# pwaldtest: Wald-style Chi-square Test and F Test In plm: Linear Models for Panel Data

 pwaldtest R Documentation

## Wald-style Chi-square Test and F Test

### Description

Wald-style Chi-square test and F test of slope coefficients being zero jointly, including robust versions of the tests.

### Usage

``````pwaldtest(x, ...)

## S3 method for class 'plm'
pwaldtest(
x,
test = c("Chisq", "F"),
vcov = NULL,
df2adj = (test == "F" && !is.null(vcov) && missing(.df2)),
.df1,
.df2,
...
)

## S3 method for class 'pvcm'
pwaldtest(x, ...)

## S3 method for class 'pgmm'
pwaldtest(x, param = c("coef", "time", "all"), vcov = NULL, ...)
``````

### Arguments

 `x` an estimated model of which the coefficients should be tested (usually of class `"plm"`/`"pvcm"`/`"pgmm"`)', `...` further arguments (currently none). `test` a character, indicating the test to be performed, may be either `"Chisq"` or `"F"` for the Wald-style Chi-square test or F test, respectively, `vcov` `NULL` by default; a `matrix` giving a variance–covariance matrix or a function which computes such; if supplied (non `NULL`), the test is carried out using the variance–covariance matrix indicated resulting in a robust test, `df2adj` logical, only relevant for `test = "F"`, indicating whether the adjustment for clustered standard errors for the second degrees of freedom parameter should be performed (see Details, also for further requirements regarding the variance–covariance matrix in `vcov` for the adjustment to be performed), `.df1` a numeric, used if one wants to overwrite the first degrees of freedom parameter in the performed test (usually not used), `.df2` a numeric, used if one wants to overwrite the second degrees of freedom parameter for the F test (usually not used), `param` (for pgmm method only): select the parameters to be tested: `"coef"`, `"time"`, or '"all"“.

### Details

`pwaldtest` can be used stand–alone with a plm object, a pvcm object, and a pgmm object (for pvcm objects only the 'random' type is valid and no further arguments are processed; for pgmm objects only arguments `param` and `vcov` are valid). It is also used in `summary.plm()` to produce the F statistic and the Chi-square statistic for the joint test of coefficients and in `summary.pgmm()`.

`pwaldtest` performs the test if the slope coefficients of a panel regression are jointly zero. It does not perform general purpose Wald-style tests (for those, see `lmtest::waldtest()` (from package lmtest) or `car::linearHypothesis()` (from package car)).

If a user specified variance-covariance matrix/function is given in argument `vcov`, the robust version of the tests are carried out. In that case, if the F test is requested (`test = "F"`) and no overwriting of the second degrees of freedom parameter is given (by supplying argument (`.df2`)), the adjustment of the second degrees of freedom parameter is performed by default. The second degrees of freedom parameter is adjusted to be the number of unique elements of the cluster variable - 1, e. g., the number of individuals minus 1. For the degrees of freedom adjustment of the F test in general, see e. g. \insertCiteCAME:MILL:15;textualplm, section VII; \insertCiteANDR:GOLS:SCMI:13plm, pp. 126, footnote 4.

The degrees of freedom adjustment requires the vcov object supplied or created by a supplied function to carry an attribute called "cluster" with a known clustering described as a character (for now this could be either `"group"` or `"time"`). The vcovXX functions of the package plm provide such an attribute for their returned variance–covariance matrices. No adjustment is done for unknown descriptions given in the attribute "cluster" or when the attribute "cluster" is not present. Robust vcov objects/functions from package clubSandwich work as inputs to `pwaldtest`'s F test because a they are translated internally to match the needs described above.

### Value

An object of class `"htest"`, except for pvcm's within model for which a data.frame with results of the Wald chi-square tests and F tests per regression is returned.

### Author(s)

Yves Croissant (initial implementation) and Kevin Tappe (extensions: vcov argument and F test's df2 adjustment)

### References

\insertRef

WOOL:10plm

\insertRef

ANDR:GOLS:SCMI:13plm

\insertRef

CAME:MILL:15plm

`vcovHC()` for an example of the vcovXX functions, a robust estimation for the variance–covariance matrix; `summary.plm()`

### Examples

``````
data("Grunfeld", package = "plm")
mod_fe <- plm(inv ~ value + capital, data = Grunfeld, model = "within")
mod_re <- plm(inv ~ value + capital, data = Grunfeld, model = "random")
pwaldtest(mod_fe, test = "F")
pwaldtest(mod_re, test = "Chisq")

# with robust vcov (matrix, function)
pwaldtest(mod_fe, vcov = vcovHC(mod_fe))
pwaldtest(mod_fe, vcov = function(x) vcovHC(x, type = "HC3"))