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.
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Notes
For those interested in an detailed explanation of the SACS Toolkit in application to our case study, see Castellani et al. (2012).
For those interested in an in-depth review of our model, see Castellani et al. (2012). Also, for those interested in downloading or running Summit-Sim, go to http://cch.ashtabula.kent.edu/summitsim.html.
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Castellani, B., Rajaram, R. Case-based modeling and the SACS Toolkit: a mathematical outline. Comput Math Organ Theory 18, 153–174 (2012). https://doi.org/10.1007/s10588-012-9114-1
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DOI: https://doi.org/10.1007/s10588-012-9114-1