# kriging_rss: Compute Distribution of z-scores of Variant j Given Other... In susieR: Sum of Single Effects Linear Regression

## Compute Distribution of z-scores of Variant j Given Other z-scores, and Detect Possible Allele Switch Issue

### Description

Under the null, the rss model with regularized LD matrix is z|R,s ~ N(0, (1-s)R + s I)). We use a mixture of normals to model the conditional distribution of z_j given other z scores, z_j | z_{-j}, R, s ~ ∑_{k=1}^{K} π_k N(-Ω_{j,-j} z_{-j}/Ω_{jj}, σ_{k}^2/Ω_{jj}), Ω = ((1-s)R + sI)^{-1}, σ_1, ..., σ_k is a grid of fixed positive numbers. We estimate the mixture weights π We detect the possible allele switch issue using likelihood ratio for each variant.

### Usage

```kriging_rss(
z,
R,
n,
r_tol = 1e-08,
s = estimate_s_rss(z, R, n, r_tol, method = "null-mle")
)
```

### Arguments

 `z` A p-vector of z scores. `R` A p by p symmetric, positive semidefinite correlation matrix. `n` The sample size. (Optional, but highly recommended.) `r_tol` Tolerance level for eigenvalue check of positive semidefinite matrix of R. `s` an estimated s from `estimate_s_rss`

### Value

a list containing a ggplot2 plot object and a table. The plot compares observed z score vs the expected value. The possible allele switched variants are labeled as red points (log LR > 2 and abs(z) > 2). The table summarizes the conditional distribution for each variant and the likelihood ratio test. The table has the following columns: the observed z scores, the conditional expectation, the conditional variance, the standardized differences between the observed z score and expected value, the log likelihood ratio statistics.

### Examples

```# See also the vignette, "Diagnostic for fine-mapping with summary
# statistics."
set.seed(1)
n = 500
p = 1000
beta = rep(0,p)
beta[1:4] = 0.01
X = matrix(rnorm(n*p),nrow = n,ncol = p)
X = scale(X,center = TRUE,scale = TRUE)
y = drop(X %*% beta + rnorm(n))
ss = univariate_regression(X,y)
R = cor(X)
attr(R,"eigen") = eigen(R,symmetric = TRUE)
zhat = with(ss,betahat/sebetahat)