a Department of Psychology , University of Notre Dame.
b Department of Psychology , University of California , Davis.
Multivariate Behav Res. 2007 Apr-Jun;42(2):283-321. doi: 10.1080/00273170701360423.
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log-likelihood of nonlinear state-space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple-subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction.
在过去的几十年中，用于估计潜在变量之间非线性关系的方法几乎完全是为了拟合横截面模型而开发的。我们提出了一种相对较新的估计方法，未扩展卡尔曼滤波器（UKF），并通过两种方式说明了其作为拟合非线性动态模型的工具的潜力：（1）作为近似非线性状态空间模型的对数似然的构建块，以及（2）拟合时变动态模型，其中参数作为其他潜在变量在线表示和估计。此外，通过（1）具有时间序列和多主体数据的经典捕食者-被捕食者模型、（2）混沌 Lorenz 系统和（3）二元交互的实证示例，展示了 UKF 的实质性实用性。
