We present an estimation procedure for nonlinear mixed-effects models in which the population trajectory is represented by penalized splines and adapted to individuals via subject-specific transformation parameters. By exploiting the mixed model representation of penalized splines, the level of smoothness can be estimated jointly with other variance components. The integration over random effects needed to obtain the marginal likelihood is carried out using the Laplace approximation. Exact derivatives for evaluation and maximization of the resulting likelihood are obtained via automatic differentiation implemented through Template Model Builder. In simulation studies, the method produces improved inferential performance and reduced computational burden when compared to the existing procedure. The approach is further illustrated through a case study on infant height growth in the first two years of life.

翻译：本文提出一种非线性混合效应模型的估计方法，其中总体轨迹通过惩罚样条表示，并通过个体特异性变换参数适应不同受试者。通过利用惩罚样条的混合模型表示形式，平滑度水平可与其他方差分量联合估计。为获得边际似然所需对随机效应的积分采用拉普拉斯近似实现。通过基于模板模型构建器实现的自动微分技术，可获取用于评估和最大化所得似然函数的精确导数。在模拟研究中，与现有方法相比，本方法在提升推断性能的同时显著降低了计算负担。通过一项针对婴儿出生后前两年身高增长的案例研究，进一步验证了该方法的有效性。