The fitting of subject-specific curves (also known as factor-by-curve interactions) is important in the analysis of grouped longitudinal data. One approach is to use a mixed model with the curves described in terms of truncated lines and the randomness expressed in terms of normal distributions (Durban et al, 2005, Ruppert et al, 2003). This approach gives simple fitting with standard mixed model software. We show that these normal assumptions can lead to biased estimates of and inappropriate confidence intervals for the population effects. Djeundje & Currie (2010) describe an alternative approach which uses a penalty argument to derive an appropriate covariance structure for a mixed model for such data. In the present paper we describe our new approach and demonstrate the effectiveness of our method with the analysis of a classic data set on spinal bone density grouped by ethnic background.
Djeundje & Currie (2010). Appropriate covariance-specification via penalties for penalized splines in mixed models for longitudinal data. Electronic Journal of Statistics, 4, 1202-1224.
Durban, Harezlak, Wand & Carroll (2005). Simple fitting of subject-specific curves to longitudinal data. Statistics in Medicine, 24, 1153-1167.
Ruppert, Wand & Carroll (2003). Semiparametric regression. Cambridge University Press.
Keywords: Longitudinal data; Smoothing; Mixed model; Penalty
Biography: Viani Djeundje is a 3rd year PhD student in statistics at Heriot-Watt University. His research is in smoothing methods applied to mortality and longitudinal data. He has published (jointly with his supervisor) one paper on longitudinal data analysis in the Electronic Journal of Statistics and one on smooth models of mortality in the Annals of Actuarial Science. He has presented work at various international conferences (Iternational Workshop on Statistical Modelling (IWSM) and Royal Statistical Society annual meeting) with a paper published in the IWSM Proceedings.