# corCAR1

##### Continuous AR(1) Correlation Structure

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.

- Keywords
- models

##### 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.

##### 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

##### Examples

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

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