R: Inference for Estimated Coefficients

coeftest {lmtest} | R Documentation

## Inference for Estimated Coefficients

### Description

`coeftest` is a generic function for performing z and (quasi-)t Wald tests of estimated coefficients. `coefci` computes the corresponding Wald confidence intervals.

### Usage

    coeftest(x, vcov. = NULL, df = NULL, ...)

    coefci(x, parm = NULL, level = 0.95, vcov. = NULL, df = NULL, ...)

### Arguments

`x` | an object (for details see below).
`vcov.` | a specification of the covariance matrix of the estimated coefficients. This can be specified as a matrix or as a function yielding a matrix when applied to `x`.
`df` | the degrees of freedom to be used. If this is a finite positive number a t test with `df` degrees of freedom is performed. In all other cases, a z test (using a normal approximation) is performed. By default it tries to use `x$df.residual` and performs a z test if this is `NULL`.
`...` | further arguments passed to the methods and to `vcov.` in the default method.
`parm` | a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
`level` | the confidence level required.

### Details

The generic function `coeftest` currently has a default method (which works in particular for `"lm"` objects) and dedicated methods for objects of class `"glm"` (as computed by `glm`), `"mlm"` (as computed by `lm` with multivariate responses), `"survreg"` (as computed by `survreg`), and `"breakpointsfull"` (as computed by `breakpoints.formula`).

The default method assumes that a `coef` methods exists, such that `coef(x)` yields the estimated coefficients.

To specify the corresponding covariance matrix `vcov.` to be used, there are three possibilities: 1. It is pre-computed and supplied in argument `vcov.`. 2. A function for extracting the covariance matrix from `x` is supplied, e.g., `sandwich`, `vcovHC`, `vcovCL`, or `vcovHAC` from package sandwich. 3. `vcov.` is set to `NULL`, then it is assumed that a `vcov` method exists, such that `vcov(x)` yields a covariance matrix. For illustrations see below.

The degrees of freedom `df` determine whether a normal approximation is used or a t distribution with `df` degrees of freedoms is used. The default method uses `df.residual(x)` and if this is `NULL` a z test is performed. The method for `"glm"` objects always uses `df = Inf` (i.e., a z test).

The corresponding Wald confidence intervals can be computed either by applying `coefci` to the original model or `confint` to the output of `coeftest`. See below for examples.

### Value

`coeftest` returns an object of class `"coeftest"` which is essentially a coefficient matrix with columns containing the estimates, associated standard errors, test statistics and p values.

`coefci` returns a matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labeled as (1-level)/2 and 1 - (1-level)/2 in percent.

### See Also

`lm`, `waldtest`

### Examples

    ## load data and fit model
    data("Mandible", package = "lmtest")
    fm <- lm(length ~ age, data = Mandible, subset=(age <= 28))

    ## the following commands lead to the same tests:
    summary(fm)
    (ct <- coeftest(fm))

    ## a z test (instead of a t test) can be performed by
    coeftest(fm, df = Inf)

    ## corresponding confidence intervals
    confint(ct)
    coefci(fm)
    ## which in this simple case is equivalent to
    confint(fm)

    if(require("sandwich")) {
    ## a different covariance matrix can be also used:
    (ct <- coeftest(fm, df = Inf, vcov = vcovHC))

    ## the corresponding confidence interval can be computed either as
    confint(ct)
    ## or based on the original model
    coefci(fm, df = Inf, vcov = vcovHC)

    ## note that the degrees of freedom _actually used_ can be extracted
    df.residual(ct)
    ## which differ here from
    df.residual(fm)

    ## vcov can also be supplied as a function with additional arguments
    coeftest(fm, df = Inf, vcov = vcovHC, type = "HC0")
    ## or as a matrix
    coeftest(fm, df = Inf, vcov = vcovHC(fm, type = "HC0"))
    }

[Package lmtest version 0.9-37 Index]