coeftest
is a generic function for performing
z and (quasi-)t Wald tests of estimated coefficients.
coefci
computes the corresponding Wald confidence
intervals.
coeftest(x, vcov. = NULL, df = NULL, …)coefci(x, parm = NULL, level = 0.95, vcov. = NULL, df = NULL, …)
an object (for details see below).
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
.
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.
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.
the confidence level required.
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.
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.
# 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")) } # }
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