We provide heritability estimation for Normal, Bernoulli, Probit, Binomial, and Poisson phenotypes. A standard LMM is used for Normal traits:
A GLMM is used to model the other type of traits:
and 𝐯 and 𝛆 are defined as before.
In both cases, the parameters are the same: 𝛂, 𝓋₀, and 𝓋₁. They are fitted via restricted maximum likelihood for LMM and via maximum likelihood for GLMM. The covariance-matrix 𝙺 given by the user is normalised before the model is fitted as follows:
K = K / K.diagonal().mean()
estimate(y, lik, K, M=None, verbose=True)
Estimate the so-called narrow-sense heritability.
It supports Normal, Bernoulli, Probit, Binomial, and Poisson phenotypes.
y (array_like) – Array of trait values of n individuals.
lik (tuple, "normal", "bernoulli", "probit", "binomial", "poisson") – Sample likelihood describing the residual distribution. Either a tuple or a string specifying the likelihood is required. The Normal, Bernoulli, Probit, and Poisson likelihoods can be selected by providing a string. Binomial likelihood on the other hand requires a tuple because of the number of trials:
("binomial", array_like). Defaults to
K (n×n array_like) – Sample covariance, often the so-called kinship matrix. It might be, for example, the estimated kinship relationship between the individuals. The provided matrix will be normalised as
K = K / K.diagonal().mean().
M (n×c array_like, optional) – Covariates matrix. If an array is passed, it will used as is; no normalisation will be performed. If
Noneis passed, an offset will be used as the only covariate. Defaults to
verbose (bool, optional) –
Trueto display progress and summary;
- Return type
>>> from numpy import dot, exp, sqrt >>> from numpy.random import RandomState >>> from limix.her import estimate >>> >>> random = RandomState(0) >>> >>> G = random.randn(150, 200) / sqrt(200) >>> K = dot(G, G.T) >>> z = dot(G, random.randn(200)) + random.randn(150) >>> y = random.poisson(exp(z)) >>> >>> print(estimate(y, 'poisson', K, verbose=False)) 0.18311439918863426
It will raise a
ValueErrorexception if non-finite values are passed. Please, refer to the
limix.qc.mean_impute()function for missing value imputation.