Predicting the Production and Depletion of Rare Earth Elements and Their Influence on Energy Sector Sustainability through the Utilization of Multilevel Linear Prediction Mixed-Effects Models with R Software

For many years, rare earth elements (REEs) have been part of a wide range of applications (from cell phones and batteries to electric vehicles and wind turbines) needed for daily life all over the world. Moreover, they are often declared to be part of “green technology”. Therefore, the data obtained from the United States Geological Survey (USGS) on the reserve and production of rare earth elements underwent treatment using the multivariate imputation by chained equations (MICE) algorithm to recover missing data. Initially, a simple linear regression model was chosen, which only considered fixed effects (β) and ignored random effects (Ui). However, recognizing the importance of accounting for random effects, the study subsequently employed the multilevel Linear Mixed-Effects (LME) model. This model allows for the simultaneous estimation of both fixed effects and random effects, followed by the estimation of variance parameters (γ, ρ, and σ2). The study demonstrated that the adjusted values closely align with the actual values, as indicated by the p-values being less than 0.05. Moreover, this model effectively captures the sample’s error, fixed, and random components. Also, in this range, the findings indicated two standard deviation measurements for fixed and random effects, along with a variance measurement, which exhibits significant predictive capabilities. Furthermore, within this timeframe, the study provided predictions for world reserves of rare earth elements in various countries until 2053, as well as world production forecasts through 2051. Notably, China is expected to maintain its dominant position in both reserve and production, with an estimated production volume of 101,985.246 tons, followed by the USA with a production volume of 15,850.642 tons. This study also highlights the periodic nature of production, with a specific scale, as well as periodicity in reserve. These insights can be utilized to define and quantify sustainability and to mitigate environmental hazards associated with the use of rare earth materials in the energy industry. Additionally, they can aid in making informed decisions regarding at-risk rare earth reserves, considering potential future trends in electric vehicle (EV) production up to the year 2050.