AR(1) Correlation Structure
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 |
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 |
an object of class corAR1
, representing an autocorrelation
structure of order 1.
José Pinheiro 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.
## 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) )
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