scholarly journals Growth curves mixture models with unknown covariance structures

2021 ◽  
pp. 104904
Author(s):  
Yating Pan ◽  
Yu Fei ◽  
Mingming Ni ◽  
Tapio Nummi ◽  
Jianxin Pan
Keyword(s):  
Mixture Models ◽  
Growth Curves ◽  
Covariance Structures ◽  
Unknown Covariance

scholarly journals Finite mixture models with fixed weights applied to growth data

2012 ◽  
Vol 49 (2) ◽  
pp. 103-119 ◽  
Author(s):  
Marek Molas ◽  
Emmanuel Lesaffre
Keyword(s):  
Mixture Models ◽  
Finite Mixture Models ◽  
Simulated Data ◽  
Growth Curves ◽  
Gaussian Mixture ◽  
Finite Mixture ◽  
Growth Data ◽  
Full Generality ◽  
Cross Sectional ◽  
Lms Method

Summary 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.

Improving convergence in growth mixture models without covariance structure constraints

2021 ◽  
pp. 096228022098174
Author(s):  
Daniel McNeish ◽  
Jeffrey R. Harring
Keyword(s):  
Mixture Models ◽  
Random Effect ◽  
Covariance Structure ◽  
Poor Performance ◽  
Covariance Structures ◽  
Parameter Estimates ◽  
Growth Mixture Models ◽  
Class Enumeration ◽  
Growth Mixture ◽  
Pattern Growth

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

scholarly journals On growth curves and mixture models

2006 ◽  
Vol 15 (6) ◽  
pp. 627-634 ◽  
Author(s):  
Jan B. Hoeksma ◽  
Henk Kelderman
Keyword(s):  
Mixture Models ◽  
Growth Curves

scholarly journals Growth Curves of Turkish Saanen Goats’ Kids Grouped for Weight and Body Mass Index

2005 ◽  
Vol 48 (2) ◽  
pp. 185-193 ◽  
Author(s):  
A. Pala ◽  
T. Savaş ◽  
F. Uğur ◽  
G. Daş
Keyword(s):  
Body Mass Index ◽  
Least Squares ◽  
Body Mass ◽  
Covariance Structure ◽  
Growth Curves ◽  
Ordinary Least Squares ◽  
Covariance Structures ◽  
Fit Statistics ◽  
Weaning Stress ◽  
Low Bmi

Abstract. Growth curves and weaning stress differences were investigated in Turkish Saanen kids grouped for their weight and Body Mass Index (BMI = weight/height2). Data included 884 records collected from 61 Turkish Saanen kids raised in Canakkale, Turkey. Slopes were calculated for each kid and were analyzed as data using ordinary least squares, and repeated weights for each kid were analyzed using various covariance structures. Differences between male and female kids were small and non-significant before weaning (P = 0.55), while larger (P = 0.06) after weaning. Heavy animals grew faster than light animals before weaning (P < 0.01) but lost their advantage after weaning (P > 0.05). Fat animals (high BMI) grew faster than lean animals (low BMI) before weaning (P < 0.01) while the differences slightly diminished after weaning (P = 0.04). This may be because light and lean kids were not affected from the weaning shock as much as the heavy and fat kids, which had stuttered growth after weaning. Fit statistics indicated that first-order ante dependence was the best fit covariance structure for these data. Analyses specifying random model and covariance structures did not have an advantage over an approach where slopes were manually calculated and analyzed as data using ordinary least squares.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

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