opts_th {OPTS}

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")