Practical Smoothing. The Joys of P-splines

Course

Practical Smoothing. The Joys of P-splines

8 & 9 March 2023

By Paul Eilers

Emeritus Professor of Biostatistics
Department of Biostatistics
Erasmus University
Rotterdam, the Netherlands

Course Description

When we fit a trendline to data, we strike a balance between two goals: smoothness of the curve and fidelity to the data. P-splines provide a tool to achieve these goals. The curve is constructed as a sum of B-splines, allowing a very flexible fit to the data, thus taking care of the fidelity. The coefficients of the B-splines can be obtained by linear regression. To control the smoothness, a penalty is added. It is based on (sums of squares of) differences between neighboring coefficients of the B-splines. The weight of the penalty allows easy tuning of the smoothness of the curve. The penalty is also a great tool for automatic handling of missing data by interpolation or extrapolation.

The most common measure of fit to the data is the sum of squares of differences between data and fit. That is adequate for (close to) normal data, but not for counts or fractions. Borrowing ideas from generalized linear models, we can replace the sum of squares by (minus) a log-likelihood. Iterative computation with linearized equations is needed then, but that is easy to implement. This gives us a powerful tool for smoothing of series of counts and other non-normal data. It is extremely useful for density estimation.

The smoothness of a P-spline fit is determined by the weight of the penalty. It is desirable to tune it to the data at hand. Cross-validation is one option, but ideas from mixed models are also very useful.

Many interesting and useful extensions are available. Tensor product P-splines are a natural extension to two or more dimensions. Shape constraints allow monotone and concave smoothing. Adaptive penalties handle data with variable smoothness. For circular and periodic data the penalty can be modified.

Learning Objectives

The course presents a mixture of theoretical concepts, mathematical consequences, and efficient computation. The goal is to give you a good understanding of theory and practice, to allow you to apply P-splines in standard situations, but also to use them as building blocks for extended models. There will be ample time for discussion.

Who is this course for?

This course is designed for epidemiologists, statisticians, and decision analysts. It is assumed that participants are familiar with linear and logistic regression.

Book

Laptop

Participants should bring their own computer, on which a recent version of R and the packages JOPS and SpATS (both available on CRAN) are installed, as well as the archive with scripts in https://psplines.bitbucket.io/Code/Scripts.zip. Internet access will be available.

Location

The course will take place in  TI 01.05 Seminarielokaal Machinezaal, TI Thermotechnisch Instituut, Kasteelpark Arenberg 41, 3001   Heverlee, Belgium. Lunch and coffee breaks are included in the registration fee. If you need a hotel accommodation (not included), you need to arrange it yourself. Accommodation options can be found on the Visit Leuven site.

Preliminary program

DAY 1

DAY 2

Registration

For additional questions, please contact Kirsten Verhaegen.