| raintest {lmtest} | R Documentation |
Rainbow test for linearity.
raintest(formula, fraction = 0.5, order.by = NULL, center = NULL, data=list())
formula |
a symbolic description for the model to be tested
(or a fitted "lm" object). |
fraction |
numeric. The percentage of observations in the subset is
determined by
fraction*n if n is the number of observations
in the model. |
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). If set to "mahalanobis" then the observations
are ordered by their Mahalanobis distances from the mean regressor. |
center |
numeric. If center is smaller than 1 it is
interpreted as percentages of data, i.e. the subset is chosen that
n*fraction observations are around observation number
n*center. If center is greater than 1 it is interpreted to be
the index of the center of the subset. By default center is 0.5.
If the Mahalanobis distance is chosen center is taken to be
the mean regressor, but can be specified to be a k-dimensional
vector if k is the number of regressors and should be in the
range of the respective regressors. |
data |
an optional data frame containing the variables in the model.
By default the variables are taken from the environment which
raintest is called from. |
The basic idea of the Rainbow test is that even if the true
relationship is
non-linear, a good linear fit can be achieved on a subsample in the "middle" of
the data. The null hypothesis is rejected whenever the overall fit is
significantly worse than the fit for the subsample. The test statistic under
H_0 follows an F distribution with parameter degrees of freedom.
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. |
J.M. Utts (1982), The Rainbow Test for Lack of Fit in Regression. Communications in Statistics - Theory and Methods 11, 1801–1815
W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica
x <- c(1:30) y <- x^2 + rnorm(30,0,2) rain <- raintest(y ~ x) rain ## critical value qf(0.95, rain$parameter[1], rain$parameter[2])