riPEERc: Graph-constrained regression with addition of a small ridge...

In mdpeer: Graph-Constrained Regression with Enhanced Regularization Parameters Selection

Description

Graph-constrained regression with addition of a diagonal matrix multiplied by a predefined (small) scalar to handle the non-invertibility of a graph Laplacian matrix (see: References).

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

Usage

riPEERc(Q, y, Z, X = NULL, lambda.2 = 0.001, 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
lambda.2	(small) scalar value of regularization parameter for diagonal matrix by adding which the Q matrix is corrected (note: correction is done before λ_Q regularization parameter value estimation; in other words: λ_Q estimation is done for the corrected Q matrix)
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
lambda.R	lambda.Q * lambda.2 value
lambda.2	lambda.2 supplied argument 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

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: 
riPEERc.out <- riPEERc(Q, y, Z, X)
plt.df <- data.frame(x = 1:p, y = riPEERc.out$b.est)
ggplot(plt.df, aes(x = x, y = y, group = 1)) + geom_line() + labs("b estimates")

## End(Not run)

## Not run: 
# riPEERc with 0.95 bootstrap confidence intervals computation
riPEERc.out <- riPEERc(Q, y, Z, X, compute.boot.CI = TRUE, boot.R = 500)
plt.df <- data.frame(x = 1:p, y = riPEERc.out$b.est, 
                     lo = riPEERc.out$boot.CI[,1], 
                     up =  riPEERc.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 2, 2019, 3:36 p.m.