Language Reference |
TPSPLNEV Call |
The TPSPLNEV subroutine evaluates the thin-plate smoothing spline (TPSS) at new data points. It is used after the TPSPLINE subroutine fits a thin-plate spline model to data.
The TPSPLNEV subroutine returns the following value:
is an vector of the predicated values of the TPSS fit evaluated at new data points.
The input arguments to the TPSPLNEV subroutine are as follows:
is an matrix of data points at which the is evaluated, where is the number of new data points and is the number of variables in the spline model.
is an matrix of design points that is used as an input of TPSPLINE call.
is the coefficient vector returned from the TPSPLINE call.
See the previous section on the TPSPLINE call for details about the TSPLNEV subroutine.
As an example, consider the following data set, which consists of two independent variables. The plot of the raw data can be found in the first panel of Figure 23.224.
x={ -1.0 -1.0, -1.0 -1.0, -0.5 -1.0, -0.5 -1.0, 0.0 -1.0, 0.0 -1.0, 0.5 -1.0, 0.5 -1.0, 1.0 -1.0, 1.0 -1.0, -1.0 -0.5, -1.0 -0.5, -0.5 -0.5, -0.5 -0.5, 0.0 -0.5, 0.0 -0.5, 0.5 -0.5, 0.5 -0.5, 1.0 -0.5, 1.0 -0.5, -1.0 0.0, -1.0 0.0, -0.5 0.0, -0.5 0.0, 0.0 0.0, 0.0 0.0, 0.5 0.0, 0.5 0.0, 1.0 0.0, 1.0 0.0, -1.0 0.5, -1.0 0.5, -0.5 0.5, -0.5 0.5, 0.0 0.5, 0.0 0.5, 0.5 0.5, 0.5 0.5, 1.0 0.5, 1.0 0.5, -1.0 1.0, -1.0 1.0, -0.5 1.0, -0.5 1.0, 0.0 1.0, 0.0 1.0, 0.5 1.0, 0.5 1.0, 1.0 1.0, 1.0 1.0 }; y = {15.54, 15.76, 18.67, 18.50, 19.66, 19.80, 18.60, 18.52, 15.87, 16.04, 10.92, 11.14, 14.81, 14.83, 16.56, 16.44, 14.91, 15.06, 10.92, 10.94, 9.61, 9.65, 14.03, 14.03, 15.77, 16.00, 14.00, 14.03, 9.56, 9.58, 11.21, 11.09, 14.84, 14.99, 16.55, 16.51, 14.98, 14.72, 11.15, 11.17, 15.83, 15.96, 18.64, 18.56, 19.54, 19.81, 18.57, 18.61, 15.87, 15.90 };
Now generate a sequence of from to so that you can study the GCV function within this range. Use the following statement:
lambda = T( do(-3.8, -3.3, 0.1) );
Use the following statement to do the thin-plate smoothing spline fit and returning the fitted values on those design points.
call tpspline(fit, coef, adiag, gcv, x, y, lambda);
The output from this call follows.
SUMMARY OF TPSPLINE CALL Number of observations 50 Number of unique design points 25 Dimension of polynomial Space 3 Number of Parameters 28 GCV Estimate of Lambda 0.00000668 Smoothing Penalty 2558.14323 Residual Sum of Squares 0.24611 Trace of (I-A) 25.40680 Sigma^2 estimate 0.00969 Sum of Squares for Replication 0.24223
After this TPSPLINE call, you obtained the fitted value. The fitted surface is plotted in the second panel of Figure 23.224. Also in Figure 23.224, panel 4, you plot the GCV function values against lambda. From panel 2, you see that because of the spare design points, the fitted surface is a little bit rough. In order to study the TPSS fit more closely, you can use the following statements to generate a more dense grid on .
xGrid = T( do(-1, 1, 0.1) ); yGrid = T( do(-1, 1, 0.1) ); do i = 1 to nrow(xGrid); x1 = x1 // repeat(xGrid[i], nrow(yGrid)); x2 = x2 // yGrid; end; xpred = x1 || x2;
Now you can use the function TPSPLNEV to evaluate on this dense grid. Here is the statement:
call tpsplnev(pred, xpred, x, coef);
The final fitted surface is plotted in Figure 23.224, panel 3.
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