A latent variable mixture model for composition-on-composition regression with application to chemical recycling

It is quite common to encounter compositional data in a regression framework in data analysis. When both responses and predictors are compositional, most existing models rely on a family of log-ratio based transformations to move the analysis from the simplex to the reals. This often makes the interpretation of the model more complex. A transformation-free regression model was recently developed, but it only allows for a single compositional predictor. However, many datasets include multiple compositional predictors of interest. Motivated by an application to hydrothermal liquefaction (HTL) data, a novel extension of this transformation-free regression model is provided that allows for two (or more) compositional predictors to be used via a latent variable mixture. A modified expectation-maximization algorithm is proposed to estimate model parameters, which are shown to have natural interpretations. Conformal inference is used to obtain prediction limits on the compositional response. The resulting methodology is applied to the HTL dataset. Extensions to multiple predictors are discussed.