gqtest(formula, point = 0.5, fraction = 0,
alternative = c("greater", "two.sided", "less"),
order.by = NULL, data = list())
Arguments
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.
Details
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.
Value
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.
References
S.M. Goldfeld & R.E. Quandt (1965),
Some Tests for Homoskedasticity.
Journal of the American Statistical Association60, 539–547
W. Krämer & H. Sonnberger (1986),
The Linear Regression Model under Test. Heidelberg: Physica
See Also
lm
Examples
## 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)