Department of Biostatistics, Boston University School of Public Health, 715 Albany Street Crosstown Center-3rd Floor Boston, MA 02118, USA.
BMC Med Res Methodol. 2010 Feb 19;10:16. doi: 10.1186/1471-2288-10-16.
Linear mixed effects models (LMMs) are a common approach for analyzing longitudinal data in a variety of settings. Although LMMs may be applied to complex data structures, such as settings where mediators are present, it is unclear whether they perform well relative to methods for mediational analyses such as structural equation models (SEMs), which have obvious appeal in such settings. For some researchers, SEMs may be more difficult than LMMs to implement, e.g. due to lack of training in the methodology or the need for specialized SEM software. It therefore is of interest to evaluate whether the LMM performs sufficiently in a scenario particularly suitable for SEMs. We focus on evaluation of the total effect (i.e. direct and indirect) of an exposure on an outcome of interest when a mediating factor is present. Our aim is to explore whether the LMM performs as well as the SEM in a setting that is conducive to using the SEM.
We simulated mediated longitudinal data from an SEM where a binary, main independent variable has both direct and indirect effects on a continuous outcome. We conducted analyses with both the LMM and SEM to evaluate the performance of the LMM in a setting where the SEM is expected to be preferable. Models were evaluated with respect to bias, coverage probability and power. Sample size, effect size and error distribution of the simulated data were varied.
Both models performed well in a range of settings. Marginal increases in power estimates were observed for the SEM, although generally there were no major differences in performance. Power for both models was good with a sample of size of 250 and a small to medium effect size. Bias did not substantially increase for either model when data were generated from distributions that were both skewed and kurtotic.
In settings where the goal is to evaluate the overall effects, the LMM excluding mediating variables appears to have good performance with respect to power, bias and coverage probability relative to the SEM. The major benefit of SEMs is that it simultaneously and efficiently models both the direct and indirect effects of the mediation process.
线性混合效应模型（LMMs）是在各种环境中分析纵向数据的常用方法。尽管 LMM 可应用于复杂的数据结构，例如存在中介变量的情况，但相对于中介分析方法（例如结构方程模型（SEMs））的性能如何尚不清楚，而在这种情况下 SEM 具有明显的吸引力。对于某些研究人员来说，SEM 可能比 LMM 更难实施，例如由于缺乏方法学方面的培训或需要专门的 SEM 软件。因此，评估在特别适合 SEM 的情况下 LMM 的性能是否足够重要。我们专注于评估存在中介变量时暴露对感兴趣结果的总效应（即直接和间接效应）。我们的目的是探索在有利于使用 SEM 的环境中，LMM 是否能像 SEM 一样表现良好。
我们从 SEM 模拟了中介纵向数据，其中二分类的主要自变量对连续结果有直接和间接影响。我们使用 LMM 和 SEM 进行分析，以评估 LMM 在 SEM 预期更可取的环境中的表现。通过偏倚、覆盖率和功效评估模型。模拟数据的样本量、效应大小和误差分布有所不同。
两种模型在各种环境下都表现良好。SEM 的功效估计略有增加，尽管总体性能差异不大。当数据来自偏态和峰态分布时，两种模型的功效都很好，样本量为 250，效应大小为小到中等。对于两种模型，偏倚都没有随着数据来自偏态和峰态分布而大幅增加。
在目标是评估总体效应的情况下，排除中介变量的 LMM 相对于 SEM 具有良好的功效、偏倚和覆盖率概率性能。SEM 的主要优势在于它可以同时高效地对中介过程的直接和间接效应进行建模。
