cellregmap.CellRegMap

class cellregmap.CellRegMap(y, E, W=None, Ls=None, E1=None, hK=None)

Mixed-model with genetic effect heterogeneity.

The CellRegMap model can be cast as:

𝐲 = W𝛂 + 𝐠𝛽₁ + 𝐠⊙𝛃₂ + 𝐞 + 𝐮 + 𝛆, (1)

where:

𝛃₂ ~ 𝓝(𝟎, 𝓋₃𝙴₀𝙴₀ᵀ), 𝐞 ~ 𝓝(𝟎, 𝓋₁ρ₁𝙴₁𝙴₁ᵀ), 𝐮 ~ 𝓝(𝟎, 𝓋₁(1-ρ₁)𝙺⊙𝙴₂𝙴₂ᵀ), and 𝛆 ~ 𝓝(𝟎, 𝓋₂𝙸).

𝐠⊙𝛃 is a random effect term which models the GxC effect. Additionally, W𝛂 models additive covariates and 𝐠𝛽₁ models persistent genetic effects. Both are modelled as fixed effects. On the other hand, 𝐞, 𝐮 and 𝛆 are modelled as random effects 𝐞 is the environment effect, 𝐮 is a background term accounting for interactions between population structure and environmental structure, and 𝛆 is the iid noise. The full covariance of 𝐲 is therefore given by:

cov(𝐲) = 𝓋₃𝙳𝙴₀𝙴₀ᵀ𝙳 + 𝓋₁ρ₁𝙴₁𝙴₁ᵀ + 𝓋₁(1-ρ₁)𝙺⊙𝙴₂𝙴₂ᵀ + 𝓋₂𝙸,

where 𝙳 = diag(𝐠). Its marginalised form is given by:

𝐲 ~ 𝓝(W𝛂 + 𝐠𝛽₁, 𝓋₃𝙳𝙴₀𝙴₀ᵀ𝙳 + 𝓋₁(ρ₁𝙴₁𝙴₁ᵀ + (1-ρ₁)𝙺⊙𝙴₂𝙴₂ᵀ) + 𝓋₂𝙸).

The CellRegMap method is used to perform an interaction test:

The interaction test compares the following hypotheses (from Eq. 1):

𝓗₀: 𝓋₃ = 0 𝓗₁: 𝓋₃ > 0

𝓗₀ denotes no GxE effects, while 𝓗₁ models the presence of GxE effects.