Package 'STOPES'

ALASSO variable selection via cross-validation regularization parameter selection

Description

alasso.cv computes the ALASSO estimator.

Usage

alasso.cv(x, y)

Arguments

x	n x p covariate matrix
y	n x 1 response vector

Value

alasso.cv returns the ALASSO estimate

alasso

the ALASSO estimator

References

Hui Zou, (2006). "The adaptive LASSO and its oracle properties", JASA, 101 (476), 1418-1429

Examples

p <- 5
n <- 100
beta <- c(2, 1, 0.5, rep(0, p - 3))
x <- matrix(nrow = n, ncol = p, rnorm(n * p))
y <- rnorm(n) + crossprod(t(x), beta)
alasso.cv(x, y)

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Optimization via Subsampling (OPTS)

Description

opts computes the OPTS MLE in low dimensional case.

Usage

opts(X, Y, m, crit = "aic", prop_split = 0.5, cutoff = 0.75, ...)

Arguments

X	n x p covariate matrix (without intercept)
Y	n x 1 binary response vector
m	number of subsamples
crit	information criterion to select the variables: (a) aic = minimum AIC and (b) bic = minimum BIC
prop_split	proportion of subsample size and sample size, default value = 0.5
cutoff	cutoff used to select the variables using the stability selection criterion, default value = 0.75
...	other arguments passed to the glm function, e.g., family = "binomial"

Value

opts returns a list:

betahat	OPTS MLE of regression parameter vector
Jhat	estimated set of active predictors (TRUE/FALSE) corresponding to the OPTS MLE
SE	standard error of OPTS MLE
freqs	relative frequency of selection for all variables

Examples

require(MASS)
P = 15
N = 100
M = 20
BETA_vector = c(0.5, rep(0.5, 2), rep(0.5, 2), rep(0, P - 5))
MU_vector = numeric(P)
SIGMA_mat = diag(P)

X <- mvrnorm(N, MU_vector, Sigma = SIGMA_mat)
linearPred <- cbind(rep(1, N), X) 
Y <- rbinom(N, 1, plogis(linearPred))

# OPTS-AIC MLE
opts(X, Y, 10, family = "binomial")

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Threshold OPTimization via Subsampling (OPTS_TH)

Description

opts_th computes the threshold OPTS MLE in low dimensional case.

Usage

opts_th(X, Y, m, crit = "aic", type = "binseg", prop_split = 0.5,
  prop_trim = 0.2, q_tail = 0.5, ...)

Arguments

X	n x p covariate matrix (without intercept)
Y	n x 1 binary response vector
m	number of subsamples
crit	information criterion to select the variables: (a) aic = minimum AIC and (b) bic = minimum BIC
type	method used to minimize the trimmed and averaged information criterion: (a) min = observed minimum subsampling trimmed average information, (b) sd = observed minimum using the 0.25sd rule (corresponding to OPTS-min in the paper), (c) pelt = PELT changepoint algorithm (corresponding to OPTS-PELT in the paper), (d) binseg = binary segmentation changepoint algorithm (corresponding to OPTS-BinSeg in the paper), (e) amoc = AMOC method.
prop_split	proportion of subsample size of the sample size; default value is 0.5
prop_trim	proportion that defines the trimmed mean; default value = 0.2
q_tail	quantiles for the minimum and maximum p-values across the subsample cutpoints used to define the range of cutpoints
...	other arguments passed to the glm function, e.g., family = "binomial"

Value

opts_th returns a list:

betahat	STOPES MLE of regression parameters
SE	SE of STOPES MLE
Jhat	set of active predictors (TRUE/FALSE) corresponding to STOPES MLE
cuthat	estimated cutpoint for variable selection
pval	marginal p-values from univariate fit
cutpoits	subsample cutpoints
aic_mean	mean subsample AIC
bic_mean	mean subsample BIC

Examples

require(MASS)
P = 15
N = 100
M = 20
BETA_vector = c(0.5, rep(0.5, 2), rep(0.5, 2), rep(0, P - 5))
MU_vector = numeric(P)
SIGMA_mat = diag(P)

X <- mvrnorm(N, MU_vector, Sigma = SIGMA_mat)
linearPred <- cbind(rep(1, N), X) 
Y <- rbinom(N, 1, plogis(linearPred))

# Threshold OPTS-BinSeg MLE
opts_th(X, Y, M, family = "binomial")

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Selection of Threshold OPtimized Empirically via Splitting (STOPES)

Description

stopes computes the STOPES estimator.

Usage

stopes(x, y, m = 20, prop_split = 0.50, prop_trim = 0.20, q_tail = 0.90)

Arguments

x	n x p covariate matrix
y	n x 1 response vector
m	number of split samples, with default value = 20
prop_split	proportion of data used for training samples, default value = 0.50
prop_trim	proportion of trimming, default prop_trim = 0.20
q_tail	proportion of truncation samples across the split samples, default values = 0.90

Value

stopes returns a list with the STOPE estimates via data splitting using 0.25 method and the PELT method:

beta_stopes	the STOPE estimate via data splitting
J_stopes	the set of active predictors corresponding to STOPES via data splitting
final_cutpoints	the final cutpoint for STOPES
beta_pelt	the STOPE estimate via PELT
J_pelt	the set of active predictors corresponding to STOPES via PELT
final_cutpoints_PELT	the final cutpoint for PELT
quan_NA	test if the vector of trimmed cutpoints has length 0, with 1 if TRUE and 0 otherwise

Author(s)

Marinela Capanu, Mihai Giurcanu, Colin Begg, and Mithat Gonen

Examples

p <- 5
n <- 100
beta <- c(2, 1, 0.5, rep(0, p - 3))
x <- matrix(nrow = n, ncol = p, rnorm(n * p))
y <- rnorm(n) + crossprod(t(x), beta)
stopes(x, y)

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