single_effect_regression: Bayesian single-effect linear regression

In susieR: Sum of Single Effects Linear Regression

Bayesian single-effect linear regression

Description

These methods fit the regression model y = Xb + e, where elements of e are i.i.d. N(0,s^2), and b is a p-vector of effects to be estimated. The assumption is that b has exactly one non-zero element, with all elements equally likely to be non-zero. The prior on the coefficient of the non-zero element is N(0,V).

Usage

single_effect_regression(
  y,
  X,
  V,
  residual_variance = 1,
  prior_weights = NULL,
  optimize_V = c("none", "optim", "uniroot", "EM", "simple"),
  check_null_threshold = 0
)

single_effect_regression_rss(
  z,
  Sigma,
  V = 1,
  prior_weights = NULL,
  optimize_V = c("none", "optim", "uniroot", "EM", "simple"),
  check_null_threshold = 0
)

single_effect_regression_ss(
  Xty,
  dXtX,
  V = 1,
  residual_variance = 1,
  prior_weights = NULL,
  optimize_V = c("none", "optim", "uniroot", "EM", "simple"),
  check_null_threshold = 0
)

Arguments

y	An n-vector.
X	An n by p matrix of covariates.
V	A scalar giving the (initial) prior variance
residual_variance	The residual variance.
prior_weights	A p-vector of prior weights.
optimize_V	The optimization method to use for fitting the prior variance.
check_null_threshold	Scalar specifying threshold on the log-scale to compare likelihood between current estimate and zero the null.
z	A p-vector of z scores.
Sigma	residual_var*R + lambda*I
Xty	A p-vector.
dXtX	A p-vector containing the diagonal elements of crossprod(X).

Details

single_effect_regression_ss performs single-effect linear regression with summary data, in which only the statistcs X^Ty and diagonal elements of X^TX are provided to the method.

single_effect_regression_rss performs single-effect linear regression with z scores. That is, this function fits the regression model z = R*b + e, where e is N(0,Sigma), Sigma = residual_var*R + lambda*I, and the b is a p-vector of effects to be estimated. The assumption is that b has exactly one non-zero element, with all elements equally likely to be non-zero. The prior on the non-zero element is N(0,V). The required summary data are the p-vector z and the p by p matrix Sigma. The summary statistics should come from the same individuals.

Value

A list with the following elements:

alpha	Vector of posterior inclusion probabilities; alpha[i] is posterior probability that the ith coefficient is non-zero.
mu	Vector of posterior means (conditional on inclusion).
mu2	Vector of posterior second moments (conditional on inclusion).
lbf	Vector of log-Bayes factors for each variable.
lbf_model	Log-Bayes factor for the single effect regression.

single_effect_regression and single_effect_regression_ss additionally output:

V	Prior variance (after optimization if optimize_V != "none").
loglik	The log-likelihood, \log p(y | X, V).

susieR documentation built on March 7, 2023, 6:11 p.m.