Nonlinear Regime-Switching State-Space (RSSS) Models
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2013 DOI : 10.1007/ S 11336-013-9330-8
NONLINEAR REGIME-SWITCHING STATE-SPACE (RSSS) MODELS
S Y-M IIN C HOW THE PENNSYLVANIA STATE UNIVERSITY
G UANGJIAN Z HANG UNIVERSITY OF NOTRE DAME 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 regimeswitching 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. Key words: regime-switching, state-space, nonlinear latent variable models, dynamic factor analysis, Kim filter.
1. Nonlinear Regime-Switching State-Space (RSSS) Models Factor analysis is widely recognized as one of the most important methodological developments in the history of psychometrics. By combining factor analysis and time series analysis, dynamic factor analysis models are one of the better known models of intensive multivariate change processes in the psychometric literature (Browne & Nesselroade, 2005; Engle & Watson, 1981; Geweke & Singleton, 1981; Molenaar, 1985; Nesselroade, McArdle, Aggen, & Meyers, 2002). They have been used to study a broad array of change processes (Chow, Nesselroade, Shifren, & McArdle, 2004; Ferrer & Nesselroade, 2003; Molenaar, 1994a; Sbarra & Ferrer, 2006). Parallel to the increased use of dynamic factor analysis models in substantive applications, various methodological advancements have also been proposed over the last two decades for fitting linear dynamic factor analysis models to continuous as well as categorical data (Molenaar, 1985; Molenaar & Nesselroade, 1998; Browne & Zhang, 2007; Engle & Watson, 1981; Zhang & Nesselroade, 2007; Zhang, Hamaker, & Nesselroade, 2008). In the present article, we propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes dynamic factor analysis models that show linear or nonlinear dynamics at the latent level as a special case. The term “regime-switching” refers to the property that individuals’ change mechanisms are contingent on the latent class or “regime” they are in at a particular time point. In addition, individuals are allowed to tra
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