corARMA {nlme} | R Documentation |

This function is a constructor for the `corARMA`

class,
representing an autocorrelation-moving average correlation structure
of order (p, q). Objects created using this constructor must later
be initialized using the appropriate `Initialize`

method.

corARMA(value, form, p, q, fixed)

`value` |
a vector with the values of the autoregressive and moving
average parameters, which must have length `p + q` and all
elements between -1 and 1. Defaults to a vector of zeros,
corresponding to uncorrelated observations. |

`form` |
a one sided formula of the form `~ t` , or ```
~ t |
g
``` , specifying a time covariate `t` and, optionally, a
grouping factor `g` . A covariate for this correlation structure
must be integer valued. When a grouping factor is present in
`form` , the correlation structure is assumed to apply only
to observations within the same grouping level; observations with
different grouping levels are assumed to be uncorrelated. Defaults to
`~ 1` , which corresponds to using the order of the observations
in the data as a covariate, and no groups. |

`p, q` |
non-negative integers specifying respectively the
autoregressive order and the moving average order of the `ARMA`
structure. Both default to 0. |

`fixed` |
an optional logical value indicating whether the
coefficients should be allowed to vary in the optimization, or kept
fixed at their initial value. Defaults to `FALSE` , in which case
the coefficients are allowed to vary. |

an object of class `corARMA`

, representing an
autocorrelation-moving average correlation structure.

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994) "Time Series Analysis: Forecasting and Control", 3rd Edition, Holden-Day.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer, esp. pp. 236, 397.

`corAR1`

,
`corClasses`

`Initialize.corStruct`

,
`summary.corStruct`

## ARMA(1,2) structure, with observation order as a covariate and ## Mare as grouping factor cs1 <- corARMA(c(0.2, 0.3, -0.1), form = ~ 1 | Mare, p = 1, q = 2) # Pinheiro and Bates, p. 237 cs1ARMA <- corARMA(0.4, form = ~ 1 | Subject, q = 1) cs1ARMA <- Initialize(cs1ARMA, data = Orthodont) corMatrix(cs1ARMA) cs2ARMA <- corARMA(c(0.8, 0.4), form = ~ 1 | Subject, p=1, q=1) cs2ARMA <- Initialize(cs2ARMA, data = Orthodont) corMatrix(cs2ARMA) # Pinheiro and Bates use in nlme: # from p. 240 needed on p. 396 fm1Ovar.lme <- lme(follicles ~ sin(2*pi*Time) + cos(2*pi*Time), data = Ovary, random = pdDiag(~sin(2*pi*Time))) fm5Ovar.lme <- update(fm1Ovar.lme, corr = corARMA(p = 1, q = 1)) # p. 396 fm1Ovar.nlme <- nlme(follicles~ A+B*sin(2*pi*w*Time)+C*cos(2*pi*w*Time), data=Ovary, fixed=A+B+C+w~1, random=pdDiag(A+B+w~1), start=c(fixef(fm5Ovar.lme), 1) ) # p. 397 fm3Ovar.nlme <- update(fm1Ovar.nlme, corr=corARMA(p=0, q=2) )

[Package *nlme* version 3.1-80 Index]