| gqtest {lmtest} | R Documentation |
Goldfeld-Quandt test against heteroskedasticity.
gqtest(formula, point = 0.5, fraction = 0, alternative = c("greater", "two.sided", "less"),
order.by = NULL, data = list())
formula |
a symbolic description for the model to be tested
(or a fitted "lm" object). |
point |
numerical. If point is smaller than 1 it is
interpreted as percentages of data, i.e. n*point is
taken to be the (potential) breakpoint in the variances, if
n is the number of observations in the model. If point
is greater than 1 it is interpreted to be the index of the breakpoint. |
fraction |
numerical. The number of central observations to be omitted.
If fraction is smaller than 1, it is chosen to be fraction*n
if n is the number of observations in the model. |
alternative |
a character string specifying the alternative hypothesis. The default is to test for increasing variances. |
order.by |
Either a vector z or a formula with a single explanatory
variable like ~ z. The observations in the model
are ordered by the size of z. If set to NULL (the
default) the observations are assumed to be ordered (e.g., a
time series). |
data |
an optional data frame containing the variables in the model.
By default the variables are taken from the environment which gqtest
is called from. |
The Goldfeld-Quandt test compares the variances of two submodels divided by a specified breakpoint and rejects if the variances differ.
Under H_0 the test statistic of the Goldfeld-Quandt test follows an F
distribution with the degrees of freedom as given in parameter.
Examples can not only be found on this page, but also on the help pages of the
data sets bondyield, currencysubstitution,
growthofmoney, moneydemand,
unemployment, wages.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
parameter |
degrees of freedom. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
S.M. Goldfeld & R.E. Quandt (1965), Some Tests for Homoskedasticity. Journal of the American Statistical Association 60, 539–547
W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica
## generate a regressor x <- rep(c(-1,1), 50) ## generate heteroskedastic and homoskedastic disturbances err1 <- c(rnorm(50, sd=1), rnorm(50, sd=2)) err2 <- rnorm(100) ## generate a linear relationship y1 <- 1 + x + err1 y2 <- 1 + x + err2 ## perform Goldfeld-Quandt test gqtest(y1 ~ x) gqtest(y2 ~ x)