# corFactor.corStruct: Factor of a corStruct Object Matrix In nlme: Linear and Nonlinear Mixed Effects Models

 corFactor.corStruct R Documentation

## Factor of a corStruct Object Matrix

### Description

This method function extracts a transpose inverse square-root factor, or a series of transpose inverse square-root factors, of the correlation matrix, or list of correlation matrices, represented by `object`. Letting `\Sigma` denote a correlation matrix, a square-root factor of `\Sigma` is any square matrix `L` such that `\Sigma = L'L`. This method extracts `L^{-t}`.

### Usage

``````## S3 method for class 'corStruct'
corFactor(object, ...)
``````

### Arguments

 `object` an object inheriting from class `"corStruct"` representing a correlation structure, which must have been initialized (using `Initialize`). `...` some methods for this generic require additional arguments. None are used in this method.

### Value

If the correlation structure does not include a grouping factor, the returned value will be a vector with a transpose inverse square-root factor of the correlation matrix associated with `object` stacked column-wise. If the correlation structure includes a grouping factor, the returned value will be a vector with transpose inverse square-root factors of the correlation matrices for each group, stacked by group and stacked column-wise within each group.

### Note

This method function is used intensively in optimization algorithms and its value is returned as a vector for efficiency reasons. The `corMatrix` method function can be used to obtain transpose inverse square-root factors in matrix form.

### Author(s)

JosÃ© Pinheiro and Douglas Bates bates@stat.wisc.edu

`corFactor`, `corMatrix.corStruct`, `recalc.corStruct`, `Initialize.corStruct`
``````cs1 <- corAR1(form = ~1 | Subject)