Rohloff Corissa T, Kohli Nidhi, Chung Seungwon
Quantitative Methods in Education, Department of Educational Psychology, University of Minnesota, Minneapolis, USA.
Cambium Assessment, Inc., Virginia, USA.
Multivariate Behav Res. 2023 Jul-Aug;58(4):723-742. doi: 10.1080/00273171.2022.2119360. Epub 2022 Oct 12.
Nonlinear mixed-effects models (NLMEMs) allow researchers to model curvilinear patterns of growth, but there is ambiguity as to what functional form the data follow. Often, researchers fit multiple nonlinear functions to data and use model selection criteria to decide which functional form fits the data "best." Frequently used model selection criteria only account for the number of parameters in a model but overlook the complexity of intrinsically nonlinear functional forms. This can lead to overfitting and hinder the generalizability and reproducibility of results. The primary goal of this study was to evaluate the performance of eight model selection criteria via a Monte Carlo simulation study and assess under what conditions these criteria are sensitive to model overfitting as it relates to functional form complexity. Results highlighted criteria with the potential to capture overfitting for intrinsically nonlinear functional forms for NLMEMs. Information criteria and the stochastic information complexity criterion recovered the true model more often than the average or conditional concordance correlation. Results also suggest that the amount of residual variance and sample size have an impact on model selection for NLMEMs. Implications for future research and recommendations for application are also provided.
非线性混合效应模型（NLMEMs）使研究人员能够对曲线生长模式进行建模，但数据遵循何种函数形式并不明确。通常，研究人员会将多个非线性函数拟合到数据上，并使用模型选择标准来确定哪种函数形式“最适合”数据。常用的模型选择标准仅考虑模型中的参数数量，却忽略了内在非线性函数形式的复杂性。这可能导致过度拟合，并阻碍结果的可推广性和可重复性。本研究的主要目标是通过蒙特卡罗模拟研究评估八种模型选择标准的性能，并评估在何种条件下这些标准对与函数形式复杂性相关的模型过度拟合敏感。结果突出了有可能捕捉NLMEMs内在非线性函数形式过度拟合情况的标准。信息标准和随机信息复杂性标准比平均或条件一致性相关性更频繁地恢复真实模型。结果还表明，残差方差量和样本量对NLMEMs的模型选择有影响。此外还提供了对未来研究的启示和应用建议。
