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An Analysis of Recent Critiques of Structural Equation Modeling.
Mathematical
Social
Sciences
97
15 (1988) 97-99
North-Holland
ABSTRACTS
This section consists of the abstracts of papers presented to the JACOB MARSCHAK INTERDISCIPLINARY COLLOQUIUM ON MATHEMATICS IN THE BEHAVIORAL SCIENCES at the Graduate School of Management, University of California, Los Angeles, California 90024. The readers who are interested in a particular article should write to the author for the entirety.
An Analysis of Recent Critiques of Structural Equation Modeling. Peter Bentler, Department of Psychology, University of California, Los Angeles, CA 90024, U.S.A. Linear structural equation models are parameterized models for random variables. The parameters of such models are designed to account for the moment structure (means, covariances, higher-order moments) of the variables. Virtually all linear models studied in multivariate statistics can be conceived of as structural equation models: regression, factor analysis, simultaneous equations, principal components, path analysis, structural relations (‘LISREL’), etc. Structural models can be considered to be statistical versions of linear systems theory models as found in engineering. Linear systems tend to be used in engineering to design a device or process having certain properties, i.e., input-output relations. In contrast, in the social and behavioral sciences where experimentation is often difficult or impossible due to ethical considerations, structural models tend not to be used to create devices but rather to evaluate whether observed data that may have been generated by a set of identical or similar devices (or from the same device at various time points) might in fact have been generated by a device with certain specific properties (i.e., input-output relations). Thus these models are used to evaluate hypotheses about black boxes. Of course, in the social and behavioral sciences the ‘black boxes’ tend to be people, institutions, countries, etc. In their ideal form, structural models represent mathematical specifications of process models that mirror a causal structure that is hypothesized to have generated a set of multivariate data. The goal is to evaluate the statistical plausibility of such a causal hypothesis, i.e., of a structural model. Thus the methods are sometimes known as ‘causal modeling’ methods. As can be imagined, structural modeling has come under attack. At issue is not only the appropriateness and correctness of a mathematical and statistical theory 01654896/88/$3.50
0
1988, Elsevier
Science
Publishers
B.V. (North-Holland)
Abstracts
98
and its limitations, but also the very goal sometimes intended by application of the theory, that is, ‘causal’ modeling. An attempt will be made to describe some of the general features of linear structural models, to discuss some of the criticisms of the methodology, and to encourage a discussion of some of the more abstract issues involved.
Nonlinear Systems, Complex Dynamics, and the Social Sciences. Ralph H. Abraham, Mathematics Board, University of California, Santa Crut, CA 95064, U.S.A. A nonlinear dynamical system, from the point of view of long-run qualitative behavior, is characterized by a phase portrait. This is a geometric map of the space of virtual states, emphasizing the attractors, basins, and separatrices. Attractors may be points (static), cycles (periodic), or (most frequently) fractal manifolds (chaotic). The typical portrait may be multistable, containing a large number of attractors with densely intertwined basins. A dynamical scheme is a dynamical system depending on control parameters. From the qualitative point of view, a scheme is characterized by a response diagram. This is a family of phase portraits, organized by the control parameters. The chief features of a response diagram are the bifurcations of the attractors as the controls are changed. Bifurcation theory has been the subject of active mathematical research for a century, and thanks to intensive computations carried out since World War II by experimental dynamicists, many important examples are known. Elementary catastrophe theory is an important branch of the theory of bifurcations. A complex dynamical system is a network of dynamical schemes, coupled by functions from the states at one node to the controls at another. These have emerged as useful models in the applications of dynamical schemes to the social and behavioral sciences. Much of the earlier literature of applied mathematics may be reinterpreted with these concepts. Chaos theory, the theory of chaotic attractors and their bifurcations, is particularly significant in the art of modeling complex systems. In this talk, we will give an illustrated introduction to these concepts, and then describe some exemplary applications to the biosphere. We may also discuss the prospects for the accellerated development of the social and behavioral sciences through massive investment in dynamical modeling and computer graphic simulations such as the animated atlas and the political weather bureau.
