Latent mixed models

The linear mixed model has been a major research interest of Dr Arthur Gilmour, motivated by problems arising in research data generated by agricultural scientists. He has developed a variety of computer packages associated with the linear mixed model. He has tirelessly assisted researchers in the analysis and interpretation of their data using these packages. In this quest to help researchers he has made several important innovations. The purpose of this paper is to review some of these innovations, including improved iterative schemes for estimating variance parameters, developing a powerful scheme for specification of linear mixed models and exploiting sparsity to reduce the computational burden. Some of these innovations are only implicitly described in computer user guides and deserve wider recognition.