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Nonlinear Regime-Switching State-Space (RSSS) Models

Published online by Cambridge University Press:  01 January 2025

Sy-Miin Chow  and
Guangjian Zhang
Sy-Miin Chow*
Affiliation:
The Pennsylvania State University
Guangjian Zhang
Affiliation:
University of Notre Dame
*
Requests for reprints should be sent to Sy-Miin Chow, The Pennsylvania State University, 422 Biobehavioral Health Building, University Park, PA 16801, USA. E-mail: [email protected]
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Abstract

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.

Keywords

regime-switchingstate-spacenonlinear latent variable modelsdynamic factor analysisKim filter
Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 4 , October 2013 , pp. 740 - 768
Copyright
Copyright © 2013 The Psychometric Society

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