% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/multivariance-functions.R
\name{dependence.structure}
\alias{dependence.structure}
\title{determines the dependence structure}
\usage{
dependence.structure(x, vec = 1:ncol(x), verbose = TRUE,
  detection.aim = NULL, ...)
}
\arguments{
\item{x}{matrix, each row of the matrix is treated as one sample}

\item{vec}{vector, it indicates which columns are initially treated together as one sample}

\item{verbose}{boolean, if \code{TRUE} details are printed during the detection and whenever a cluster is newly detected the (so far) detected dependence structure is plotted.}

\item{detection.aim}{\code{=NULL} or a list of vectors which indicate the expected detection, see below for more details}

\item{...}{these are passed to \code{\link{find.cluster}}}
}
\value{
returns a list with elements:
\describe{
  \item{\code{multivariances}}{calculated multivariances,}
  \item{\code{cdms}}{calculated centered distance matrices,}
  \item{\code{graph}}{graph representing the dependence structure.}
  \item{\code{detected}}{boolean, this is only included if a \code{detection.aim} is given.}
}
}
\description{
Determines the dependence structure as described in [3].
}
\details{
Performs the detection of the dependence structure as described in [3].

If \code{fixed.rejection.level} is not provided, the significance level \code{alpha} is used to determine which multivariances are significant using the distribution-free rejection level. As default the Holm method is used for p-value correction corresponding to multiple testing.

The resulting graph can be simplified (pairwise dependence can be represented by edges instead of vertices) using \code{\link{clean.graph}}.

Advanced:
The argument \code{detection.aim} can be used to check, if an expected dependence structure was detected. This might be useful for simulation studies to determine the empirical power of the detection algorithm. Hereto  \code{detection.aim} is set to a list of vectors which indicate the expected detected dependence structures (one for each run of \code{\link{find.cluster}}). The vector has as first element the \code{k} for which k-tuples are detected (for this aim the detection stops without success if no k-tuple is found), and the other elements, indicate to which clusters all present vertices belong after the detection, e.g. \code{c(3,2,2,1,2,1,1,2,1)} expects that 3-tuples are detected and in the graph are 8 vertices (including those representing the detected 3 dependencies), the order of the 2's and 1's indicate which vertices belong to which cluster. If \code{detection.aim} is provided, the vector representing the actual detection is printed, thus one can use the output with copy-paste to fix successively the expected detection aims.

Note that a failed detection might invoke the warning:
\preformatted{
run$mem == detection.aim[[k]][-1] :
longer object length is not a multiple of shorter object length
}
}
\examples{
\donttest{
# structures for the datasets included in the package
dependence.structure(dep_struct_several_26_100)
dependence.structure(dep_struct_star_9_100)
dependence.structure(dep_struct_iterated_13_100)
dependence.structure(dep_struct_ring_15_100)

# basic examples:

dependence.structure(coins(100)) # 3-dependent
dependence.structure(coins(100),vec = c(1,1,2))
# 3-dependent rv of which the first two rv are used together as one rv, thus 2-dependence.

dependence.structure(cbind(coins(200),coins(200,k=5)),verbose = TRUE)
#1,2,3 are 3-dependent, 4,..,9 are 6-dependent

# similar to the the previous example, but
# the pair 1,3 is treated as one sample,
# anagously the pair 2,4. In the resulting structure one does not
# see anymore that the dependence of 1,2,3,4 with the rest is due
# to 4.
dependence.structure(cbind(coins(200),coins(200,k=5)),
                           vec = c(1,2,1,2,3,4,5,6,7),verbose = TRUE)


### Advanced:

# How to check the empirical power of the detection algorithm?
# Use a dataset for which the structure is detected, e.g. dep_struct_several_26_100.
# run:
dependence.structure(dep_struct_several_26_100,
                     detection.aim = list(c(ncol(dep_struct_several_26_100))))
# The output provides the first detection aim. Now we run the same line with the added
# detection aim
dependence.structure(dep_struct_several_26_100,detection.aim = list(c(3,1, 1, 1, 2, 2, 2, 3, 4,
  5, 6, 7, 8, 8, 8, 9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 8, 9),
  c(ncol(dep_struct_several_26_100))))
# and get the next detection aim ... thus we finally obtain all detection aims.
# now we can run the code with new sample data ....
N = 100
dependence.structure(cbind(coins(N,2),tetrahedron(N),coins(N,4),tetrahedron(N),
                           tetrahedron(N),coins(N,3),coins(N,3),rnorm(N)),
                     detection.aim = list(c(3,1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8, 8, 8,
  9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 8, 9),
  c(4,1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11,
    11, 12, 1, 2, 8, 9, 10, 11),
  c(5, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 1,
    2, 4, 5, 6, 7, 3),
  c(5, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 1,
    2, 4, 5, 6, 7, 3)))$detected
# ... and one could start to store the results and compute the rate of successes.

# ... or one could try to check how many samples are necessary for the detection:
re = numeric(100)
for (i in 2:100) {
  re[i] =
    dependence.structure(dep_struct_several_26_100[1:i,],verbose = FALSE,
                         detection.aim = list(c(3,1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8,
      8, 8, 9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 8, 9),
      c(4,1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11,
        11, 11, 12, 1, 2, 8, 9, 10, 11),
      c(5, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7,
        8, 1, 2, 4, 5, 6, 7, 3),
      c(5, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7,
        8, 1, 2, 4, 5, 6, 7, 3)))$detected
  print(paste("First", i,"samples. Detected?", re[i]==1))
}
cat(paste("Given the 1 to k'th row the structure is not detected for k =",which(re == FALSE),"\\n"))
}
}
\references{
For the theoretic background see the reference [3] given on the main help page of this package: \link{multivariance-package}.
}