caw: Iterative procedure for confounder correction with a...
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

Quoth the Raven "Caw, caw!"

caw(
  Y,
  X,
  k = NULL,
  cov_of_interest = ncol(X),
  limmashrink = TRUE,
  weight_func = ash_wrap,
  weight_args = list(),
  fa_func = pca_naive,
  fa_args = list(),
  scale_var = TRUE,
  include_intercept = TRUE,
  weight_init = c("all_null", "random", "limma"),
  weight_func_input = c("summary2"),
  degrees_freedom = NULL,
  min_scale = 0.8
)

`Y`	A matrix of numerics. These are the response variables where each column has its own variance. In a gene expression study, the rows are the individuals and the columns are the genes.
`X`	A matrix of numerics. The covariates of interest.
`k`	A non-negative integer.The number of unobserved confounders. If not specified and the R package sva is installed, then this function will estimate the number of hidden confounders using the methods of Buja and Eyuboglu (1992).
`cov_of_interest`	A vector of positive integers. The column numbers of the covariates in X whose coefficients you are interested in. The rest are considered nuisance parameters and are regressed out by OLS.
`limmashrink`	A logical. Should we apply hierarchical shrinkage to the variances (`TRUE`) or not (`FALSE`)? If `degrees_freedom = NULL` and `limmashrink = TRUE` and `likelihood = "t"`, then we'll also use the limma returned degrees of freedom.
`weight_func`	The function that returns the weights (or lfdr's). Many forms of input are allowed. See `weight_func_input` for details.
`weight_args`	Additional arguments to pass to `weight_func`.
`fa_func`	A factor analysis function. The function must have as inputs a numeric matrix `Y` and a rank (numeric scalar) `r`. It must output numeric matrices `alpha` and `Z` and a numeric vector `sig_diag`. `alpha` is the estimate of the coefficients of the unobserved confounders, so it must be an `r` by `ncol(Y)` matrix. `Z` must be an `r` by `nrow(Y)` matrix. `sig_diag` is the estimate of the column-wise variances so it must be of length `ncol(Y)`. The default is the function `pca_naive` that just uses the first `r` singular vectors as the estimate of `alpha`. The estimated variances are just the column-wise mean square.
`fa_args`	A list. Additional arguments you want to pass to fa_func.
`scale_var`	A logical. Should we scale the variance (`TRUE`) or not (`FALSE`)?
`include_intercept`	A logical. If `TRUE`, then it will check `X` to see if it has an intercept term. If not, then it will add an intercept term. If `FALSE`, then `X` will be unchanged.
`weight_init`	A character. How should we initialize the weights? The options are to initialize in the all-null setting (`"all_null"`), draw the weights randomly form iid uniforms (`"random"`), or run an iteration of `weight_func` prior to the first round of estimating the confounders (`"limma"`). This last step uses limma-ebayes.
`weight_func_input`	The form of input for `weight_func`. Right now only `"summary2"` is supported, but I intend to support all of the following in the future. If `weight_func_input = "summary1"` then the function only takes p-values as input (called `pvalues`). If `weight_func_input = "summary2"`, then the function only takes a vector of effect estimates `betahat`, a vector of standard errors `sebetahat`, and a vector of degrees of freedom `degrees_freedom`. If `weight = "summary3"`, then the input is a matrix of effects `betamat`, an array of covariances `cov_array` where the each `cov_array[,,i]` is the covariance of the elements of `betamat[i, ]`, and a vector of degrees of freedom `dfvec`. If `weight_func_input = "full"`, then the input is just a response matrix `Y` and a covariate matrix `X`.
`degrees_freedom`	if `likelihood = "t"`, then this is the user-defined degrees of freedom for that distribution. If `degrees_freedom` is `NULL` then the degrees of freedom will be the sample size minus the number of covariates minus `k`.
`min_scale`	The minimum estimate for the variance inflation term.