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Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function

机译：通过线性化估计非线性增长模型：使用Gompertz函数的模拟研究

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摘要

A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.
机译：考虑了一种基于泰勒级数展开的非线性混合效应模型的位置参数和方差分量估计方法。该方法的一个吸引人的特性是容易实现算法的机会。非线性混合效果模型的估计可以通过线性混合效果模型的常用方法完成，因此，可以在进行少量修改后使用现有程序。通过使用Gompertz函数生长模型对猪进行仿真，研究了该算法在动物育种中的适用性。分析了两个生长数据集：完整的数据集包含整个生长期的观察结果，以及截短的时间轨迹集，其中包含过早宰杀的动物，这在猪的繁殖中很常见。来自具有完整数据集的50个模拟重复的结果表明，线性化方法能够令人满意地估计原始参数。但是，在数据集被截断的情况下，与成人体重有关的参数的估计变得不稳定。

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