Documentation for ‘sibreg’ module

Documentation for the sibreg model class.

class sibreg.model(y, X, labels)

Define a linear model with within-class correlations.

Parameters:

y : array

1D array of phenotype observations

X : array

Design matrix for the fixed mean effects.

labels : array

1D array of sample labels

Returns:

model : sibreg.model

Methods

alpha_mle(self, tau[, sigma2, compute_cov])	Compute the MLE of alpha given variance parameters
likelihood_and_gradient(self, sigma2, tau)	Compute the loss function, which is -2 times the likelihood along with its gradient
optimize_model(self, init_params)	Find the parameters that minimise the loss function for a given regularisation parameter
predict(self, X)	Predict new observations based on model regression coefficients

set_alpha

alpha_mle(self, tau, sigma2=nan, compute_cov=False)

Compute the MLE of alpha given variance parameters

Parameters:

sigma2 : float

variance of model residuals

tau : float

ratio of variance of model residuals to variance explained by mean differences between classes

Returns:

alpha : array

MLE of alpha

likelihood_and_gradient(self, sigma2, tau)

Compute the loss function, which is -2 times the likelihood along with its gradient

Parameters:

sigma2 : float

variance of model residuals

tau : float

ratio of variance of model residuals to variance explained by mean differences between classes

Returns:

L, grad : float

loss function and gradient, divided by sample size

optimize_model(self, init_params)

Find the parameters that minimise the loss function for a given regularisation parameter

Parameters:

init_param : array

initial values for residual variance (sigma^2_epsilon) followed by ratio of residual variance to within-class variance (tau)

Returns:

optim : dict

dictionary with keys: ‘success’, whether optimisation was successful (bool); ‘warnflag’, output of L-BFGS-B algorithm giving warnings; ‘sigma2’, MLE of residual variance; ‘tau’, MLE of ratio of residual variance to within-class variance; ‘likelihood’, maximum of likelihood.

predict(self, X)

Predict new observations based on model regression coefficients

Parameters:

X : array

matrix of covariates to predict from

Returns:

y : array

predicted values

sibreg.simulate(n, alpha, sigma2, tau)

Simulate from a linear model with correlated observations within-class. The mean for each class

is drawn from a normal distribution.

Parameters:

n : int

sample size

alpha : array

value of regression coefficeints

sigma2 : float

variance of residuals

tau : float

ratio of variance of residuals to variance of distribution of between individual means

Returns:

model : regrnd.model

linear model with repeated observations