Bergrún Tinna Magnúsdóttir: Simultaneous estimation of parameters in the bivariate Emax model

We explore inference in multi-response, nonlinear models. By multi-response we mean models with m>1 response variables and accordingly m relations. We study a system estimation approach for simultaneous computation and inference of the model and (co)variance parameters. A simulation study is carried out that compares the system estimation approach to equation-by-equation estimation for the bivariate Emax model. The simulation results show that when there are dependencies among relations system estimation increases the precision of some but not necessarily all parameter estimates in the bivariate Emax model. We reason that system estimation uses the correlation information to increase the precision for parameters that are difficult to estimate, sometimes at the expenses of other parameters. The overall gain in precision for the parameters in the bivariate Emax model is however positive and the stronger the dependencies the more we gain in precision by using system estimation rather than equation-by-equation estimation.