mdpeer (version 1.0.1)

riPEERc: Graph-constrained regression with addition of a small ridge term to handle the non-invertibility of a graph Laplacian matrix

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 \(\lambda_Q\) regularization parameter value estimation; in other words: \(\lambda_Q\) 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 \(\beta\) coefficient estimates

lambda.Q

\(\lambda_Q\) 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")
## ---------------------------------------------

## 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)
## ---------------------------------------------