tslmm is a complex trait analysis toolkit based on the tskit succinct tree sequence ecosystem.
It fits the following linear mixed model:
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$N$ ,$F$ , and$E$ are the number of individuals, fixed effects, and edges (of the tree sequence). -
$\mathbf{y} \in \mathbb{R}^N$ ,$X \in \mathbb{R}^{N \times F}$ , and$Z \in \mathbb{R}^{N \times E}$ are the trait vector, fixed effects design matrix, and random effects design matrix. -
$\mathbf{b} \in \mathbb{R}^F$ and$\mathbf{u} \in \mathbb{R}^E$ are fixed and random effects coefficients.$\mathbf{u} \sim \mathcal{N}\left(\mathbf{0}, Q_{\mathbf{u}}^{-1}\right)$ where$Q_{\mathbf{u}}$ is the precision matrix. -
$\boldsymbol{\varepsilon}$ is the non-genetic error terms.
See this example for full use.