Existing methods for fitting generalized additive mixed models to longitudinal repeated measures data rely on Laplace-approximate marginal likelihood for estimation of variance components and smoothing penalty parameters. This is thought to be appropriate due to the Laplace approximation being established as an appropriate tool for smoothing penalty parameter estimation in spline models and the well-known connection between penalized regression and random effects. This paper argues that the Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models leading to estimates that exhibit increasing bias and decreasing confidence interval coverage as more groups are sampled. A novel estimation strategy based on penalizing an adaptive quadrature approximate marginal likelihood is proposed that solves this problem and leads to estimates exhibiting the correct statistical properties.

翻译：现有用于将广义可加混合模型拟合到纵向重复测量数据的方法依赖于拉普拉斯近似边际似然来估计方差分量和平滑惩罚参数。这被认为是合适的，因为拉普拉斯近似已被确立为样条模型中平滑惩罚参数估计的适当工具，且惩罚回归与随机效应之间存在众所周知的关联。本文认为，在广义可加混合模型中，拉普拉斯近似有时对于平滑参数估计不够精确，导致随着采样组数增加，估计值表现出日益增大的偏差和不断降低的置信区间覆盖率。本文提出了一种基于自适应求积近似边际似然惩罚的新型估计策略，该策略解决了此问题，并能产生具有正确统计特性的估计结果。