Moderator regression and the cusp catastrophe: Application of two-stage personnel selection, training, therapy, and policy evaluation

Guastello, Stephen J.

doi:10.1002/bs.3830270305

Cited by 72 publications

(70 citation statements)

References 62 publications

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“…Cobb (1978Cobb ( , 1980Cobb, Koppstein, & Chen, 1983;Cobb & Watson, 1980;Cobb & Zacks, 1985) tried to solve this problem by developing stochastic catastrophe theory. Other approaches to catastrophe modeling (Guastello's, 1982(Guastello's, , 1992Oliva, Desarbo, Day, & Jedidi's, 1987, GEMCAT technique) have met with some criticism (Alexander, Herbert, Deshon, & Hanges, 1992;Hartelman, van der Maas, & Molenaar, 1998). Cobb showed that, by using stochastic differential equations, there is a cusp family of probability density functions.…”

Section: Catastrophe Theorymentioning

confidence: 99%

Stochastic catastrophe analysis of switches in the perception of apparent motion

Ploeger

Maas

Hartelman

2002

Psychonomic Bulletin & Review

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An important objective when the dynamics of visual perception are studied is to discover the nonlinear basis for cooperative phenomena such as bistability and hysteresis, phenomenathat are not readily explainedby a linear model. Bistability means that more than one percept is possible for a single stimulus. Hysteresis means that what is perceived at any moment depends on the preceding state of the visual system. As a result, perception depends on the direction of parameter change. When a parameter is gradually increased, changes in percept will occur at a different point from changes in percept that occur when the parameter is gradually decreased. That is, the initial percept is likely to persist, although the parameter has changed to a value that favors the alternative percept.It is clear that a linear model ( y = ax + b) cannot explain bistability and hysteresis. According to a linear model, one stimulus should provoke one and only one percept (i.e., in the formula of the linear model, every value of x gives a single value of y, not two or more different values). A nonlinear model is needed to deal with these dynamical phenomena. A logistic model is not sufficient; it can explain rapid changes in responses, but not the occurrence of two different percepts for the same stimulus. We will propose a subset of dynamical system models, so-called stochastic catastrophe models, to explain phenomena such as bistability and hysteresis. A new prediction, that hysteresis must be accompanied by another dynamical phenomenon called divergence, is derived. The derivation of this new prediction is one of the main advantages of using catastrophe theory to explain nonlinear phenomena. Other theories do not have this mathematical link between hysteresis and divergence.We will show on a conceptual level why hysteresis must go together with divergence, and we will present the first empirical evidence of the existence of divergence in perception. We also show that stochastic catastrophe theory offers indices for model selection, which is seen as a major problem in psychology, and we show that we can test the fit of different catastrophe models efficiently.We use two existing paradigms based on apparent motion (Hock, Kelso, & Schöner, 1993;Hock, Kogan, & Espinoza, 1997) that clearly show that hysteresis and bistability do exist in visual perception. Apparent motion is an important subject in the study of the nonlinear dynamics of perception because, contrary to static stimuli, it has an extended time scale and parameters, such as speed and direction, that are relatively easy to manipulate. A lot of studies on dynamics have been done with static stimuli like Fisher's man's-face/woman's-figure-picture (Fisher, 1967). This drawing can be interpreted either as a man's face or as a woman's figure (i.e., the percept is bistable). These studies show that the dynamics of visual perception can be studied with static stimuli. However, by changing qualitative parts of pictures, it is not exactly clear which parameter is changed. The changing pa...

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Section: Catastrophe Theorymentioning

confidence: 99%

Stochastic catastrophe analysis of switches in the perception of apparent motion

Ploeger

Maas

Hartelman

2002

Psychonomic Bulletin & Review

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“…Catastrophe theory (Thom, 1975;Zeeman, 1977) can offer an appealing approximation for understanding these dynamical changes (Ceja and Navarro, 2011). It has provided successful approximations for other organizational processes, such as work motivation (e.g., Guastello, 1987), employee turnover (e.g., Sheridan, 1985;Sheridan and Abelson, 1983), decision making (e.g., Wright, 1983), personnel selection (e.g., Guastello, 1982), organizational change (e.g., Bigelow, 1982), and competitive dynamics (e.g., Kauffman and Oliva, 1994). However, scholars have not yet tested such models directly in work/health relationships.…”

