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A standard measure of goodness of fit is the mean residual sum of squares
The estimator that results from minimizing S()is called a thin-plate smoothing spline estimator. Wahba and Wendelberger (1980) derived a closed form expression for the thin-plate smoothing spline estimator.
Note | The computations for a thin-plate smoothing spline are time intensive, especially for large data sets. |
The smoothing parameter controls the amount of smoothing; that is, it controls the trade-off between the goodness of fit to the data and the smoothness of the fit. You select a smoothing parameter by specifying a constant c in the formula
The values of the explanatory variables are scaled by their corresponding interquartile ranges before the computations. This makes the computations independent of the units of X1 and X2.
After choosing Graphs:Surface Plot:Spline from the menu, you specify a smoothing parameter selection method in the Spline Fit dialog.
The default Method:GCV uses a c value that minimizes the generalized cross validation mean squared error .Figure 39.29 displays smoothing spline estimates with c values of 0.0000831 (the GCV value) and 0.4127 (DF=6). Use the slider in the table to change the c value of the spline fit.
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