# corAR1: AR(1) Correlation Structure In nlme: Linear and Nonlinear Mixed Effects Models

 corAR1 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)

JosÃ© 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.

`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) )
``````

nlme documentation built on Nov. 27, 2023, 5:09 p.m.