Banded Correlation Structure

DESCRIPTION:

This function is a constructor for the corBand class, representing a banded correlation structure. The internal representation of this structure, in terms of unconstrained parameters, uses the spherical parameterization defined in Pinheiro and Bates (1996). Objects created using this constructor must later be initialized using the appropriate initialize method.

USAGE:

corBand(value, form, fixed, ord) 

OPTIONAL ARGUMENTS:

value
an optional vector with the parameter values. Default is numeric(0), which results in a vector of zeros of appropriate dimension being assigned to the parameters when object is initialized (corresponding to an identity correlation structure).
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 such that its unique values form a sequence of consecutive integers. 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.
ord
an optional integer specifying the order of the banded matrix represented by the returned corBand object, defined as the number of nonzero diagonals in the upper-triangular part of the matrix. Defaults to 2.

VALUE:

an object of class corBand representing a banded correlation structure.

REFERENCES:

Pinheiro, J.C. and Bates., D.M. (1996) "Unconstrained Parametrizations for Variance-Covariance Matrices", Statistics and Computing, 6, 289-296.

SEE ALSO:

EXAMPLES:

## covariate is observation order and grouping factor is Subject 
cs1 <- corBand(form = ~ 1 | Subject)