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Introduction to Smoothing and P-spline Techniques using R



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Introduction to Smoothing and P-spline Techniques using R

taught by Brian Marx
and Paul Eilers

Aim of Course:

The linear model is ubiquitous in classical statistics, yet real-life data rarely follow a purely linear pattern.  In fact, real-life data often do not follow a pattern that is well-described by a single simple function of any sort.  Splines are combinations of different functions that are used to describe and model data differentially in a smooth fashion over different ranges.

P-splines are especially popular (over 500 citations for the instructors' original article in Statistical Science introducing P-splines) because they are widely applicable and effective. In this course, you will learn how to use R software for data smoothing via P-splines - a combination of regression on a B-spline basis (basis splines) and difference penalties (on the B-spline coefficients).

We survey a variety of scatterplot smoothing techniques, including running means, running lines, kernel, loess, and smoothing splines, and basis function approaches, e.g. using B-splines. We focus on P-splines, which is a combination of regression on a B-spline basis (basis splines) and difference penalties (on the B-spline coefficients). We will see that P-splines are especially popular because they are effective, widely applicable, and are easily extended in to generalized linear smoothing, density estimation, variance smoothing, generalized additive models, and 2-dimensional smoothing. In this online course, "Introduction to Smoothing and P-spline Techniques using R" you will learn how to use a variety of R software for standard data smoothing, as well as via P-splines.


This course may be taken individually (one-off) or as part of a certificate program.

Course Program:

WEEK 1:  Smoothing via Regression - Local vs Global Bases

  • Overview of smoothing techniques:kernels to smoothing splines
  • Global bases can be ineffective
  • Local bases are attractive
  • B-splines
  • Difference penalties


WEEK 2: Introducing P-splines

  • Dealing with non-normal data
  • Moving from GLM to P-spline
  • Density estimation
  • Variance smoothing


WEEK 3: Optimizing the Smoothing

  • Fidelity to the data vs smooth curve
  • Cross-validation, AIC
  • Error bands


WEEK 4: Multidimensional Smoothing

  • Generalized Additive Models
  • Varying coefficient models
  • Tensor products


Homework in this course consists of guided data analysis problems using software and guided data modeling problems using software.

In addition to assigned readings, this course also has practice exercises, end of course data modeling project, example software codes, and supplemental readings available online.

Introduction to Smoothing and P-spline Techniques using R


To be scheduled.

Course Fee: $629

Do you meet course prerequisites? What about book & software? (Click here to learn more)

Tuition Savings:  When you register online for 3 or more courses, $200 is automatically deducted from the total tuition. (This offer cannot be combined and is only applicable to courses of 3 weeks or longer.)

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Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment. Please use this printed registration form, for these and other special orders.

Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date, unless you specify otherwise.

Introduction to Smoothing and P-spline Techniques using R

taught by Brian Marx
and Paul Eilers

Who Should Take This Course:

Medical and social science researchers, data miners, environmental analysts;  any researcher who must develop statistical models with "messy" data.


ADVANCED / INTERMEDIATE - see prerequisites

These are listed for your benefit so you can determine for yourself, whether you have the needed background, whether from taking the listed courses, or by other experience.
Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement: about 15 hours per week, at times of  your choosing.

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:
  1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
  2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
  3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:
The text will be provided.


We emphasize the use of modern softwar and we provide functions for R/S-Plus.  The text and R-code will be provided.  You must have a copy of R for the course. Click Here for information on obtaining a free copy.

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