Electronic Journal of Statistics

Appropriate covariance-specification via penalties for penalized splines in mixed models for longitudinal data

Viani A.B. Djeundje and Iain D. Currie

Full-text: Open access

Abstract

A popular approach to smooth models for longitudinal data is to express the model as a mixed model, since this often leads to immediate model fitting with standard procedures. This approach is particularly appealing when truncated polynomials are used as a basis for the smoothing, as the mixed model representation is almost immediate. We show that this approach can lead to a severely biased estimate of the overall population effect and to confidence intervals with undesirable properties. We use penalization to investigate an alternative approach with either B-spline or truncated polynomial bases and show that this new approach does not suffer from the same defects. Our models are defined in terms of B-splines or truncated polynomials with appropriate penalties, but can be expressed as mixed models; this also gives access to fitting with standard procedures. We illustrate our methods with an analysis of two data sets: (a) a balanced data set on Canadian weather and (b) an unbalanced data set on the growth of children.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 1202-1224.

Dates
First available in Project Euclid: 8 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1289226499

Digital Object Identifier
doi:10.1214/10-EJS583

Mathematical Reviews number (MathSciNet)
MR2735884

Zentralblatt MATH identifier
1329.62198

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62J07: Ridge regression; shrinkage estimators

Keywords
B-splines longitudinal data mixed models penalties smoothing truncated lines

Citation

Djeundje, Viani A.B.; Currie, Iain D. Appropriate covariance-specification via penalties for penalized splines in mixed models for longitudinal data. Electron. J. Statist. 4 (2010), 1202--1224. doi:10.1214/10-EJS583. https://projecteuclid.org/euclid.ejs/1289226499


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Supplemental materials

  • Supplementary Material: Supplementary materials for ‘‘Appropriate covariance-specification via penalties for penalized splines in mixed models for longitudinal data’’ by Djeundje and Currie. The suppementary materials contain R-code to reproduce Table 1 and various Figures in the paper. A guide to using this code is also included.