Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale

Random intercept models are linear mixed models (LMM) including error and intercept random effects. Sometimes heteroscedasticity is included and the response variable is transformed into a logarithmic scale, while inference is required in the original scale; thus, the response variable has a log-normal distribution. Hence, correction terms should be included to predict the response in the original scale. These terms multiply the exponentiated predicted response variable, which subestimates the real values. We derive the correction terms, simulations and real data about the income of elderly are presented to show the importance of using them to obtain more accurate predictions. Generalizations for any LMM are also presented.

Automated summary

The study demonstrates the importance of using correction terms in linear mixed models to obtain more accurate predictions, especially when considering log-normal distribution. Through simulations and real data analysis, it is proven the significance of correction terms in improving prediction accuracy.