Linear Mixed Model (LMM) is a common statistical approach to model the relation between exposure and outcome while capturing individual variability through random effects. However, this model assumes the homogeneity of the error term's variance. Breaking this assumption, known as homoscedasticity, can bias estimates and, consequently, may change a study's conclusions. If this assumption is unmet, the mixed-effect location-scale model (MELSM) offers a solution to account for within-individual variability. Our work explores how LMMs and MELSMs behave when the homoscedasticity assumption is not met. Further, we study how misspecification affects inference for MELSM. To this aim, we propose a simulation study with longitudinal data and evaluate the estimates' bias and coverage. Our simulations show that neglecting heteroscedasticity in LMMs leads to loss of coverage for the estimated coefficients and biases the estimates of the standard deviations of the random effects. In MELSMs, scale misspecification does not bias the location model, but location misspecification alters the scale estimates. Our simulation study illustrates the importance of modelling heteroscedasticity, with potential implications beyond mixed effect models, for generalised linear mixed models for non-normal outcomes and joint models with survival data.

翻译：线性混合模型（LMM）是一种常见的统计方法，用于建模暴露与结局之间的关系，同时通过随机效应捕捉个体间的变异性。然而，该模型假设误差项的方差具有同质性。若违反这一同方差性假设，可能导致估计偏差，进而改变研究的结论。若该假设不成立，混合效应位置尺度模型（MELSM）提供了一种解决方案，能够考虑个体内的变异性。本研究探讨了当同方差性假设不满足时，LMM与MELSM的表现。进一步地，我们研究了误设如何影响MELSM的统计推断。为此，我们提出了一项基于纵向数据的模拟研究，并评估了估计的偏差与覆盖概率。模拟结果显示，在LMM中忽略异方差性会导致估计系数的覆盖概率下降，并使随机效应标准差的估计产生偏差。在MELSM中，尺度部分的误设不会对位置模型的估计造成偏差，但位置部分的误设会影响尺度参数的估计。本模拟研究阐明了建模异方差性的重要性，其影响可能超越混合效应模型本身，延伸至针对非正态结局的广义线性混合模型以及结合生存数据的联合模型。