Biometrical Letters Vol. 49(2), 2012, pp. 103-119

To model cross-sectional growth data the LMS method is widely applied. In this method the distribution is summarized by three parameters: the Box-Cox power that converts outcome to normality (L); the median (M); and the coeficient of variation (S). Here, we propose an alternative approach based on fitting finite mixture models with several components which may perform better than the LMS method in case the data show an unusual distribution. Further, we explore fixing the weights of the mixture components in contrast to the standard approach where weights are estimated. Having fixed weights improves the speed of computation and the stability of the solution. In addition, fixing the weights provides almost as good a fit as when the weights are estimated. Our methodology combines Gaussian mixture modelling and spline smoothing. The estimation of the parameters is based on the joint modelling of mean and dispersion. We illustrate the methodology on the Fourth Dutch Growth Study, which is a cross-sectional study that contains information on the growth of 7303 boys as a function of age. This information is used to construct centile curves, so-called growth curves, which describe the distribution of height as a smooth function of age. Further, we analyse simulated data showing a bimodal structure at some time point. In its full generality, this approach permits the replacement of the Gaussian components by any parametric density. Further, different components of the mixture can have a different probabilistic (multivariate) structure, allowing for censoring and truncation.

mixture models, growth curves, splines, IWLS algorithm, exible distributions