corAR1 {nlme} | R Documentation

## AR(1) Correlation Structure

### Description

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.

### 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.

### Author(s)

José Pinheiro and Douglas Bates bates@stat.wisc.edu

### 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

    ## 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) )

[Package nlme version 3.1-128 Index]