Journal
ASTA-ADVANCES IN STATISTICAL ANALYSIS
Volume 96, Issue 1, Pages 47-68Publisher
SPRINGER
DOI: 10.1007/s10182-011-0161-6
Keywords
Dirichlet process mixture; Mixed models; Nonparametric Bayes inference; Penalized splines
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Funding
- German National Science Foundation (DFG) [FA 128/5-1, FA 128/5-2]
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Longitudinal data often require a combination of flexible time trends and individual-specific random effects. For example, our methodological developments are motivated by a study on longitudinal body mass index profiles of children collected with the aim to gain a better understanding of factors driving childhood obesity. The high amount of nonlinearity and heterogeneity in these data and the complexity of the data set with a large number of observations, long longitudinal profiles and clusters of observations with specific deviations from the population model make the application challenging and prevent the application of standard growth curve models. We propose a fully Bayesian approach based on Markov chain Monte Carlo simulation techniques that allows for the semiparametric specification of both the trend function and the random effects distribution. Bayesian penalized splines are considered for the former, while a Dirichlet process mixture (DPM) specification allows for an adaptive amount of deviations from normality for the latter. The advantages of such DPM prior structures for random effects are investigated in terms of a simulation study to improve the understanding of the model specification before analyzing the childhood obesity data.
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