Diffey, Simon; Welsh, Alan; Smith, Alison; and Cullis, Brian R., A faster and computationally more efficient REML (PX)EM algorithm for linear mixed models, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 2-13, 2013, 8.
Residual maximum likelihood is the preferred method for estimating variance parameters associated with a linear mixed model. Typically an iterative algorithm is required for the estimation of these parameters. Two algorithms which can be used for this purpose are the EM algorithm and the PX-EM algorithm. Both require specification of the complete data which comprises the incomplete and missing data. We consider a new incomplete data specification which is computationally more efficient than alternative specifications. In the example considered the new incomplete data specification results in the algorithm converging in 30% fewer iterations than the alternative specification. We describe the conditions necessary for this faster rate of convergence to apply in other cases.