Splines in SASGLIMMIX

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Splines in SAS/GLIMMIX

• Andrew Redd

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What is GLIMMIX?

• Generalized Linear Mixed Model
• Non-normal response
• Random Effects

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What are Splines?

• Mathematical tool for approximating functions
• Smooth functions
• In statistics we use penalized splines.
• Fit by optimizing penalized likelihood.

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Why Splines?

• Fast
• Stable
• Can be implemented with mixed model software
• Downside?
• Requires knot selection and penalty parameter

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How are Splines Used in GLIMMIX

• Radial Smoother
• The RSmooth option in RANDOM statement
• Depends only on the distance between points
• Scales to any dimension
• Thin Plan Splines
• Default automatic bivariate smoother given in
  Ruppert, Wand, and Carroll (2003)
• Less a random component than a semiparametric
  component

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Types of Data

• Time
• Spatial
• Repeated Measures

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Knot Selection

• K-D Tree
• Uniform
• Fixed
• For use with alternative methods such as space
  filling algorithms

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Examples

• Simple Spline
• State expenditures by percent of the population
  living in a metropolitan area
• Bivariate Spline
• Ground Zinc pollution levels surrounding a
  factory in West Virginia.