Dynamic panel models are a popular approach to study interrelationships between repeatedly measured variables. Often, dynamic panel models are specified and estimated within a structural equation modeling (SEM) framework. An endemic problem threatening the validity of such models is unmodelled heterogeneity. Recently, individual parameter contribution (IPC) regression was proposed as a flexible method to study heterogeneity in SEM parameters as a function of observed covariates. In the present paper, we derive how IPCs can be calculated for general maximum likelihood estimates and evaluate the performance of IPC regression to estimate group differences in dynamic panel models in discrete and continuous time. We show that IPC regression can be slightly biased in samples with large group differences and present a bias correction procedure. IPC regression showed generally promising results for discrete time models. However, due to highly nonlinear parameter constraints, caution is indicated when applying IPC regression to continuous time models.

中文翻译：

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使用单个参数贡献回归识别动态面板模型中的异质性

动态面板模型是研究重复测量变量之间相互关系的流行方法。通常，动态面板模型是在结构方程建模 (SEM) 框架内指定和估计的。威胁此类模型有效性的一个普遍问题是未建模的异质性。最近，个人参数贡献 (IPC) 回归被提出作为一种灵活的方法来研究 SEM 参数的异质性作为观察到的协变量的函数。在本文中，我们推导出如何计算一般最大似然估计的 IPC，并评估 IPC 回归的性能，以估计离散和连续时间动态面板模型中的组差异。我们表明，IPC 回归在具有较大组差异的样本中可能会略有偏差，并提出了偏差校正程序。IPC 回归对离散时间模型显示出普遍有希望的结果。然而，由于高度非线性的参数约束，在将 IPC 回归应用于连续时间模型时要小心。