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Degrees of Freedom

When the Grid Search Method is used, the degree of freedom for the estimated regression coefficient is d=n*-2(k+1), where k is the number of joinpoints and n* is the effective number of data points after deleting offending observations, data points that are on joinpoints.

When Hudson's Method is used for a continuous fitting, the degree of freedom is adjusted in a continuous manner instead of subtracting the offending observations. The idea is to delete, with higher probabilities, the observations whose x-values are closer to joinpoints, while no more than one observation is deleted around each joinpoint. See Kim et al. (Kim, H.-J., Yu, B. and Feuer, E.J. (2008) "Inference in segmented line regression: A simulation study", Journal of Statistical Computation and Simulation 78(11), 1087-1103) for details.