| corAR1 {nlme} | R Documentation |
This function is a constructor for the corAR1 class,
representing an autocorrelation structure of order 1. Objects
created using this constructor must later be initialized using the
appropriate Initialize method.
corAR1(value, form, fixed)
value |
the value of the lag 1 autocorrelation, which must be between -1 and 1. Defaults to 0 (no autocorrelation). |
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. |
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 corAR1, representing an autocorrelation
structure of order 1.
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. 235, 397.
ACF.lme,
corARMA,
corClasses,
Dim.corSpatial,
Initialize.corStruct,
summary.corStruct
## covariate is observation order and grouping factor is Mare
cs1 <- corAR1(0.2, form = ~ 1 | Mare)
# Pinheiro and Bates, p. 236
cs1AR1 <- corAR1(0.8, form = ~ 1 | Subject)
cs1AR1. <- Initialize(cs1AR1, data = Orthodont)
corMatrix(cs1AR1.)
# Pinheiro and Bates, p. 240
fm1Ovar.lme <- lme(follicles ~ sin(2*pi*Time) + cos(2*pi*Time),
data = Ovary, random = pdDiag(~sin(2*pi*Time)))
fm2Ovar.lme <- update(fm1Ovar.lme, correlation = corAR1())
# Pinheiro and Bates, pp. 255-258: use in gls
fm1Dial.gls <-
gls(rate ~(pressure + I(pressure^2) + I(pressure^3) + I(pressure^4))*QB,
Dialyzer)
fm2Dial.gls <- update(fm1Dial.gls,
weights = varPower(form = ~ pressure))
fm3Dial.gls <- update(fm2Dial.gls,
corr = corAR1(0.771, form = ~ 1 | Subject))
# 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
fm2Ovar.nlme <- update(fm1Ovar.nlme,
corr=corAR1(0.311) )