Bayesian growth curves using normal mixtures with nonparametric weights

Luisa Scaccia & Peter J. Green

Reference growth curves estimate the distribution of a measurement as it changes according to some covariate, often age. We present a new methodology to estimate growth curves based on mixture models and splines. We propose a mixture of normal distributions with an unknown number of components and model the dependence of the observations on the covariate through the weights. We model the weights as a smooth function of the covariate using B-splines. In this way the growth curves respect the continuity of the covariate and there is no need for arbitrary grouping of the observations. The method is illustrated with data on triceps skinfold in Gambian girls and women.

Some key words: Allocation, Bayesian hierarchical model, Centile curves, Finite mixture distributions, Growth curves, Heterogeneity, Markov chain Monte Carlo, Normal mixtures, Path sampling, Reversible jump algorithms, Semiparametric model, Splines, Split/merge moves.

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