# corAR1

##### 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.

- Keywords
- models

##### Usage

`corAR1(value, form, fixed)`

##### Arguments

- 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.

##### Value

an object of class `corAR1`

, representing an autocorrelation
structure of order 1.

##### References

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.

##### See Also

`ACF.lme`

,
`corARMA`

,
`corClasses`

,
`Dim.corSpatial`

,
`Initialize.corStruct`

,
`summary.corStruct`

##### Examples

```
# NOT RUN {
## 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) )
# }
```

*Documentation reproduced from package nlme, version 3.1-145, License: GPL (>= 2) | file LICENCE*