Documentation for ‘hetlm’ module

Documentation for the heteroskedastic linear model class.

class hetlm.model(y, X, V)[source]

Define a heteroskedastic linear model and calculate likelihood, gradients, and maximum likelihood estimates of parameters.

Parameters:
y : array

1D array of phenotype observations

X : array

Design matrix for the fixed mean effects.

V : array

Design matrix for the fixed variance effects.
Returns:
model : hetlm.model

heteroskedastic linear model class with input data

Methods

alpha_mle(beta) Compute the maximum likelihood estimate of the fixed mean effect parameters, given particular fixed variance effect parameters and variance of random effects
alpha_ols() Compute the ordinary least squares (OLS) estimate of the fixed mean effect parameters
approx_beta_mle() Analytical approximation to the maximum likelihood estimate of the fixed variance effects
grad_beta(beta, alpha) Compute the gradient with respect to the fixed variance effects of -2*L/n-log(2*pi), where L is the log-likelihood, the function that is minimized to find the MLE
likelihood(beta, alpha[, negative]) Compute the log of the likelihood, the likelihood at the maximum likelihood for the fixed mean effects
optimize_model() Find the maximum likelihood estimate (MLE) of the parameters and their sampling distribution.
alpha_cov  
beta_cov  
alpha_mle(beta)[source]

Compute the maximum likelihood estimate of the fixed mean effect parameters, given particular fixed variance effect parameters and variance of random effects

Parameters:
beta : array

value of fixed variance effects
Returns:
alpha : array

maximum likelihood estimate of alpha given beta
alpha_ols()[source]

Compute the ordinary least squares (OLS) estimate of the fixed mean effect parameters

Returns:
alpha : array

ordinary least-squares estimate of alpha
approx_beta_mle()[source]

Analytical approximation to the maximum likelihood estimate of the fixed variance effects

Returns:
beta : array

approximate MLE of beta
grad_beta(beta, alpha)[source]

Compute the gradient with respect to the fixed variance effects of -2*L/n-log(2*pi), where L is the log-likelihood, the function that is minimized to find the MLE

Parameters:
beta : array

value of fixed variance effects

alpha : array

value of fixed mean effects to gradient for
Returns:
grad_beta : array
likelihood(beta, alpha, negative=False)[source]

Compute the log of the likelihood, the likelihood at the maximum likelihood for the fixed mean effects

Parameters:
alpha : array

value of fixed mean effects to compute likelihood for

beta : array

value of fixed variance effects to compute likelihood for

negative : bool

compute -2*L/n-log(2*pi), where L is the log-likelihood, the function that is minimized to find the MLE. Default is False.
Returns:
L : float

log-likelihood of data given parameters.
optimize_model()[source]

Find the maximum likelihood estimate (MLE) of the parameters and their sampling distribution.

Returns:
optim : dict

keys: MLEs (‘alpha’, fixed mean effects; ‘beta’, fixed variance effects), their standard errors (‘alpha_se’, ‘beta_se’), covariance matrix for sampling distribution of parameter vectors (‘beta_cov’ and ‘alpha_cov’), maximum likelihood (‘likelihood’), whether optimisation was successful (‘success’),