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A method for fitting regression splines with varying polynomial order in the linear mixed model
Author(s) -
Edwards Lloyd J.,
Stewart Paul W.,
MacDougall James E.,
Helms Ronald W.
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2232
Subject(s) - multivariate adaptive regression splines , polynomial regression , proper linear model , mathematics , mixed model , spline (mechanical) , linear regression , polynomial , piecewise , segmented regression , regression analysis , linear model , nonparametric regression , piecewise linear function , mathematical optimization , computer science , statistics , mathematical analysis , geometry , structural engineering , engineering
The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis‐driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicity constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed‐knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S‐plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV‐1 infection and an analysis of 24‐hour ambulatory blood pressure profiles. Copyright © 2005 John Wiley & Sons, Ltd.