# coeftest

##### Inference for Estimated Coefficients

`coeftest`

is a generic function for performing
z and (quasi-)t Wald tests of estimated coefficients.
`coefci`

computes the corresponding Wald confidence
intervals.

- Keywords
- htest

##### 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

##### Examples

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

*Documentation reproduced from package lmtest, version 0.9-37, License: GPL-2 | GPL-3*