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# How can I interpret the parameter estimates of the B-spline basis functions in SAS 9.4?

I am using the effect statement in SAS 9.4 in order to estimate a nonparametric quantile regression with quadratic B-splines. I had chosen 2 internal knots and therefore got 5 basis functions. But I am struggling with the interpretation of the output. How can I read the table containing the parameter estimates? What is the meaning of the values? Why do I get an additional row with zeros?

My output looks similar to the second table given on this page:

http://support.sas.com/kb/57/682.html

In this example, there is also an extra row for the parameter of "sWeight7" which contains zeros.

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‎07-06-2016 12:02 PM
SAS Super FREQ
Posts: 3,556

## Re: How can I interpret the parameter estimates of the B-spline basis functions in SAS 9.4?

A sentence just before the table that you reference says

"This flexibility comes at the cost of largely removing any meaningful interpretation of the individual parameter estimates."

Therefore you should not expect the results to be interpretable in terms of the underlying explanatory variable.

If you question is "what do these coefficients mean," then the answer is given in the SAS/STAT doc in the section "Splines and Spline Bases."  Each coefficient represents the coefficient of a B-spline basis that are placed at uniformly spaced knots. The predicted values are represented as a linear combination of those coefficients times the corresponding basis functions.

As shown in the documentation of the TRANSREG procedure, a spline effect generates columns in a design matrix. The extra row of zeros occurs because you are using a SAS procedure (QUANTREG?) that uses a GLM parameterization of classification effects.

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‎07-06-2016 12:02 PM
SAS Super FREQ
Posts: 3,556

## Re: How can I interpret the parameter estimates of the B-spline basis functions in SAS 9.4?

A sentence just before the table that you reference says

"This flexibility comes at the cost of largely removing any meaningful interpretation of the individual parameter estimates."

Therefore you should not expect the results to be interpretable in terms of the underlying explanatory variable.

If you question is "what do these coefficients mean," then the answer is given in the SAS/STAT doc in the section "Splines and Spline Bases."  Each coefficient represents the coefficient of a B-spline basis that are placed at uniformly spaced knots. The predicted values are represented as a linear combination of those coefficients times the corresponding basis functions.

As shown in the documentation of the TRANSREG procedure, a spline effect generates columns in a design matrix. The extra row of zeros occurs because you are using a SAS procedure (QUANTREG?) that uses a GLM parameterization of classification effects.

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