Complexity Theory and its Applications. Christos H. Papadimitriou, Stanford University, Stanford, CA 90403, U.S.A. and National Technical University of Athens The observation
by Turing, Giidel, and others that there exist concrete computa-
Social
Sciences
97
15 (1988) 97-99
North-Holland
ABSTRACTS
This section consists of the abstracts of papers presented to the JACOB MARSCHAK INTERDISCIPLINARY COLLOQUIUM ON MATHEMATICS IN THE BEHAVIORAL SCIENCES at the Graduate School of Management, University of California, Los Angeles, California 90024. The readers who are interested in a particular article should write to the author for the entirety.
An Analysis of Recent Critiques of Structural Equation Modeling. Peter Bentler, Department of Psychology, University of California, Los Angeles, CA 90024, U.S.A. Linear structural equation models are parameterized models for random variables. The parameters of such models are designed to account for the moment structure (means, covariances, higher-order moments) of the variables. Virtually all linear models studied in multivariate statistics can be conceived of as structural equation models: regression, factor analysis, simultaneous equations, principal components, path analysis, structural relations (‘LISREL’), etc. Structural models can be considered to be statistical versions of linear systems theory models as found in engineering. Linear systems tend to be used in engineering to design a device or process having certain properties, i.e., input-output relations. In contrast, in the social and behavioral sciences where experimentation is often difficult or impossible due to ethical considerations, structural models tend not to be used to create devices but rather to evaluate whether observed data that may have been generated by a set of identical or similar devices (or from the same device at various time points) might in fact have been generated by a device with certain specific properties (i.e., input-output relations). Thus these models are used to evaluate hypotheses about black boxes. Of course, in the social and behavioral sciences the ‘black boxes’ tend to be people, institutions, countries, etc. In their ideal form, structural models represent mathematical specifications of process models that mirror a causal structure that is hypothesized to have generated a set of multivariate data. The goal is to evaluate the statistical plausibility of such a causal hypothesis, i.e., of a structural model. Thus the methods are sometimes known as ‘causal modeling’ methods. As can be imagined, structural modeling has come under attack. At issue is not only the appropriateness and correctness of a mathematical and statistical theory 01654896/88/$3.50
0
1988, Elsevier
Science
Publishers
B.V. (North-Holland)
Abstracts
98
and its limitations, but also the very goal sometimes intended by application of the theory, that is, ‘causal’ modeling. An attempt will be made to describe some of the general features of linear structural models, to discuss some of the criticisms of the methodology, and to encourage a discussion of some of the more abstract issues involved.
Nonlinear Systems, Complex Dynamics, and the Social Sciences. Ralph H. Abraham, Mathematics Board, University of California, Santa Crut, CA 95064, U.S.A. A nonlinear dynamical system, from the point of view of long-run qualitative behavior, is characterized by a phase portrait. This is a geometric map of the space of virtual states, emphasizing the attractors, basins, and separatrices. Attractors may be points (static), cycles (periodic), or (most frequently) fractal manifolds (chaotic). The typical portrait may be multistable, containing a large number of attractors with densely intertwined basins. A dynamical scheme is a dynamical system depending on control parameters. From the qualitative point of view, a scheme is characterized by a response diagram. This is a family of phase portraits, organized by the control parameters. The chief features of a response diagram are the bifurcations of the attractors as the controls are changed. Bifurcation theory has been the subject of active mathematical research for a century, and thanks to intensive computations carried out since World War II by experimental dynamicists, many important examples are known. Elementary catastrophe theory is an important branch of the theory of bifurcations. A complex dynamical system is a network of dynamical schemes, coupled by functions from the states at one node to the controls at another. These have emerged as useful models in the applications of dynamical schemes to the social and behavioral sciences. Much of the earlier literature of applied mathematics may be reinterpreted with these concepts. Chaos theory, the theory of chaotic attractors and their bifurcations, is particularly significant in the art of modeling complex systems. In this talk, we will give an illustrated introduction to these concepts, and then describe some exemplary applications to the biosphere. We may also discuss the prospects for the accellerated development of the social and behavioral sciences through massive investment in dynamical modeling and computer graphic simulations such as the animated atlas and the political weather bureau.
Complexity Theory and its Applications. Christos H. Papadimitriou, Stanford University, Stanford, CA 90403, U.S.A. and National Technical University of Athens The observation
by Turing, Giidel, and others that there exist concrete computa-