Section: Introductionmentioning

confidence: 99%

‘Suddenly I get into the zone’: Examining discontinuities and nonlinear changes in flow experiences at work

Ceja

Navarro

2012

Human Relations

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Work-related flow is defined as a sudden and enjoyable merging of action and awareness that represents a peak experience in the daily lives of workers. Employees' perceptions of challenge and skill and their subjective experiences in terms of enjoyment, interest, and absorption were measured using the experience sampling method, yielding a total of 6,981 observations from a sample of 60 employees. Linear and nonlinear approaches were applied in order to model both continuous and sudden changes. According to the R 2 , AICc, and BIC indexes, the nonlinear dynamical systems model (i.e., cusp catastrophe model) fit the data better than the linear and logistic regression models. Likewise, the cusp catastrophe model appears to be especially powerful for modeling those cases of high levels of flow. Overall, flow represents a nonequilibrium condition that combines continuous and abrupt changes across time. Research and intervention efforts concerned with this process should focus on the variable of challenge, which, according to our study, appears to play a key role in the abrupt changes observed in work-related flow.

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“…Stochastic formulations of catastrophe theory have been found, and statistical methods have been developed that allow quantitative comparison of catastrophe models with data (Cobb and Ragade 1978;Cobb and Watson 1980;Cobb 1981;Cobb et al 1983;Guastello 1982;Oliva, Desarbo, Day, and Jedidi 1987;Lange, Oliva, and McDade 2000;Wagenmakers, Molenaar, Grasman, Hartelman, and van der Maas 2005a;Guastello 1992). Of these methods, the maximum likelihood approach of Cobb and Watson (1980); Cobb et al (1983) is arguably most appealing for reasons that we discuss in the Appendix A.…”

mentioning

confidence: 99%

Fitting the Cusp Catastrophe inR: AcuspPackage Primer

Grasman¹,

Maas²,

Wagenmakers³

2009

J. Stat. Soft.

116

169

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Of the seven elementary catastrophes in catastrophe theory, the "cusp" model is the most widely applied. Most applications are however qualitative. Quantitative techniques for catastrophe modeling have been developed, but so far the limited availability of flexible software has hindered quantitative assessment. We present a package that implements and extends the method of Cobb (Cobb and Watson 1980;Cobb, Koppstein, and Chen 1983), and makes it easy to quantitatively fit and compare different cusp catastrophe models in a statistically principled way. After a short introduction to the cusp catastrophe, we demonstrate the package with two instructive examples.Keywords: catastrophe theory, cusp, modeling.Catastrophe theory studies qualitative changes in behavior of systems under smooth gradual changes of control factors that determine their behavioral state. In doing so, catastrophe theory has been able to explain for example, how sudden abrupt changes in behavior can result from minute changes in the controlling factors, and why such changes occur at different control factor configurations depending on the past states of the system. Specifically, catastrophe theory predicts all the types of qualitative behavioral changes that can occur in the class of so called gradient systems, under influence of gradual changes in controlling factors (Poston and Stewart 1996).Catastrophe theory was popularized in the 1970's (Thom 1973;Thom and Fowler 1975;Gilmore 1993), and was suggested as a strategy for modeling in various disciplines, like physics, biology, psychology, and economics, by Zeeman (1971)-as cited in Stewart and Peregoy (1983), Zeeman (1973), Zeeman (1974), Isnard and Zeeman (1976), and Poston and Stewart (1996. Although catastrophe theory is well established and applied in the physical sciences, its applications in the biological sciences, and especially in the social and behavioral sciences, has been criticized (Sussmann and Zahler 1978;Rosser 2007). Applications in the latter fields range from modeling of exchange market crashes in economics (Zeeman 1974), to

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Moderator regression and the cusp catastrophe: Application of two-stage personnel selection, training, therapy, and policy evaluation

Cited by 72 publications

References 62 publications

Stochastic catastrophe analysis of switches in the perception of apparent motion

Stochastic catastrophe analysis of switches in the perception of apparent motion

‘Suddenly I get into the zone’: Examining discontinuities and nonlinear changes in flow experiences at work

Fitting the Cusp Catastrophe inR: AcuspPackage Primer

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