then the number of iterations may play a more important role. Consistent with this, we found GEMMA to be 12 times faster than the Lippert et al algorithm, implemented in FaST-LMM, for the smaller HMDP dataset (33 minutes vs 6.8 hours), but only 2 times faster for the WTCCC data (3.3 hours vs 6.2 hours). It is possible that implementational issues, which are important but conceptually less fundamental, also contribute to this difference in speed. Besides this difference in speed, which might be considered a minor issue, by providing efficient methods to compute derivatives our work here lays the foundations for similar efficient analyses for LMMs with multivariate phenotypes17, where multidimensional optimization is required and evaluating the target functions alone is unlikely to suffice.
