Open AccessThe cusp catastrophe model as cross-sectional and longitudinal mixture structural equation models.
Author(s) -
Sy Miin Chow,
Katie Witkiewitz,
Raoul P. P. P. Grasman,
Stephen A. Maisto
Publication year - 2015
Publication title -
psychological methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.981
H-Index - 151
eISSN - 1939-1463
pISSN - 1082-989X
DOI - 10.1037/a0038962
Subject(s) - catastrophe theory , cusp (singularity) , structural equation modeling , variety (cybernetics) , mathematics , statistical physics , econometrics , statistics , geometry , engineering , physics , geotechnical engineering
Catastrophe theory (Thom, 1972, 1993) is the study of the many ways in which continuous changes in a system's parameters can result in discontinuous changes in 1 or several outcome variables of interest. Catastrophe theory-inspired models have been used to represent a variety of change phenomena in the realm of social and behavioral sciences. Despite their promise, widespread applications of catastrophe models have been impeded, in part, by difficulties in performing model fitting and model comparison procedures. We propose a new modeling framework for testing 1 kind of catastrophe model-the cusp catastrophe model-as a mixture structural equation model (MSEM) when cross-sectional data are available; or alternatively, as an MSEM with regime-switching (MSEM-RS) when longitudinal panel data are available. The proposed models and the advantages offered by this alternative modeling framework are illustrated using 2 empirical examples and a simulation study.