vruv2_old: Old version of Calibrated RUV2 that doesn't really work.
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

Description Usage Arguments Details Author(s) References

This function will perform a variant of Removing Unwanted Variation 2-step (RUV2) (Gagnon-Bartsch et al, 2013), where we include a variance inflation parameter in the second step and estimate it by maximum likelihood.

vruv2_old(
  Y,
  X,
  ctl,
  k = NULL,
  cov_of_interest = ncol(X),
  likelihood = c("t", "normal"),
  limmashrink = TRUE,
  degrees_freedom = NULL,
  include_intercept = TRUE,
  gls = TRUE,
  fa_func = pca_naive,
  fa_args = list()
)

`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.
`ctl`	A vector of logicals of length `ncol(Y)`. If position i is `TRUE` then position i is considered a negative control.
`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.
`likelihood`	Either `"normal"` or `"t"`. If `likelihood = "t"`, then the user may provide the degrees of freedom via `degrees_freedom`.
`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.
`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`.
`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.
`gls`	A logical. Should we estimate the part of the confounders associated with the nuisance parameters with gls (`TRUE`) or with ols (`FALSE`).
`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.

See vruv4 for a description of the model.

The variances of the non-control genes using the adjustment for RUV2 are unchanged. The variances for the control genes are the ones that are inflated. Hence, for this method to adjust the variances of the genes of interest (the non-control genes) you must use hierarchical shrinkage of the variances. That is, you must set limmashrink = TRUE.

David Gerard

Buja, A. and Eyuboglu, N., 1992. "Remarks on parallel analysis." Multivariate behavioral research, 27(4), pp.509-540. doi: 10.1207/s15327906mbr2704_2
Gagnon-Bartsch, J., Laurent Jacob, and Terence P. Speed, 2013. "Removing unwanted variation from high dimensional data with negative controls." Berkeley: Department of Statistics. University of California. https://statistics.berkeley.edu/tech-reports/820
Gerard, David, and Matthew Stephens. 2021. "Unifying and Generalizing Methods for Removing Unwanted Variation Based on Negative Controls." Statistica Sinica, 31(3), 1145-1166. doi: 10.5705/ss.202018.0345