[R] Create an AR(1) covariance matrix

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.be
Fri May 11 16:45:20 CEST 2007

one option is the following:

times <- 1:5
rho <- 0.5
sigma <- 2
H <- abs(outer(times, times, "-"))
V <- sigma * rho^H
p <- nrow(V)
V[cbind(1:p, 1:p)] <- V[cbind(1:p, 1:p)] * sigma

I hope it helps.


Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/

----- Original Message ----- 
From: "Rick DeShon" <deshon at msu.edu>
To: <r-help at stat.math.ethz.ch>
Sent: Friday, May 11, 2007 4:29 PM
Subject: [R] Create an AR(1) covariance matrix

> Hi All.
> I need to create a first-order autoregressive covariance matrix
> (AR(1)) for a longitudinal mixed-model simulation.  I can do this
> using nested "for" loops but I'm trying to improve my R coding
> proficiency and am curious how it might be done in a more elegant
> manner.
> To be clear, if there are 5 time points then the AR(1) matrix is 5x5
> where the diagonal is a constant variance (sigma^2) and the
> covariances depend on the number of "steps" between trials.  So, the
> first off-diagonal of the matrix is sigma*rho, the second 
> off-diagonal
> is sigma*rho^2, the third off-diagonal is sigma*rho^3, and so forth.
> Any suggestions for an elegant method to flexibly create this 
> matrix?
> Rick DeShon
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> PLEASE do read the posting guide 
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> and provide commented, minimal, self-contained, reproducible code.

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