updategraph {MultiGroupSequential}

Update graph

Description

updategraph() updates the graph when only a subset of original hypotheses is concerned.

Usage

updategraph(
  S1 = c(2, 3),
  W0 = c(0.5, 0.5, 0, 0),
  G0 = rbind(c(0, 0, 1, 0), c(0, 0, 0, 1), c(0, 1, 0, 0), c(1, 0, 0, 0)),
  S0 = seq(1, length(W0), by = 1)
)

Arguments

S1

Integer indices of the subset of hypotheses, S1 must be a non-empty subset of S0 and must be sorted increasingly.

W0

Numeric vector for the initial weights of the graph.

G0

Numeric matrix of dimesion length(W0) by length(W0) for the initial transition matrix of the graph.

S0

Integer indices for the set of hypotheses from 1 to length of W0.

Value

List with the following elements

• S1: Integer indices the same as the input S1.

• W1: Numeric vector for weights of the updated graph.

• G1: Numeric transition of the updated graph.

Author(s)

Xiaodong Luo

Examples

## We can use the function to produce a closed testing tree
## A function to create power set
powerset <- function(x) {
  sets <- lapply(1:(length(x)), function(i) combn(x, i, simplify = FALSE))
  unlist(sets, recursive = FALSE)
}

n <- 3    # number of hypotheses
pn <- 2^n-1
pset <- powerset(seq(1, n, by = 1))    # create the power set
df <- data.frame(matrix(ncol = 1+n, nrow = 0))    # create the dataset
colnames(df) <- c("Test", paste0("H", seq(1, n, by = 1), sep = ""))

W0 <- c(1/3, 1/3, 1/3)    # the weights of the graph
m <- rbind(H1 = c(0, 1/2, 1/2),
           H2 = c(1/2, 0, 1/2),
           H3 = c(1/2, 1/2, 0))
G0 <- matrix(m, nrow = 3, ncol = 3)    # the transition matrix of the graph

for (j in 1:pn){
    abc <- updategraph(S1 = pset[[j]], W0 = W0, G0 = G0)
    temp <- rep("-", n)
    temp[pset[[j]]] <- abc$W1
    temp <- c(paste(pset[[j]], collapse = ""), temp)
    df[j, ] <- temp
}
df    # the dataframe lists the closed testing tree