When collecting longitudinal patient MRI data, every few years the protocols for running an MRI scan are updated. When this happens, the volumes calculated from the scanner are shifted by a multiplicative factor "alpha". The script simulates brain volume data for 100 patients over ten time points, using realistic values for noise and covariance. The slope of the brain volume decay is then shifted at time point 5 by alpha, simulating a protocol shift for the MRI scanner. The professor I was interning for hypothesized that taking the log of the data would make it easier to accutetely deduce alpha since it would then become an additive factor. This script attempts to prove this hypothesis by creating 1000 different data sets with shifts in them, and then uses a MLEM (Mixed Linear Effects Model) to estimate alpha on both the normal and logged data. It then compares the accuracy of the two methods in the long run and found that the log method both gave slightly more accurate results for estimating alpha. (See Results.txt for more)