Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in studies with modest samples. Bayesian estimation is a logical alternative to ML for LGMs, but there is a lack of research providing guidance on when Bayesian estimation may be preferable to ML or vice versa. This study compared the performance of Bayesian versus ML estimators for LGMs by evaluating their accuracy via Monte Carlo (MC) simulations. For the MC study, longitudinal data sets were generated and estimated using LGM via both ML and Bayesian estimation with three different priors, and parameter recovery across the two estimators was evaluated to determine their relative performance. The findings suggest that ML estimation is a reasonable choice for most LGMs, unless it fails to converge, which can occur with limiting data situations (i.e., just a few time points, no covariate or outcome, modest sample sizes). When models do not converge using ML, we recommend Bayesian estimation with one caveat that the influence of the priors on estimation may have to be carefully examined, per recent recommendations on Bayesian modeling for applied researchers.

中文翻译：

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在存在二元结果的情况下，贝叶斯估计与潜在增长模型的最大似然估计的比较。


潜在生长模型 (LGM) 是结构方程模型的一种应用，经常用于发育和临床研究，以分析纵向结果随时间的变化。最大似然 (ML) 是估计 LGM 的最常见方法，在复杂的 LGM 中可能无法收敛或产生有偏差的估计，尤其是在样本量不大的研究中。对于 LGM，贝叶斯估计是 ML 的合理替代方案，但缺乏研究来指导贝叶斯估计何时优于 ML，反之亦然。本研究通过蒙特卡罗 (MC) 模拟评估 LGM 的贝叶斯估计器与 ML 估计器的准确性，从而比较它们的性能。对于 MC 研究，使用 LGM 通过具有三种不同先验的 ML 和贝叶斯估计来生成和估计纵向数据集，并对两个估计器的参数恢复进行评估以确定它们的相对性能。研究结果表明，ML 估计对于大多数 LGM 来说是一个合理的选择，除非它无法收敛，这种情况可能在有限的数据情况下发生（即只有几个时间点、没有协变量或结果、适度的样本量）。当使用机器学习模型无法收敛时，我们建议使用贝叶斯估计，但需要注意的是，根据最近针对应用研究人员的贝叶斯建模建议，可能必须仔细检查先验对估计的影响。