Wiley StatsRef: Statistics Reference Online 2015
DOI: 10.1002/9781118445112.stat06427.pub2
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Elementary Catastrophe Theory

Abstract: Catastrophe theory describes how small, continuous changes in control parameters (i.e., independent variables that influence the state of a system) can have sudden, discontinuous effects on dependent variables. Such discontinuous, jumplike changes are called phase‐transitions or catastrophes . Examples include the sudden collapse of a bridge under slowly mounting pressure, and the freezing of water when temperature is gradually decreased. This entry expands on th… Show more

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Cited by 8 publications
(15 citation statements)
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“…We removed 141 trials from the IAT (0.4% of the trials) in Data Set 1, 4,850 trials from the IAT (3.2% of the trials) in Data Set 2, 377 trials from the IAT (0.8% of the trials) in Data Set 3,626 trials from the IAT (1.1% of the trials) in Data Set 4, 4,054 trials from the IAT (2.7% of the trials) in Data Set 5, 1,017 trials from the IAT (2.1% of the trials) in Data Set 6, and 136 trials from the IAT (0.2% of the trials) in Data Set 7. As suggested by Wagenmakers et al (2007), we corrected the percentage of correct responses that equaled exactly 1.0 by subtracting half an error from the percentage of correct responses before running further analyses. We also corrected the percentage of correct responses that equaled exactly 0 and 0.5 by adding half an error, respectively.…”
Section: Iatsmentioning
confidence: 99%
“…We removed 141 trials from the IAT (0.4% of the trials) in Data Set 1, 4,850 trials from the IAT (3.2% of the trials) in Data Set 2, 377 trials from the IAT (0.8% of the trials) in Data Set 3,626 trials from the IAT (1.1% of the trials) in Data Set 4, 4,054 trials from the IAT (2.7% of the trials) in Data Set 5, 1,017 trials from the IAT (2.1% of the trials) in Data Set 6, and 136 trials from the IAT (0.2% of the trials) in Data Set 7. As suggested by Wagenmakers et al (2007), we corrected the percentage of correct responses that equaled exactly 1.0 by subtracting half an error from the percentage of correct responses before running further analyses. We also corrected the percentage of correct responses that equaled exactly 0 and 0.5 by adding half an error, respectively.…”
Section: Iatsmentioning
confidence: 99%
“…For non-decision time T er Wabersich and Vandekerckhove (2014). EZ and EZ2 refer to estimation methods for the simple DDM developed by Wagenmakers et al (2007) and Grasman et al (2009), respectively. and across-trial variability in non-decision time s T er , the selected model was a zero-bounded truncated t distribution (wAIC = 1 for both T er and s T er ).…”
Section: Resultsmentioning
confidence: 99%
“…When the DDM was applied to the same data across different articles, we extracted the parameter estimates from the first application; if the first application did not report parameter estimates, we used the most recent application that reported parameter estimates. Finally, articles that obtained estimates using the EZ (Wagenmakers et al, 2007) or EZ2 (Grasman et al, 2009) methods, or the RWiener R package (Wabersich and Vandekerckhove, 2014), which all fit the simple diffusion model estimating only the four main DDM parameters (Stone, 1960), were excluded due to concerns about potential distortions caused by ignoring across-trial parameter variability (Ratcliff, 2008). Note that we did not automatically exclude all articles without across-trial variability parameters.…”
Section: Data Extractionmentioning
confidence: 99%
“…Using simpler process models for empirical research is supportive of previous literature, with the notion that "less is more" when it comes to selecting a psychometric model for accurately estimating predictor and participant effects from experimental data. For example, van Ravenzwaaij, Donkin, and Vandekerckhove (2016) show that simpler SSMs with fewer parameters (e.g., the EZ-diffusion model, Wagenmakers, Van Der Maas, & Grasman, 2007) recovered the significant predictor effects in experiments better than their more complex counterparts, the Diffusion Decision Model (DDM, Ratcliff, 1978;Ratcliff & Smith, 2004;Ratcliff & McKoon, 2008). Such findings also highlight the growing differences between simple SSMs as apt measurement (quantitative, data-driven, psychometric) models, and others which are more suited for theoretical exploration (simulation testing, data-producing) of specific neural dynamics.…”
Section: Discussionmentioning
confidence: 99%