Chow Sy-Miin, Zhang Guangjian
The Pennsylvania State University, 422 Biobehavioral Health Building, University Park, PA, 16801, USA,
Psychometrika. 2013 Oct;78(4):740-68. doi: 10.1007/s11336-013-9330-8. Epub 2013 Mar 5.
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
非线性动态因子分析模型通过允许时间序列过程在潜在层面是非线性的（例如，涉及两个潜在过程之间的相互作用）来扩展标准线性动态因子分析模型。在实践中，识别系统具有明显不同动态特征的阶段（即潜在的“状态”或类别）通常很有意义。我们提出了一类新的模型，称为非线性状态切换状态空间（RSSS）模型，它将状态切换非线性动态因子分析模型作为一个特例包含在内。在非线性RSSS模型中，使用状态空间模型表示的状态内变化过程被允许是非线性的。提出了一种通过结合扩展卡尔曼滤波器和金氏滤波器得到的估计程序，作为估计非线性RSSS模型的一种方法。我们通过将具有特定状态交叉回归参数的非线性动态因子分析模型拟合到一组经验抽样情感数据，来说明非线性RSSS模型的效用。简要讨论了非线性RSSS模型与文献中其他著名离散变化模型之间的相似之处。
