corCAR1 {nlme} | R Documentation |

## Continuous AR(1) Correlation Structure

### Description

This function is a constructor for the `corCAR1`

class,
representing an autocorrelation structure of order 1, with a
continuous time covariate. Objects created using this constructor must
be later initialized using the appropriate `Initialize`

method.

### Usage

corCAR1(value, form, fixed)

### Arguments

`value` |
the correlation between two observations one unit of time
apart. Must be between 0 and 1. Defaults to 0.2. |

`form` |
a one sided formula of the form `~ t` , or ```
~ t |
g
``` , specifying a time covariate `t` and, optionally, a
grouping factor `g` . Covariates for this correlation structure
need not 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 `corCAR1`

, representing an autocorrelation
structure of order 1, with a continuous time covariate.

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com 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.

Jones, R.H. (1993) "Longitudinal Data with Serial Correlation: A
State-space Approach", Chapman and Hall.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models
in S and S-PLUS", Springer, esp. pp. 236, 243.

### See Also

`corClasses`

,
`Initialize.corStruct`

,
`summary.corStruct`

### Examples

## covariate is Time and grouping factor is Mare
cs1 <- corCAR1(0.2, form = ~ Time | Mare)
# Pinheiro and Bates, pp. 240, 243
fm1Ovar.lme <- lme(follicles ~
sin(2*pi*Time) + cos(2*pi*Time),
data = Ovary, random = pdDiag(~sin(2*pi*Time)))
fm4Ovar.lme <- update(fm1Ovar.lme,
correlation = corCAR1(form = ~Time))

[Package

*nlme* version 3.1-80

Index]