Linear Mixed-Effects Models in chemistry: A tutorial

A common goal in chemistry is to study the relationship between a measured signal and the variability of certain factors. To this end, researchers often use Design of Experiment to decide which experiments to conduct and (Multiple) Linear Regression, and/or Analysis of Variance to analyze the collected data. Among the assumptions to the very foundation of this strategy, all the experiments are independent, conditional on the settings of the factors. Unfortunately, due to the presence of uncontrollable factors, real-life experiments often deviate from this assumption, making the data analysis results unreliable. In these cases, Mixed-Effects modeling, despite not being widely used in chemometrics, represents a solid data analysis framework to obtain reliable results. Here we provide a tutorial for Linear Mixed-Effects models. We gently introduce the reader to these models by showing some motivating examples. Then, we discuss the theory behind Linear Mixed-Effect models, and we show how to fit these models by making use of real-life data obtained from an exposome study. Throughout the paper we provide R code so that each researcher is able to implement these useful model themselves.