# single_effect_regression: Bayesian single-effect linear regression In susieR: Sum of Single Effects Linear Regression

 single_effect_regression R Documentation

## 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
)

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.