MIXED LINEAR MODELS B´ eatrice Byukusenge Link¨ oping University First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017 First Network Meeting for Sida- B´ eatrice Byukusenge (UR and LiU) Presentation at the 2016 APM / 6
My Advisors Martin Singull Dietrich von Rosen Nzabanita Joseph Main advisor Assistant advisor Assistant advisor Link¨ oping University Swedish University of Agricultural Science University of Rwanda First Network Meeting for Sida- B´ eatrice Byukusenge (UR and LiU) Presentation at the 2016 APM / 6
About the research Suppose we are following n individuals at each of the p occasions. We can represent the data in a matrix X ∈ R p × n where each column corresponds to one individual. Usually, there are more than one treatment group among the individuals. Mathematically, we represent the model as follows X p × n = A p × m B m × r C r × n + E p × n . where, X is the response or observation matrix; A is the within individual design matrix; B is the parameter matrix; C is the between individual design matrix and E is the error matrix. This is called a growth curve model (GCM). There are several assumptions! First Network Meeting for Sida- B´ eatrice Byukusenge (UR and LiU) Presentation at the 2016 APM / 6
About the research We are interested in the GCM where there is the presence of a random effect. X p × n = A p × m B m × r C r × n + Z p × k ∆ ′ k × n + E p × n . where, Z is a design matrix for random effects and ∆ represents the random effects parameters in the model. We put the following assumptions on the model: that k ≤ m , that C ( Z ) ⊆ C ( A ), where C ( Z ) denotes the linear space generated by the columns of Z and that Z and A are of full column rank matrices. The problem 1: Estimate the parameters B and ∆ . The problem 2: Calculate and analyze residuals. First Network Meeting for Sida- B´ eatrice Byukusenge (UR and LiU) Presentation at the 2016 APM / 6
Impact and Applications of My Research Analysis of repeated measurements data, with the random effects taken into account New research results concerning residuals in high dimension, Contribution to effective research at UR Qualified for teaching and research First Network Meeting for Sida- B´ eatrice Byukusenge (UR and LiU) Presentation at the 2016 APM / 6
THANK YOU First Network Meeting for Sida- B´ eatrice Byukusenge (UR and LiU) Presentation at the 2016 APM / 6
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