A0834
Title: Weighted vs unweighted multivariate bilinear regression models
Authors: Jemila Hamid - University of Ottawa (Canada) [presenting]
Abstract: Inference for the growth curve models (GCMs) and the generalized multivariate analysis of variance (GMANOVA) models in general leads to bilinear projections. For this reason, the GCMs are referred to as multivariate bilinear regression models. Assuming multivariate normality, explicit likelihood solutions for the parameters of the GCMs exist. Both the least squares and the likelihood procedures lead to weighted inference, where the weight is the pooled sample variance-covariance matrix. Nevertheless, the variance-covariance estimator for such bilinear regression models is different from the pooled sample variance-covariance matrix; hence, other weighting considerations can be made. It is hypothesized that weights that take the bilinear nature of the design into consideration may, in fact, lead to better inference, at least in some situations. The aim is to present results from extensive simulations performed to examine the relative efficiency gained by using weighted bilinear regression compared to unweighted inference. The relative bias and relative efficiency of the available weighting strategies are also discussed, and a novel weighting algorithm is introduced, involving iteratively re-weighted likelihood estimators, which also accounts for the bilinear nature of the GCMs. Using simulations, it is demonstrated that this iteratively re-weighted approach leads to robust estimators in the presence of outliers and when the model is misfitted.
