seqgendiff (version 1.2.2)

effective_cor: Estimates the effective correlation.

Description

Will return the estimated correlation between the design matrix and the surrogate variables when you assign a target correlation. The method is described in detail in Gerard (2020).

Usage

effective_cor(
  design_perm,
  sv,
  target_cor,
  calc_first = c("cor", "mean"),
  method = c("optmatch", "hungarian", "marriage"),
  iternum = 1000
)

Arguments

design_perm

A numeric design matrix whose rows are to be permuted (thus controlling the amount by which they are correlated with the surrogate variables). The rows index the samples and the columns index the variables. The intercept should not be included (though see Section "Unestimable Components").

sv

A matrix of surrogate variables

target_cor

A numeric matrix of target correlations between the variables in design_perm and the surrogate variables. The rows index the observed covariates and the columns index the surrogate variables. That is, target_cor[i, j] specifies the target correlation between the ith column of design_perm and the jth surrogate variable. The surrogate variables are estimated either using factor analysis or surrogate variable analysis (see the parameter use_sva). The number of columns in target_cor specifies the number of surrogate variables. Set target_cor to NULL to indicate that design_perm and the surrogate variables are independent.

calc_first

Should we calculate the correlation of the mean design_perm and sv (calc_first = "mean"), or should we calculate the mean of the correlations between design_perm and sv (calc_first = "cor")? This should only be changed by expert users.

method

Should we use the optimal matching technique from Hansen and Klopfer (2006) ("optmatch"), the Gale-Shapley algorithm for stable marriages ("marriage") (Gale and Shapley, 1962) as implemented in the matchingR package, or the Hungarian algorithm (Papadimitriou and Steiglitz, 1982) ("hungarian") as implemented in the clue package (Hornik, 2005)? The "optmatch" method works really well but does take a lot more computational time if you have, say, 1000 samples. If you use the "optmatch" option, you should note that the optmatch package uses a super strange license: https://cran.r-project.org/package=optmatch/LICENSE. If this license doesn't work for you (because you are not in academia, or because you don't believe in restrictive licenses), then try out the "hungarian" method.

iternum

The total number of simulated correlations to consider.

Value

A matrix of correlations. The rows index the observed covariates and the columns index the surrogate variables. Element (i, j) is the estimated correlation between the ith variable in design_perm and the jth variable in sv.

Details

This function permutes the rows of design_perm many times, each time calculating the Pearson correlation between the columns of design_perm and the columns of sv. It then returns the averages of these Pearson correlations. The permutation is done using permute_design.

References

• Gale, David, and Lloyd S. Shapley. "College admissions and the stability of marriage." The American Mathematical Monthly 69, no. 1 (1962): 9-15.

• Gerard, D (2020). "Data-based RNA-seq simulations by binomial thinning." BMC Bioinformatics. 21(1), 206. doi: 10.1186/s12859-020-3450-9.

• Hansen, Ben B., and Stephanie Olsen Klopfer. "Optimal full matching and related designs via network flows." Journal of computational and Graphical Statistics 15, no. 3 (2006): 609-627.

• Hornik K (2005). "A CLUE for CLUster Ensembles." Journal of Statistical Software, 14(12). doi: 10.18637/jss.v014.i12

• C. Papadimitriou and K. Steiglitz (1982), Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs: Prentice Hall.

Examples

# NOT RUN {
## Generate the design matrices and set target correlation -----------------
n <- 10
design_perm <- cbind(rep(c(0, 1), each = n / 2),
                     rep(c(0, 1), length.out = n))
sv <- matrix(rnorm(n))
target_cor <- matrix(c(0.9, 0.1), ncol = 1)

## Get estimated true correlation ------------------------------------------
## You should use a much larger iternum in practice
effective_cor(design_perm = design_perm,
              sv = sv,
              target_cor = target_cor,
              iternum = 10)

# }