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This program computes the three-way interaction information in bits using Krippendorff’s (2009a, at p. 200) algorithm for the decomposition I(ABC→AB:AC:BC). The user is prompted for the eight (= 2^3) frequency values (which can also be considered as values at the eight corners of a cube). Only positive values are accepted because the program transforms these values into a probability distribution.
In addition to I(ABC→AB:AC:BC) in millibits of information, the program computes the mutual information in three dimensions T_{xyz} or μ* (Yeung, 2008), and the redundancy R = I + T (Krippendorff, 2009b).
References:
Krippendorff, K. (2009a). “Ross Ashby’s information theory: a bit of history, some solutions to problems, International Journal of General Systems 38(2), 189-212.
Krippendorff, K. (2009b). Concerning the Information of Interactions in Complex Systems, International Journal of General Systems, forthcoming.
Leydesdorff, L. (2009a). Interaction Information: Linear and Nonlinear Interpretations. International Journal of General Systems, forthcoming.
Leydesdorff, L. (2009b). “Structuration” by Intellectual Organization: The Configuration of Knowledge in Relations among Scientific Texts; <pdf-version>
Yeung, R. W. (2008). Information Theory and Network Coding. New York, NY: Springer; available at http://iest2.ie.cuhk.edu.hk/~whyeung/post/main2.pdf .
Please, provide feedback if you find an error. The source code can be found here.
Krippendorff’s original program (in Fortran) can be retrieved from http://www.pdx.edu/sysc/research-discrete-multivariate-modeling.
@ Loet Leydesdorff, April 2009