Changes

== Modeling Relatedness ==

== Modeling Relatedness ==

we use a variance component model to handle familial relationships. In a sample of n individuals, we model the observed phenotype vector ('''y''') as a sum of covariate effects (specified by a design matrix '''X''' and a vector of covariate effects '''β'''), additive genetic effects (modeled in vector '''g''') and non-shared environmental effects (modeled in vector '''ε'''). Thus the null model is:  

we use a variance component model to handle familial relationships. In a sample of n individuals, we model the observed phenotype vector (<math>\mathbf{y}</math>) as a sum of covariate effects (specified by a design matrix <math>\mathbf{X}</math> and a vector of covariate effects <math>\boldsymbol{\beta}</math>), additive genetic effects (modeled in vector <math>\mathbf{g}</math>) and non-shared environmental effects (modeled in vector '''ε'''). Thus the null model is:  

<math>\mathbf{y}=\mathbf{X}\boldsymbol{\beta} +\mathbf{g}+ \boldsymbol{\varepsilon}</math>

<math>\mathbf{y}=\mathbf{X}\boldsymbol{\beta} +\mathbf{g}+ \boldsymbol{\varepsilon}</math>