# vrPEER: Graph-constrained regression with variable-reduction... In mdpeer: Graph-Constrained Regression with Enhanced Regularization Parameters Selection

## Description

Graph-constrained regression with variable-reduction procedure to handle the non-invertibility of a graph-originated penalty matrix (see: References).

Bootstrap confidence intervals computation is available (not set as a default option).

## Usage

 1 2 3 vrPEER(Q, y, Z, X = NULL, sv.thr = 1e-05, compute.boot.CI = FALSE, boot.R = 1000, boot.conf = 0.95, boot.set.seed = TRUE, boot.parallel = "multicore", boot.ncpus = 4, verbose = TRUE) 

## Arguments

 Q graph-originated penalty matrix (p \times p); typically: a graph Laplacian matrix y response values matrix (n \times 1) Z design matrix (n \times p) modeled as random effects variables (to be penalized in regression modeling); assumed to be already standarized X design matrix (n \times k) modeled as fixed effects variables (not to be penalized in regression modeling); should contain colum of 1s if intercept is to be considered in a model sv.thr threshold value above which singular values of Q are considered "zeros" compute.boot.CI logical whether or not compute bootstrap confidence intervals for b regression coefficient estimates boot.R number of bootstrap replications used in bootstrap confidence intervals computation boot.conf confidence level assumed in bootstrap confidence intervals computation boot.set.seed logical whether or not set seed in bootstrap confidence intervals computation boot.parallel value of parallel argument in boot function in bootstrap confidence intervals computation boot.ncpus value of ncpus argument in boot function in bootstrap confidence intervals computation verbose logical whether or not set verbose mode (print out function execution messages)

## Value

 b.est vector of b coefficient estimates beta.est vector of β coefficient estimates lambda.Q λ_Q regularization parameter value boot.CI data frame with two columns, lower and upper, containing, respectively, values of lower and upper bootstrap confidence intervals for b regression coefficient estimates

## References

Karas, M., Brzyski, D., Dzemidzic, M., J., Kareken, D.A., Randolph, T.W., Harezlak, J. (2017). Brain connectivity-informed regularization methods for regression. doi: https://doi.org/10.1101/117945

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 set.seed(1234) n <- 200 p1 <- 10 p2 <- 90 p <- p1 + p2 # Define graph adjacency matrix A <- matrix(rep(0, p*p), nrow = p, ncol = p) A[1:p1, 1:p1] <- 1 A[(p1+1):p, (p1+1):p] <- 1 L <- Adj2Lap(A) # Define Q penalty matrix as graph Laplacian matrix normalized) Q <- L2L.normalized(L) # Define Z,X design matrices and aoutcome y Z <- matrix(rnorm(n*p), nrow = n, ncol = p) b.true <- c(rep(1, p1), rep(0, p2)) X <- matrix(rnorm(n*3), nrow = n, ncol = 3) beta.true <- runif(3) intercept <- 0 eta <- intercept + Z %*% b.true + X %*% beta.true R2 <- 0.5 sd.eps <- sqrt(var(eta) * (1 - R2) / R2) error <- rnorm(n, sd = sd.eps) y <- eta + error ## Not run: # run vrPEER vrPEER.out <- vrPEER(Q, y, Z, X) plt.df <- data.frame(x = 1:p, y = vrPEER.out$b.est) ggplot(plt.df, aes(x = x, y = y, group = 1)) + geom_line() ## End(Not run) ## Not run: # run vrPEER with 0.95 confidence intrvals vrPEER.out <- vrPEER(Q, y, Z, X, compute.boot.CI = TRUE, boot.R = 500) plt.df <- data.frame(x = 1:p, y = vrPEER.out$b.est, lo = vrPEER.out$boot.CI[,1], up = vrPEER.out$boot.CI[,2]) ggplot(plt.df, aes(x = x, y = y, group = 1)) + geom_line() + geom_ribbon(aes(ymin=lo, ymax=up), alpha = 0.3) ## End(Not run) 

mdpeer documentation built on May 31, 2017, 5:21 a.m.