Modeling environmental factors for pedigrees

Specialeforsvar ved Eleni Vradi

Titel: Modeling environmental factors for pedigrees

abstract: When analysing family data it is common to sample families or related individuals because they contain an aggregation of the genes that might in uence a phenotype of interest. The genetic correlation between any two family members can be computed by applying simple probability computations based on the Mendelian law of segregation. But families do not just share genes, they also share unmeasured environmental factors. For modelling such data, we will consider the following linear mixed e ects model, Y = X + Zu + . If we assume that all individuals (n) in a pedigree are equally correlated from their environmental factors, then we can introduce a compount symmetrix matrix of correlation equal to one. In this thesis we propose a modied correlation matrix for the environmental relationship between the family members by introducing two parameters in the correlation matrix A,  - the correlation between the spouses- and  - the probability that the unmeasured latent environmental e ect will be segregated to o springs. We use graph theory and path analysis to end the shorthest path that connect two individuals in a given pedigree which will give the desired covariance structure. In this thesis we show that the proposed modied covariance matrix is well de
ned, but mainly we are interested to examine if the modied matrix is a better tool for estimating environmental correlations. Moreover we estimate the unknown parameters,  and  by Maximum Likehood Estimation, and we use AIC scores for model selection. Simulated data were used to illustrated our proposed method. The results show that the modied environmental model give good estimates for the xed and random e ect parameters in the model. In our simulations we also show that the introducetion of two extra parameters,  and  in the modied environmental matrix, does not result in higher AIC score, which gives the proposed model a good model  t, or sometimes even better
t that the other models we compare it with.

Vejledere: Susanne Ditlevsen /Claus Ekstrøm, SUND
Censor: Ulrich Halekoh, SDU