CVEK (version 0.1-2)

cvek: Conducting Cross-validated Kernel Ensemble

Description

Conducting Cross-validated Kernel Ensemble based on user-specified formula.

Usage

cvek(
  formula,
  kern_func_list,
  data,
  formula_test = NULL,
  mode = "loocv",
  strategy = "stack",
  beta_exp = 1,
  lambda = exp(seq(-10, 5)),
  test = "boot",
  alt_kernel_type = "linear",
  B = 100,
  verbose = FALSE
)

Arguments

formula

(formula) A user-supplied formula for the null model. Should contain at least one kernel term.

kern_func_list

(list) A list of kernel functions in the kernel library.

data

(data.frame, n*d) A data.frame, list or environment (or object coercible by as.data.frame to a data.frame), containing the variables in formula. Neither a matrix nor an array will be accepted.

formula_test

(formula) A user-supplied formula indicating the alternative effect to test. All terms in the alternative mode must be specified as kernel terms.

mode

(character) A character string indicating which tuning parameter criteria is to be used.

strategy

(character) A character string indicating which ensemble strategy is to be used.

beta_exp

(numeric/character) A numeric value specifying the parameter when strategy = "exp" ensemble_exp.

lambda

(numeric) A numeric string specifying the range of tuning parameter to be chosen. The lower limit of lambda must be above 0.

test

(character) Type of hypothesis test to conduct. Must be either 'asymp' or 'boot'.

alt_kernel_type

(character) Type of alternative kernel effect to consider. Must be either "linear" or "ensemble".

B

(numeric) Number of bootstrap samples.

verbose

(logical) Whether to print additional messages.

Value

lambda

(numeric) The selected tuning parameter based on the estimated ensemble kernel matrix.

beta

(matrix, d_fixed*1) Fixed effect estimates.

alpha

(matrix, n*1) Kernel effect estimates.

K

(matrix, n*n) Estimated ensemble kernel matrix.

u_hat

(vector of length K) A vector of weights of the kernels in the library.

base_est

(list) The detailed estimation results of K kernels.

pvalue

(numeric) If formula_test is given, p-value of the test is returned.

Details

Perform Cross-validated Kernel Ensemble and optionally test for kernel effect based on user-specified formula.

References

Xihong Lin. Variance component testing in generalised linear models with random effects. June 1997.

Arnab Maity and Xihong Lin. Powerful tests for detecting a gene effect in the presence of possible gene-gene interactions using garrote kernel machines. December 2011.

Petra Bu z kova, Thomas Lumley, and Kenneth Rice. Permutation and parametric bootstrap tests for gene-gene and gene-environment interactions. January 2011.

See Also

estimation

method: generate_kernel

mode: tuning

strategy: ensemble

Examples

# NOT RUN {
kern_par <- data.frame(method = rep("rbf", 3),
l = rep(3, 3), p = rep(2, 3), 
stringsAsFactors = FALSE)
# define kernel library
kern_func_list <- define_library(kern_par)

n <- 10
d <- 4
formula <- y ~ x1 + x2 + k(x3, x4)
formula_test <- y ~ k(x1, x2) * k(x3, x4)
set.seed(1118)
data <- as.data.frame(matrix(
  rnorm(n * d),
  ncol = d,
  dimnames = list(NULL, paste0("x", 1:d))
))
beta_true <- c(1, .41, 2.37)
lnr_kern_func <- generate_kernel(method = "rbf", l = 3)
kern_effect_lnr <-
  parse_kernel_variable("k(x3, x4)", lnr_kern_func, data)
alpha_lnr_true <- rnorm(n)

data$y <- as.matrix(cbind(1, data[, c("x1", "x2")])) %*% beta_true +
  kern_effect_lnr %*% alpha_lnr_true

data_train <- data

pvalue <- cvek(formula,
               kern_func_list,
               data_train,
               formula_test,
               mode = "loocv",
               strategy = "stack",
               beta_exp = 1,
               lambda = exp(seq(-2, 2)),
               test = "asymp",
               alt_kernel_type = "linear",
               verbose = FALSE)$pvalue

# }