raintest               package:lmtest               R Documentation

_R_a_i_n_b_o_w _T_e_s_t

_D_e_s_c_r_i_p_t_i_o_n:

     Rainbow test for linearity.

_U_s_a_g_e:

     raintest(formula, fraction = 0.5, order.by = NULL, center = NULL,
        data=list())

_A_r_g_u_m_e_n_t_s:

 formula: a symbolic describtion for the model to be tested.

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 formula or a string. A formula with a single
          explanatory variable like `~ x'. The observations in the
          model are ordered by the size of `x'. 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 distance of the data.

  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.

_D_e_t_a_i_l_s:

     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 inferious to
     the fit of 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'.

_V_a_l_u_e:

     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.

_R_e_f_e_r_e_n_c_e_s:

     J.M. Utts (1982), The Rainbow Test for Lack of Fit in Regression.
     Communications in Statistics - Theory and Methods 11, 1801-1815

     W. Kraemer & H. Sonnberger (1986), The Linear Regression Model
     under Test. Heidelberg: Physica

_S_e_e _A_l_s_o:

     `lm'

_E_x_a_m_p_l_e_s:

     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])

