Fast estimation of mixed-effects location-scale regression models

As a result of advances in data collection technology and study design, modern longitudinal datasets can be much larger than they historically have been. Such "intensive" longitudinal datasets are rich enough to allow for detailed modeling of the variance of a response as well as the mean, and a flexible class of models called mixed-effects location-scale (MELS) regression models are commonly used to do so. However, fitting MELS models can pose computational challenges related to the numerical evaluation of multi-dimensional integrals; the slow runtime of current methods is inconvenient for data analysis and makes bootstrap inference impractical. In this paper, we introduce a new fitting technique, called FastRegLS, that is considerably faster than existing techniques while still providing consistent estimators for the model parameters.