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Random local temporal structure of category fluency responses

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Abstract

The Category Fluency Test (CFT) provides a sensitive measurement of cognitive capabilities in humans related to retrieval from semantic memory. In particular, it is widely used to assess progress of cognitive impairment in patients with dementia. Previous research shows that, in the first approximation, the intensity of tested individuals’ responses within a standard 60-s test period decays exponentially with time, with faster decay rates for more cognitively impaired patients. Such decay rate can then be viewed as a global (macro) diagnostic parameter of each test. In the present paper we focus on the statistical properties of the properly de-trended time intervals between consecutive responses (inter-call times) in the Category Fluency Test. In a sense, those properties reflect the local (micro) structure of the response generation process. We find that a good approximation for the distribution of the de-trended inter-call times is provided by the Weibull Distribution, a probability distribution that appears naturally in this context as a distribution of a minimum of independent random quantities and is the standard tool in industrial reliability theory. This insight leads us to a new interpretation of the concept of “navigating a semantic space” via patient responses.

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Notes

  1. It would be more elegant to work here with the exponential function of the form 2 − t/τ (instead of e  − t/τ) in which case the “latency constant”, τ, would be the time by which the individual reaches 2−1 = 50% of his total capacity, but we elected not to do it as such a choice would make other calculations more messy.

  2. Even worse, as a result, the crucial de-trending process discussed in Section 3 sometimes resulted in negative inter-arrival times.

  3. The coefficient 2 in the discounting exponential factor has been chosen for mathematical convenience so that we can distribute the two factors of \(e^{t_k\nu} \) into the squared term in parentheses.

  4. All computing and graphing in this paper has been done in the symbolic manipulation language Mathematica.

  5. The idea of using the Garage Band originated with our student coauthors (JM, and TS) who administered actual CFTs for young adults YA 01–17, and older adults OA 01–17. The data for OA 01–09 were supplied by another of our coauthors (JK).

  6. Some sort of independence, perhaps fairly week, within the sequence δt 1,..., δt N , and thus, δT 1,...,δT N , is needed to justify employment of the standard statistical inference tools here. This is a delicate issue as consecutive responses are probably not completely statistically independent, and the problem is related to the global temporal structure of the category fluency tests. On the other hand, one can reasonably assume that the detrended inter-call sequences for different individuals are statistically independent.

  7. Note that the information about the total number of responses in each test is already embedded in the usual parameter N 60, we do not need it anymore.

  8. A more subtle parametric model that automatically takes into account the burstiness of the recall process will be studied in another paper.

  9. We have found recently, that a similar argument was used by Logan (1995) in the context of what he calls the “instance theory of automaticity”.

  10. This property is often called the heavy-tail property, and it means that the probabilities of big values are much larger than the corresponding probabilities for Gaussian or exponential distributions.

  11. Coincidentaly, the paper was written fifty years ago when Fred Leone was director of the Statistical Laboratory here at Case.

  12. Here we used the FindRoot facility in Mathematica.

  13. In statistics, this approach to parameteric estimation is called the Method of Moments.

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Acknowledgements

This research has been supported by the U.S. National Science Foundation Grant “Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences” (DUE-0634612) administered by PJT; the first three authors were undergraduate students in biology and mathematics at Case while this work has been done. PJT was supported by the National Science Foundation’s program in Mathematical Biology (DMS-0720142), and acknowledges research support from the Oberlin College Libraries. JK was supported by grants from the National Institute on Aging (P30AG024978, P30AG08017 and R01AG024059).

The authors are grateful to the anonymous referees for helping us understand the broad and rich history of the studies of the distributional properties of inter-response times about which which we were initially quite ignorant partly because of the terminological diversity in the relevant literature. The paper benefited from their kind and generous advice.

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Authors and Affiliations

  1. Case Western Reserve University, 11900 Euclid Avenue, Cleveland, OH, 44106, USA

    David J. Meyer, Jason Messer & Tanya Singh

  2. Departments of Mathematics, Biology and Cognitive Science, Case Western Reserve University, 11900 Euclid Avenue, Cleveland, OH, 44106, USA

    Peter J. Thomas

  3. Department of Neuroscience, Oberlin College, Oberlin, OH, 44074, USA

    Peter J. Thomas

  4. Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, 11900 Euclid Avenue, Cleveland, OH, 44106, USA

    Wojbor A. Woyczynski

  5. Departments of Neurology and Biomedical Engineering, Oregon Health and Science University, Portland, OR, 97239, USA

    Jeffrey Kaye

  6. Portland Veterans Affairs Medical Center, Portland, OR, 97239, USA

    Jeffrey Kaye

  7. Department of Neurology, Case Medical Center, Case Western Reserve University, 11900 Euclid Avenue, Cleveland, OH, 44106, USA

    Alan J. Lerner

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  1. David J. Meyer
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Correspondence to Wojbor A. Woyczynski.

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Meyer, D.J., Messer, J., Singh, T. et al. Random local temporal structure of category fluency responses. J Comput Neurosci 32, 213–231 (2012). https://doi.org/10.1007/s10827-011-0349-5

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  • DOI: https://doi.org/10.1007/s10827-011-0349-5

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