% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/glla.R
\name{glla}
\alias{glla}
\title{Generalized Local Linear Approximation}
\usage{
glla(x, n.embed, tau, delta, order)
}
\arguments{
\item{x}{Numeric vector.
An observed time series}

\item{n.embed}{Numeric (length = 1).
Number of embedded dimensions (the number of observations 
to be used in the \code{\link[EGAnet]{Embed}} function)}

\item{tau}{Numeric (length = 1).
Number of observations to offset successive embeddings in 
the \code{\link[EGAnet]{Embed}} function. A \code{tau} of one 
uses adjacent observations.
Default is \code{1}}

\item{delta}{Numeric (length = 1).
The time between successive observations in the time series.
Default is \code{1}}

\item{order}{Numeric (length = 1).
The maximum order of the derivative to be estimated. For example,
\code{"order = 2"} will return a matrix with three columns with the estimates
of the observed scores and the first and second derivative for each row of the embedded
matrix (i.e. the reorganization of the time series implemented via
the \code{\link[EGAnet]{Embed}} function)}
}
\value{
Returns a matrix containing \emph{n} columns in which \emph{n}
is one plus the maximum order of the derivatives to be estimated via 
generalized local linear approximation
}
\description{
Estimates the derivatives of a time series using generalized 
local linear approximation (GLLA). GLLA is a filtering method for 
estimating derivatives from data that uses time delay embedding and a 
variant of Savitzky-Golay filtering to accomplish the task.
}
\examples{
# A time series with 8 time points
tseries <- 49:56
deriv.tseries <- glla(tseries, n.embed = 4, tau = 1, delta = 1, order = 2)

}
\references{
\strong{GLLA implementation} \cr
Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2010)
Generalized local linear approximation of derivatives from time series. In S.-M. Chow, E. Ferrer, & F. Hsieh (Eds.),
\emph{The Notre Dame series on quantitative methodology. Statistical methods for modeling human dynamics: An interdisciplinary dialogue},
(p. 161-178). \emph{Routledge/Taylor & Francis Group}.

Deboeck, P. R., Montpetit, M. A., Bergeman, C. S., & Boker, S. M. (2009)
Using derivative estimates to describe intraindividual variability at multiple time scales.
\emph{Psychological Methods}, \emph{14(4)}, 367-386.

\strong{Filtering procedure} \cr
Savitzky, A., & Golay, M. J. (1964).
Smoothing and differentiation of data by simplified least squares procedures.
\emph{Analytical Chemistry}, \emph{36(8)}, 1627-1639.
}
\author{
Hudson Golino <hfg9s at virginia.edu>
}
