spline transformation t series

[lanamarmalade]

when I do proc transreg and specify the spline or sspline option for a variable at the model statement, the output forecast dataset always contains a new column containing the variable name and a prefix t. May I know how this tVariable series is derived during spline or spline transformation of the variable?

For example, work._fcst contains a series tX. Is there a closed form formula that describes the relation between tX and X? Thousands thanks ahead!

proc transreg data=work._0;

ID timestamp;

model identity(Y)=spline(X);

/*or sspline transformation*/

/*model identity(Y)=sspline(X / sm=20);*/

output out=work._fcst;

run;

[jiltao]

The variable tx contains the transformed x values. The documentation below describes the spline basis that is used to compute the transformed x --

https://go.documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=v_009&docsetId=statug&docsetTarget=stat...

The following sample program illustrates how the predicted values for a spline model in PROC TRANSREG are computed, including how the transformed Tx values are computed. It is a function of the spline basis.

data test;

   do x = 1 to 10;

      y = x + log(x) + 2 * sin(x) + 10 * normal(7);

      output;

   end;

run;

**transreg doesn't output the bspline... save coefficients here

  for bspline basis output in next transreg run with ODS;

**save regression coefficients using output statement;

title2 'Fit Curve, Get Predicted Values for All Observations';

proc transreg data=test detail ;

   model ide(y) = spline(x / degree=3) / detail nomiss;

   output out=spline p mrc;

   ods output details=sdetails;

   run;

proc print data=spline;

  title 'TRANSREG OUT= data set using SPLINE transformation';

run;

proc print data=sdetails;

  title 'TRANSREG DETAILS= data set using SPLINE transformation';

run;

*compare regression with transreg after transformation on x;

*note that parameters here agree with last obs of out=spline data set;

proc reg data=spline outest=outest;

   model y=tx;

   title 'REG output for Y vs. Transformed X variable';

quit;

*get the regression coefficients (only) from transreg run;

data regcoeff;

   set spline(where=(upcase(_name_)='TY'));

   keep tintercept tx;

   rename tintercept=regb0 tx=regb1;

run;

proc print data=regcoeff;

  title 'TRANSREG coefficients using SPLINE transformation';

run;

*** so the model is Py = regb0 + regb1*tx =  -1.98554  +  1.54593*tx;

*** Tx is the transformed variable that comes from the spline basis, which is illustrated next;

*** the following program illustrates how tx is computed;

/*-------------------get TX manually-----------------------*/

proc transreg data=x; /* get the B-spline basis */

   model ide(y) = bspline(x) / detail nomiss;

   output out=manually;

run;

proc print data=manually;

  title 'TRANSREG OUT= data set using BSPLINE transformation';

run;

*get transformation coefficients and restructure data set;

data getcoeff;

   set sdetails(where=(term=2 & part>=9));

   part=9-part;

   keep numericvalue part;

run;

proc print data=getcoeff;

run;

proc transpose data=getcoeff out=splinecoef prefix=bx;

   id part;

   var numericvalue;

run;

proc print data=regcoeff;

  title 'Subset of SDETAILS output';

run;

proc print data=splinecoef;

run;

data manually; /* Plug in the coefficients from DETAIL */

   set manually;

   if _n_=1 then set splinecoef;

   if _n_=1 then set regcoeff;

   tx =  bx0 * x_0 + bx_1*x_1 + bx_2* x_2 + bx_3*x_3 ;

   predicty=regb0+regb1*tx;

run;

**compare predicty with Py from out=spline;

data compare;

   merge spline(keep=Py _name_ where=(upcase(_name_)^='TY'))

         manually(keep=predicty);

run;

proc print data=compare;

  title 'Compare resulting computations';

run;

[lanamarmalade]

Hi Jill Tao,

Thanks for your prompt reply. 

What about smoothing spline (the SSPLINE option)? When I use "model identity(Y)=smooth(X/xm=20)", smoothing spline transformation is done in (x,y) pairs and no tX produced. If I use "model identity(y)=sspline(x/xm=20)", however, a tX is present in the output dataset. How is this tX from SSPLINE derived? 

SAS documentation also mentions smoothing spline transformation uses penalty function similar to PSLINE. The problem is PSLINE has a list of different penalty functions to choose from. Which specific penalty function is used by SMOOTH or SSPLINE in SAS Transreg?

Thanks again,

Lana