variable approach to shift from discrete to continuous explanatory variables in experimental settings

Silvia D’Angelo, Trinity College Dublin

Abstract: In experimental settings, continuous explanatory variables of interest often have to be discretized to doses, in order to investigate their impact on an outcome variable. We discuss a latent variable approach that allows to flexibly infer the relationship between the outcome and the input doses in experimental settings, by introducing a prior distribution on the doses which permits to model their continuous counterparts, treated as latent variables. The proposed framework can be used for predictive purposes, and further allows to shift the focus on predicting the explanatory variables given some desired values of the outcome variable. The method is illustrated in application to the Switzerland grassland diversity experiment dataset.