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Case-based modeling and the SACS Toolkit: a mathematical outline

Author

Listed:
  • Brian Castellani

    (Kent State University)

  • Rajeev Rajaram

    (Kent State University)

Abstract

Researchers in the social sciences currently employ a variety of mathematical/computational models for studying complex systems. Despite the diversity of these models, the majority can be grouped into one of three types: agent (rule-based) modeling, dynamical (equation-based) modeling and statistical (aggregate-based) modeling. The purpose of the current paper is to offer a fourth type: case-based modeling. To do so, we review the SACS Toolkit: a new method for quantitatively modeling complex social systems, based on a case-based, computational approach to data analysis. The SACS Toolkit is comprised of three main components: a theoretical blueprint of the major components of a complex system (social complexity theory); a set of case-based instructions for modeling complex systems from the ground up (assemblage); and a recommended list of case-friendly computational modeling techniques (case-based toolset). Developed as a variation on Byrne (in Sage Handbook of Case-Based Methods, pp. 260–268, 2009), the SACS Toolkit models a complex system as a set of k-dimensional vectors (cases), which it compares and contrasts, and then condenses and clusters to create a low-dimensional model (map) of a complex system’s structure and dynamics over time/space. The assembled nature of the SACS Toolkit is its primary strength. While grounded in a defined mathematical framework, the SACS Toolkit is methodologically open-ended and therefore adaptable and amenable, allowing researchers to employ and bring together a wide variety of modeling techniques. Researchers can even develop and modify the SACS Toolkit for their own purposes. The other strength of the SACS Toolkit, which makes it a very effective technique for modeling large databases, is its ability to compress data matrices while preserving the most important aspects of a complex system’s structure and dynamics across time/space. To date, while the SACS Toolkit has been used to study several topics, a mathematical outline of its case-based approach to quantitative analysis (along with a case study) has yet to be written–hence the purpose of the current paper.

Suggested Citation

  • Brian Castellani & Rajeev Rajaram, 2012. "Case-based modeling and the SACS Toolkit: a mathematical outline," Computational and Mathematical Organization Theory, Springer, vol. 18(2), pages 153-174, June.
    • Handle: RePEc:spr:comaot:v:18:y:2012:i:2:d:10.1007_s10588-012-9114-1
    DOI: 10.1007/s10588-012-9114-1
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    References listed on IDEAS

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    1. Cummins, Steven & Curtis, Sarah & Diez-Roux, Ana V. & Macintyre, Sally, 2007. "Understanding and representing 'place' in health research: A relational approach," Social Science & Medicine, Elsevier, vol. 65(9), pages 1825-1838, November.
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    Cited by:

    1. Davide Secchi & Raffaello Seri, 2017. "Controlling for false negatives in agent-based models: a review of power analysis in organizational research," Computational and Mathematical Organization Theory, Springer, vol. 23(1), pages 94-121, March.
    2. Rajaram, R. & Castellani, B., 2016. "An entropy based measure for comparing distributions of complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 35-43.

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