<abstract xmlns="http://www.w3.org/1999/xhtml"> 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. </abstract>

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.

Finite mixture models with fixed weights applied to growth data

Department of Biostatistics, Erasmus MC, P.O. Box 2040, 3000 CA Rotterdam, Netherlands

Catholic University of Leuven, L-Biostat, U.Z. St. Rafael, Kapucijnenvoer 35, 3000 Leuven, Belgium

Biometrical Letters

{"article-title":"Finite mixture models with fixed weights applied to growth data"}

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...

Finite mixture models with fixed weights applied to growth data

Published Online: Aug 17, 2013

Page range: 103 - 119

DOI: https://doi.org/10.2478/bile-2013-0008

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

This content is open access.

Finite mixture models with fixed weights applied to growth data

Published Online: Aug 17, 2013

Page range: 103 - 119

DOI: https://doi.org/10.2478/bile-2013-0008

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

This content is open access.

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