specifies the significance level of the confidence limits on the final thin-plate smoothing spline estimate when you request confidence limits to be included in the output data set. Specify number as a value between 0 and 1. The default value is . See the section OUTPUT Statement for more information about the OUTPUT statement.

specifies the degrees of freedom of the thin-plate smoothing spline estimate, defined as

where is the hat matrix. Specify number as a value between zero and the number of unique design points . Smaller values cause more penalty on the roughness and thus smoother fits.

defines a range such that if the distance between two data points and satisfies

then these data points are treated as replicates, where are the smoothing variables and are the regression variables.

You can use the DISTANCE=  option to reduce the number of unique design points by treating nearby data as replicates. This can be useful when you have a large data set. Larger DISTANCE=  option values cause fewer points. The default value is 0.

PROC TPSPLINE uses the DISTANCE=  value to group points as follows: The data are first sorted by the smoothing variables in the order in which they appear in the MODEL statement. The first point in the sorted data becomes the first unique point. Subsequent points have their x-values set equal to that point until the first point where the maximum distance in one dimension is larger than . This point becomes the next unique point, and so on. Because of this sequential processing, the set of unique points differs depending on the order of the smoothing variables in the MODEL statement.

For example, with a model that has two smoothing variables (x1,x2), the data are first sorted by x1 and x2 (in that order), and then uniqueness is assessed sequentially. The first point in the sorted data becomes the first unique point, . Subsequent points are set equal to until the algorithm comes to a point with . This point becomes the second unique point , and we proceed from there.

specifies the smoothing parameter, , to be used in the thin-plate smoothing spline estimate. By default, PROC TPSPLINE uses the parameter that minimizes the GCV function for the final fit. The LAMBDA0=  value must be positive. Larger values cause smoother fits.

specifies a set of values for the parameter. PROC TPSPLINE returns a GCV value for each point that you specify. You can use the LAMBDA= option to study the GCV function curve for a set of values for . All values listed in the LAMBDA=  option must be positive.

specifies the smoothing parameter on the scale. If you specify both the LOGNL0=  and LAMBDA0=  options, only the value provided by the LOGNL0=  option is used. Larger values cause smoother fits. By default, PROC TPSPLINE uses the parameter that minimizes the GCV function for the estimate.

specifies a set of values for the parameter on the scale. PROC TPSPLINE returns a GCV value for each point that you specify. You can use the LOGNLAMBDA=  option to study the GCV function curve for a set of values. If you specify both the LOGNL=  and LAMBDA=  options, only the list of values provided by the LOGNL=  option is used.

In some cases, the LOGNL=  option might be preferred over the LAMBDA=  option. Because the LAMBDA=  value must be positive, a small change in that value can result in a major change in the GCV value. If you instead specify on the scale, the allowable range is enlarged to include negative values. Thus, the GCV function is less sensitive to changes in LOGNLAMBDA.

The DF=  option, LAMBDA0=  option, and LOGNLAMBDA0=  option all specify exact smoothness of a nonparametric fit. If you want to fit a model with specified smoothness, the DF=  option is preferable to the other two options because , the range of , is much smaller in length than of and of .

specifies the order of the derivative in the penalty term. The M=  value must be a positive integer. The default value is , where is the number of smoothing variables.