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The TPSPLINE Procedure

MODEL Statement

MODEL dependents = < regression variables > (smoothing variables) < /options > ;

The MODEL statement specifies the dependent variables, the independent regression variables, which are listed with no parentheses, and the independent smoothing variables, which are listed inside parentheses.

The regression variables are optional. At least one smoothing variable is required, and it must be listed after the regression variables. No variables can be listed in both the regression variable list and the smoothing variable list.

If you specify more than one dependent variable, PROC TPSPLINE calculates a thin-plate smoothing spline estimate for each dependent variable, using the regression variables and smoothing variables specified on the right-hand side.

If you specify regression variables, PROC TPSPLINE fits a semiparametric model using the regression variables as the linear part of the model.

You can specify the following options in the MODEL statement.

ALPHA=number
specifies the significance level \alpha 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 0.05. See the "OUTPUT Statement" section for more information on the OUTPUT statement.

DF=number
specifies the degrees of freedom of the thin-plate smoothing spline estimate, defined as
df=trace(A(\lambda))
where A(\lambda) is the hat matrix. Specify number as a value between zero and the number of unique design points.

DISTANCE=number
D=number
defines a range such that if two data points (xi, zi) and (xj, zj) satisfy
max_k | x_{ik}-x_{jk}| \leq D/2
then these data points are treated as replicates, where xi are the smoothing variables and zi 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. The default value is 0.

LAMBDA0=number
specifies the smoothing parameter, \lambda_0, to be used in the thin-plate smoothing spline estimate. By default, PROC TPSPLINE uses the \lambda parameter that minimizes the GCV function for the final fit. The LAMBDA0= value must be positive.

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

LOGNLAMBDA0=number
LOGNL0=number
specifies the smoothing parameter \lambda_0 on the log10(n\lambda) scale. If you specify both the LOGNL0= and LAMBDA0= options, only the value provided by the LOGNL0= option is used. By default, PROC TPSPLINE uses the \lambda parameter that minimizes the GCV function for the estimate.

LOGNLAMBDA=list-of-values
LOGNL=list-of-values
specifies a set of values for the \lambda parameter on the log10(n\lambda) scale. PROC TPSPLINE returns a GCV value for each \lambda point that you specify. You can use the LOGNLAMBDA= option to study the GCV function curve for a set of \lambda values. If you specify both the LOGNL= and LAMBDA= options, only the list of values provided by LOGNL= option is used.

In some cases, the LOGNL= option may be prefered 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 \lambda on the log10 scale, the allowable range is enlarged to include negative values. Thus, the GCV function is less sensitive to changes in LOGNLAMBDA.

M=number
specifies the order of the derivative in the penalty term. The M= value must be a positive integer. The default value is the max(2, INT(d/2)+1), where d is the number of smoothing variables.

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