Lecturer: Tatjana von Rosen (Stockholm University)
Title: On Prediction in Mixed Linear Models with Structured Covariance Matrices
The mixed linear models have become a powerful and widely used tool for the analysis of data having complicated structures and exhibiting various dependence patterns, e.g. repeated measures or longitudinal data containing multiple sources of variation. Prediction problems in univariate mixed linear models have got considerable attention due to numerous applications in small area estimation, school effectiveness studies and animal breeding, among others. Despite complexity of real-life phenomena, the multivariate mixed linear models have received little attention. This work concerns prediction of linear combinations involving both fixed and random effects in balanced multivariate mixed liner models which can handle both the multivariate response and spatial or/and temporal dependence. More specifically, the equality of linear predictors under two multivariate mixed effects models with different covariance matrices is of interest. In practice, it can be difficult to decide about an appropriate covariance structure of random effect, so using equivalent linear models can resolve that problem and possibly reduce computations. The task is rather complicated if one aim is to get explicit results, hence we shall focus on a certain class of covariance matrices whose structure is preserved under matrix inversion.
Lecturer: Toni Duras (Jönköping University)
Title: Estimations and applications of common principal component analysis.
In this presentation, we describe some basic properties of Common Principal Component Analysis (CPCA) originally proposed by Flury (1984). We discuss the difference between the maximum likelihood estimator and a simplified estimator proposed by Krzanowski (1984). Some applications of CPCA are discussed and an empirical case study of Swedish municipality-level data is presented where we compare the two estimators.