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
corARMA(value, form, p, q, fixed)
- a vector with the values of the autoregressive and moving average parameters, which must have length
p + qand all elements between -1 and 1. Defaults to a vector of zeros, corresponding to uncorrelated observations.
- a one sided formula of the form
~ t, or
~ t | g, specifying a time covariate
tand, 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
ARMAstructure. Both default to 0.
- 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.
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.
## 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) )
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