tslmm

tslmm is a complex trait analysis toolkit based on the tskit succinct tree sequence ecosystem.

It fits the following linear mixed model:

$$\mathbf{y} = X\mathbf{b} + Z\mathbf{u} + \boldsymbol{\varepsilon}$$

• $N$, $F$, 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.