Class "DAG" for storing the result of the DAG multiple testing method
The class DAG is the output of a call to DAGmethod. It stores which hypotheses have been rejected and can be used to calculate confidence sets for the number of true and/or false hypotheses among a selected set of hypotheses.
These slots are not meant to be directly accessed by the user.
sets:Object of class "list". Stores unique original sets that are to be tested.
method:Object of class "character". Stores whether the any-parent, all-parents or structuredHolm method has been used.
isadjusted:Object of class "logical". Stores whether adjusted p-values are calculated.
allpvalues:Object of class "numeric". Stores (adjusted) p-values for all hypotheses. Has value NA if adjusted p-value is larger than alpha.
implications:Object of class "logical". Stores whether hypotheses are implications at chosen alpha-level
alpha:Object of class "numeric". The type I error level chosen.
rejected:Object of class "logical". Stores for each hypothesis wether this hypothesis has been rejected
leaf_based_sets:Object of class "list". Stores sets expressed in the indices of their corresponding leaf nodes (which are sets itself).
twoway:Object of class "logical". Is TRUE if the final DAG structure has twoway logical relationships.
(DAG): Prints how many hypotheses there are in total and how many of them were rejected.
(DAG): Prints the test results (as show).
(DAG): Retrieves the maximal alpha_value from the DAG object.
(DAG): Retrieves the implications from a given DAG object.
(DAG,indicator): Retrieves pvalues for all possible hypotheses (as specified by indicator) from the DAG object.
Rosa Meijer: r.j.meijer@lumc.nl
#Generate data, where the response Y is associated with two (out of 4) covariates
set.seed(1)
n=100
p=4
X <- matrix(rnorm(n*p),n,p)
beta <- c(0,0.5,0.5,0)
Y <- X %*% beta + rnorm(n)
# Let us assume we have the following sets that we want to test:
sets <- list(c(1,2,3,4), c(1,2), c(2,3,4), c(2,3), 1, 2, 3, 4)
names(sets) <- c(1234, 12, 234, 23, 1, 2, 3, 4)
# Start by making the corresponding graph structure
struct <- construct(sets)
# Check whether the DAG has toway logical relations:
istwoway(struct)
# Define the local test to be used in the closed testing procedure.
# This test expects a set as input.
mytest <- function(set)
{
X <- X[,set,drop=FALSE]
lm.out <- lm(Y ~ X)
x <- summary(lm.out)
return(pf(x$fstatistic[1],x$fstatistic[2],x$fstatistic[3],lower.tail=FALSE))
}
# Perform the DAG procedure (default is all-parents method).
DAG <- DAGmethod(struct, mytest, isadjusted=TRUE)
summary(DAG)
# What are the smallest sets that are found to be significant? If the sets have names,
# as in our example, the implications function will return the names
# of the implying sets, together with their (adjusted) p-value.
# If no names are provided, indices will be used instead of the names.
implications(DAG)
# What is the adjusted p-value of the null-hypothesis corresponding to the fourth set,
# which is set c(2,3)?
# To look up the pvalue, the function uses the index or name of the set
# in the list of sets stored in the DAGstructure.
# (Note that, if there were duplicate sets in the original list, this index can be different from
# the one in the original list given to \code{construct})
pvalue(DAG,4)
pvalue(DAG, "23") #as above, but while using names
# How many of the elementary hypotheses (the last 4 sets) have to be false
# with probability 1-alpha?
# Sets (don't have to be elementary hypotheses in general) must be specified
# by their index or name.
DAGpick(DAG, 5:8)
DAGpick(DAG, c("1","2","3","4")) #as above, but while using namesPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.