% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/Causation.R
\name{NNS.caus}
\alias{NNS.caus}
\title{NNS Causation}
\usage{
NNS.caus(
  x,
  y = NULL,
  factor.2.dummy = FALSE,
  tau = 0,
  plot = FALSE,
  p.value = FALSE,
  nperm = 100L,
  permute = c("y", "x", "both"),
  seed = NULL,
  conf.int = 0.95
)
}
\arguments{
\item{x}{a numeric vector, matrix or data frame.}

\item{y}{\code{NULL} (default) or a numeric vector with compatible dimensions to \code{x}.}

\item{factor.2.dummy}{logical; \code{FALSE} (default) Automatically augments variable matrix with numerical dummy variables based on the levels of factors.  Includes dependent variable \code{y}.}

\item{tau}{options: ("cs", "ts", integer); 0 (default) Number of lagged observations to consider (for time series data).  Otherwise, set \code{(tau = "cs")} for cross-sectional data.  \code{(tau = "ts")} automatically selects the lag of the time series data, while \code{(tau = [integer])} specifies a time series lag.}

\item{plot}{logical; \code{FALSE} (default) Plots the raw variables, tau normalized, and cross-normalized variables.}

\item{p.value}{logical; \code{FALSE} (default) If \code{TRUE}, runs a permutation test to compute empirical p-values for the signed causation from x -> y.}

\item{nperm}{integer; number of permutations to use when \code{p.value = TRUE}. Default 100.}

\item{permute}{one of "both", "y", or "x"; which variable(s) to shuffle when constructing the null distribution.}

\item{seed}{optional integer seed for reproducibility of the permutation test.}

\item{conf.int}{numeric; 0.95 (default) confidence level for the partial-moment based interval computed on the permutation null distribution.}
}
\value{
If \code{p.value=FALSE} returns the original causation vector of length 3 (directional given/received and net), named either "C(x--->y)" or "C(y--->x)" in the third slot.  If \code{p.value=TRUE} returns a list with components:
 * \code{causation}: the original causation vector as above.
 * \code{p.value}: a list with empirical two-sided and one-sided p-values (x_causes_y, y_causes_x), the null distribution, the observed signed statistic, and metadata (permute, nperm).
If \code{p.value=TRUE} for a matrix, the function returns a list with components:
  * \code{causality}: the causality matrix.
  * \code{lower_CI}: matrix of lower confidence bounds (partial-moment based).
  * \code{upper_CI}: matrix of upper confidence bounds (partial-moment based).
  * \code{p.value}: matrix of empirical two-sided p-values.
}
\description{
Returns the causality from observational data between two variables.
}
\examples{

\dontrun{
## x causes y...
set.seed(123)
x <- rnorm(1000) ; y <- x ^ 2
NNS.caus(x, y, tau = "cs")

## Causal matrix without per factor causation
NNS.caus(iris, tau = 0)

## Causal matrix with per factor causation
NNS.caus(iris, factor.2.dummy = TRUE, tau = 0)
}
}
\references{
Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995, 2nd edition: \url{https://ovvo-financial.github.io/NNS/book/})
}
\author{
Fred Viole, OVVO Financial Systems
}
