# varIdent: Constant Variance Function In nlme: Linear and Nonlinear Mixed Effects Models

 varIdent R Documentation

## Constant Variance Function

### Description

This function is a constructor for the `varIdent` class, representing a constant variance function structure. If no grouping factor is present in `form`, the variance function is constant and equal to one, and no coefficients required to represent it. When `form` includes a grouping factor with M > 1 levels, the variance function allows M different variances, one for each level of the factor. For identifiability reasons, the coefficients of the variance function represent the ratios between the variances and a reference variance (corresponding to a reference group level). Therefore, only M-1 coefficients are needed to represent the variance function. By default, if the elements in `value` are unnamed, the first group level is taken as the reference level.

### Usage

```varIdent(value, form, fixed)
```

### Arguments

 `value` an optional numeric vector, or list of numeric values, with the variance function coefficients. If no grouping factor is present in `form`, this argument is ignored, as the resulting variance function contains no coefficients. If `value` has length one, its value is repeated for all coefficients in the variance function. If `value` has length greater than one, it must have length equal to the number of grouping levels minus one and names which identify its elements to the levels of the grouping factor. Only positive values are allowed for this argument. Default is `numeric(0)`, which results in a vector of zeros of appropriate length being assigned to the coefficients when `object` is initialized (corresponding to constant variance equal to one). `form` an optional one-sided formula of the form `~ v`, or `~ v | g`, specifying a variance covariate `v` and, optionally, a grouping factor `g` for the coefficients. The variance covariate is ignored in this variance function. When a grouping factor is present in `form`, a different coefficient value is used for each of its levels less one reference level (see description section below). Several grouping variables may be simultaneously specified, separated by the `*` operator, like in `~ v | g1 * g2 * g3`. In this case, the levels of each grouping variable are pasted together and the resulting factor is used to group the observations. Defaults to `~ 1`. `fixed` an optional numeric vector, or list of numeric values, specifying the values at which some or all of the coefficients in the variance function should be fixed. It must have names identifying which coefficients are to be fixed. Coefficients included in `fixed` are not allowed to vary during the optimization of an objective function. Defaults to `NULL`, corresponding to no fixed coefficients.

### Value

a `varIdent` object representing a constant variance function structure, also inheriting from class `varFunc`.

### Author(s)

José Pinheiro and Douglas Bates bates@stat.wisc.edu

### References

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

`varClasses`, `varWeights.varFunc`, `coef.varIdent`
```vf1 <- varIdent(c(Female = 0.5), form = ~ 1 | Sex)