Mathematical tools for hazard function analysis

Chechile, Richard A.

doi:10.1016/s0022-2496(03)00063-4

Cited by 52 publications

(66 citation statements)

References 35 publications

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“…Unfortunately, estimates of momentary hazard rates are often unreliable, with local irregularities amplified especially as response frequencies diminish toward the lower tail of the survivor function (see Cechile, 2003;Luce, 1986;Houpt & Townsend, 2012;Van Zandt, 2000). The integrated, H(t), functions can bypass aspects of this estimation problem (see Houpt & Townsend, 2012;Wenger & Gibson, 2004).…”

Section: General Methodsmentioning

confidence: 99%

The channel capacity of visual awareness divided among multiple moving objects

Lappin

Morse

Seiffert

2016

Atten Percept Psychophys

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If attention is distributed among multiple moving objects, how does this divided attention affect the temporal process for detecting a specific target motion? Well-trained observers in three experiments monitored ongoing random motions of multiple objects, trying to rapidly detect nonrandom target motions. Response time hazard rates revealed a simple lawful structure of the detection processes. Target detection rates (hazard rates, in bits/s) were inversely proportional to the number of observed objects. Detection rates at any response time and in any condition equaled a product of two parallel (functionally independent and concurrent) visual processes: visual awareness and motion integration. The rate of visual awareness was inversely proportional to Set Size (n = 1-12), constant over time, and invariant with integrated motion information. Thus, a single rate parameter, indicating a constant channel capacity of visual awareness, described detection rates over a wide range of conditions and response times. During an initial interval of roughly 0.5 s, detection rates increased proportionally with the duration and length of motion; but after this initial integration, detection rates were constant, independent of the time the target remained undetected. The relationship between the quantity of visual information and detection rates was simpler than anticipated by contemporary theories of attention, perception, and performance.

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Section: General Methodsmentioning

confidence: 99%

The channel capacity of visual awareness divided among multiple moving objects

Lappin

Morse

Seiffert

2016

Atten Percept Psychophys

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“…The hazard function has been employed since then frequently as a labor-static design (not to exclude the possibility that a participant might tire or warm up during a session, but the experimenter is not so manipulating the task). In addition, certain powerful stochastic methods have recently been enlisted that considerably enhance the utility and statistical sensitivity of hazard function analyses with psychological data (Chechile, 2003;Wenger & Gibson, 2004).…”

Section: Measures Of Capacity and Their Interrelationshipsmentioning

confidence: 99%

Workload capacity spaces: A unified methodology for response time measures of efficiency as workload is varied

2011

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Increasing the number of available sources of information may impair or facilitate performance, depending on the capacity of the processing system. Tests performed on response time distributions are proving to be useful tools in determining the workload capacity (as well as other properties) of cognitive systems. In this article, we develop a framework and relevant mathematical formulae that represent different capacity assays (Miller's race model bound, Grice's bound, and Townsend's capacity coefficient) in the same space. The new space allows a direct comparison between the distinct bounds and the capacity coefficient values and helps explicate the relationships among the different measures. An analogous common space is proposed for the AND paradigm, relating the capacity index to the Colonius-Vorberg bounds. We illustrate the effectiveness of the unified spaces by presenting data from two simulated models (standard parallel, coactive) and a prototypical visual detection experiment. A conversion table for the unified spaces is provided.

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“…Others have described ways that the hazard function can be used to identify cognitive processing properties (Ashby, 1982;Chechile, 2003;Townsend & Ashby, 1983;Van Zandt & Ratcliff, 1995). Systems factorial technology (SFT), developed by Townsend and colleagues, uses a number of ''functionals'' based on the cdf F (t|θ) and the survivor function S(t|θ) to determine different characteristics of multichannel cognitive processing systems (Houpt & Townsend, 2010Schweickert, Fisher, & Sung, 2012;Townsend & Nozawa, 1995;Townsend & Wenger, 2004).…”

Section: Notationmentioning

confidence: 99%

Semiparametric Bayesian approaches to systems factorial technology

Houpt

MacEachern

Peruggia

et al. 2016

Journal of Mathematical Psychology

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h i g h l i g h t s• A semiparametric piecewise exponential model is used to estimate response time hazard functions. • This semiparametric model is fit to data in a Bayesian hierarchy.• The resulting posterior estimates of the hazard functions can be used to compute the posterior estimates of systems factorial functionals. a b s t r a c tSystems factorial technology (e.g., Townsend and Nozawa, 1995) is a toolbox of methods to test characteristics of multichannel processing systems. In this paper, we present a semiparametric Bayesian model of response times based on a piecewise-exponential model. This model allows us to compute the posterior estimates of the response time distribution hazard function and the systems factorial technology functionals that can be computed from it, including the survivor function interaction contrast and the capacity coefficient. We then compute posterior estimates of statistics that reflect different behaviors of the functionals, and so arrive at a fully Bayesian and theoretically-motivated approach to systems factorial technology. Simulation studies demonstrate the effectiveness of the approach, and we apply it to a published data set.

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Mathematical tools for hazard function analysis

Cited by 52 publications

References 35 publications

The channel capacity of visual awareness divided among multiple moving objects

The channel capacity of visual awareness divided among multiple moving objects

Workload capacity spaces: A unified methodology for response time measures of efficiency as workload is varied

Semiparametric Bayesian approaches to systems factorial technology

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