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Finite mixture models with fixed weights applied to growth data

100%

Molas M. , Lesaffre E.

Biometrical Letters

2012

tom 49

nr 2

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 diferent probabilistic (multivariate) structure, allowing for censoring and truncation.

Why life histories are diverse

58%

Kozlowski J.

Polish Journal of Ecology

2006

tom Vol. 54, nr 4

585-605

Why do some animals weigh a fraction of a milligram and others many tons? Why do some animals mature after a few days and others need several years? Why do some animals grow and then reproduce without growing, while others continue growing after maturation? Why are growth curves so often well-approximated by von Bertalanffy's equation? Why do some animals produce myriads of tiny eggs and others produce only a few large offspring? Evolution of life histories is driven basically by the size-dependences of three parameters: the resource acquisition rate, metabolic rate and mortality risk. The combinations of size-dependences of this trio produce a plethora of locally optimal life histories, and even more sub-optimal strategies which must coexist with optimal ones in the real world. Additionally, selection forces differ depending on whether a population stays most of the time at equilibrium or in an expansion phase. Life history evolution cannot be understood without mathematical modelling, and optimization of life-time resource allocation is a powerful approach to that, though not the only one. Modelling outcomes from studies based on resource allocation optimization are presented here mainly as graphs.