Comments on: Thurs Apr 5 http://www.stat.cmu.edu/~kass/smnp/?p=116 Thu, 26 Apr 2012 14:07:02 +0000 hourly 1 http://wordpress.org/?v=3.0.4 By: Rob Rasmussen http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-281 Rob Rasmussen Thu, 05 Apr 2012 13:17:24 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-281 I am having trouble seeing how the spline regression is solved by fitting equation 16.3 I am having trouble seeing how the spline regression is solved by fitting equation 16.3

]]> By: Rich Truncellito http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-280 Rich Truncellito Thu, 05 Apr 2012 12:44:20 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-280 In reading about choosing a number of knots for creating splines, I initially found it counterintuitive that choosing more knots to create more splines generates a less smooth fit than choosing fewer knots to create fewer splines. Does choosing more knots generate a less smooth fit, because with more knots the whole fitted curve becomes overly sensitive to slight changes in the data? In reading about choosing a number of knots for creating splines, I initially found it counterintuitive that choosing more knots to create more splines generates a less smooth fit than choosing fewer knots to create fewer splines. Does choosing more knots generate a less smooth fit, because with more knots the whole fitted curve becomes overly sensitive to slight changes in the data?

]]> By: Amanda Markey http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-279 Amanda Markey Thu, 05 Apr 2012 12:39:23 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-279 On page 486, I'm not sure why x4 = (0,0,0,1,8,27,64)T. On page 486, I’m not sure why x4 = (0,0,0,1,8,27,64)T.

]]> By: Matt Bauman http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-278 Matt Bauman Thu, 05 Apr 2012 12:26:18 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-278 One powerful feature of regression is its ability to compare different datasets. How would one compare two datasets when fitting with splines? Do you keep the knot locations constant? Or simply the number of knots? Is this even done? More specifically, can you obtain a p-value in comparison to some null hypothesis (e.g., there's only one spline segment)? One powerful feature of regression is its ability to compare different datasets. How would one compare two datasets when fitting with splines? Do you keep the knot locations constant? Or simply the number of knots? Is this even done? More specifically, can you obtain a p-value in comparison to some null hypothesis (e.g., there’s only one spline segment)?

]]> By: Matt Panico http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-277 Matt Panico Thu, 05 Apr 2012 06:21:54 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-277 Are splines useful with multiple predictors? That many equations might overload processing time. Are splines useful with multiple predictors? That many equations might overload processing time.

]]> By: David Zhou http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-276 David Zhou Thu, 05 Apr 2012 06:19:10 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-276 I realize that this might be problematic, but what is the major error in choosing knots from points of inflection from a derivative of the curve that you're trying to fit? I'm guessing that's building some assumptions of behavior into the regression, so can you talk about some of the things that choice of the knot set is trying to avoid? I realize that this might be problematic, but what is the major error in choosing knots from points of inflection from a derivative of the curve that you’re trying to fit? I’m guessing that’s building some assumptions of behavior into the regression, so can you talk about some of the things that choice of the knot set is trying to avoid?

]]> By: Jay Scott http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-275 Jay Scott Thu, 05 Apr 2012 05:09:38 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-275 p489 and 490, I am having a lot of difficulty understanding what you mean by "A second intuition is obtained by replacing the least-squares problem of minimizing the sum of squares with the penalized least squares problem of minimizing the penalized sum of squares where λ is a constant." Also if the squared 2nd derivative is a "roughness penalty" and it's integral is a roughness measure, does that simply mean that the 1st derivative is the roughness measure? If yes, could would a derivative of any roughness measure be its penalty? p489 and 490, I am having a lot of difficulty understanding what you mean by “A second intuition is obtained by replacing the least-squares problem of minimizing the sum of squares with the penalized least squares problem of minimizing the penalized sum of squares where λ is a constant.”

Also if the squared 2nd derivative is a “roughness penalty” and it’s integral is a roughness measure, does that simply mean that the 1st derivative is the roughness measure? If yes, could would a derivative of any roughness measure be its penalty?

]]> By: Shubham Debnath http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-274 Shubham Debnath Thu, 05 Apr 2012 04:39:38 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-274 Are there other nonlinear smoothers aside from BARS? Are they useful at all? And how much slower are they than linear smoothers or BARS? Are there other nonlinear smoothers aside from BARS? Are they useful at all? And how much slower are they than linear smoothers or BARS?

]]> By: Ben Dichter http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-273 Ben Dichter Thu, 05 Apr 2012 04:39:21 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-273 it seems the roughness penalty plays a similar role to correction term we used earlier to prevent overfitting of multivariate regression. Is the second derivative always something you want to minimize? Would you penalize anything else? it seems the roughness penalty plays a similar role to correction term we used earlier to prevent overfitting of multivariate regression. Is the second derivative always something you want to minimize? Would you penalize anything else?

]]> By: Rex Tien http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-272 Rex Tien Thu, 05 Apr 2012 03:54:27 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=116#comment-272 We focus mainly on cubic splines. But we could theoretically use any type of polynomial for splines. Are the splines limited to polynomials in order to use the regression method for calculating the splines? Or can we use any type of function? If so is there a method for determining what form of function is best for the splines? We focus mainly on cubic splines. But we could theoretically use any type of polynomial for splines. Are the splines limited to polynomials in order to use the regression method for calculating the splines? Or can we use any type of function? If so is there a method for determining what form of function is best for the splines?

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