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The TPSPLINE Procedure |

**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 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
*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
(
and (*x*_{i},*z*_{i})satisfy*x*_{j},*z*_{j})are the smoothing variables and*x*_{i}are the regression variables.*z*_{i}

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, , 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.

**LAMBDA=***list-of-values*-
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.

**LOGNLAMBDA0=***number***LOGNL0=***number*-
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. By default,
PROC TPSPLINE uses the parameter
that minimizes the GCV function for the estimate.

**LOGNLAMBDA=***list-of-values***LOGNL=***list-of-values*-
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 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 on the*log*scale, the allowable range is enlarged to include negative values. Thus, the GCV function is less sensitive to changes in LOGNLAMBDA._{10} **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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