statsmodels.stats.diagnostic.linear_rainbow

statsmodels.stats.diagnostic.linear_rainbow(res, frac=0.5, order_by=None, use_distance=False, center=None)[source]

Rainbow test for linearity

The null hypothesis is the fit of the model using full sample is the same as using a central subset. The alternative is that the fits are difference. The rainbow test has power against many different forms of nonlinearity.

Parameters:

  • res (RegressionResults) – A results instance from a linear regression.

  • frac (float, default 0.5) – The fraction of the data to include in the center model.

  • order_by ({ndarray, str, List[str]}, default None) – If an ndarray, the values in the array are used to sort the observations. If a string or a list of strings, these are interpreted as column name(s) which are then used to lexicographically sort the data.

  • use_distance (bool, default False) – Flag indicating whether data should be ordered by the Mahalanobis distance to the center.

  • center ({float, int}, default None) – If a float, the value must be in [0, 1] and the center is center * nobs of the ordered data. If an integer, must be in [0, nobs) and is interpreted as the observation of the ordered data to use.

Returns:

  • fstat (float) – The test statistic based on the F test.

  • pvalue (float) – The pvalue of the test.

Notes

This test assumes residuals are homoskedastic and may reject a correct linear specification if the residuals are heteroskedastic.