| Description of Projects | |||||||||||||||||||||||||||||||||||||||
Introduction: the Metamatrix ApproachThe metamatrix approach (Krackhardt and Carley, 1998; Carley and Krackhardt, 1999; Carley et al., 2000; Carley 1999, 2001a,b; Carley and Hill, 2001; Carley and Ren, 2001) provides a representational framework and family of methods for the analysis of organizational data. Stemming from work by Kathleen Carley, David Krackhardt, Yuquing Ren, and others, this approach builds heavily on recent network-oriented treatments of organizational structure, as well as ideas from the information processing school of organizational theory (March and Simon, 1958; Simon, 1973; Galbraith, 1977) and operations research. Under this model, organizations are conceived of as being composed of a set of \emph{elements}, each of which belongs to one of five classes:
The organization is then defined by the set of elements, together with the dyadic relationships among these elements. It is the analysis of these dyadic relationships which lies at the heart of the metamatrix approach. The term ``organizational metamatrix'' itself derives from a useful conceptualization of the inter-element relationships described above. By taking each of the five element types and using them to define the rows and columns of a matrix, we arrive at something like the table below. Note that each cell of this matrix can be interpreted as a particular organizational substructure. Thus, the ``PP'' cell can be thought of as reflecting Personnel x Personnel relations, the ``RT'' cell can be seen as containing Resource x Task relationships, and so forth. Since each of these relations can in turn be expressed via an adjacency matrix (a matrix in which the ijth cell is 1 if element i sends a tie to element j), the larger structure can be thought of as a matrix of matrices, or a ``metamatrix.'' Since each cell of the metamatrix tends to carry a distinct substantive meaning (e.g., the PT cell provides the assignment of Personnel to Tasks), it is often useful to treat the total organizational structure in metamatrix form. On the other hand, the above table suggests another useful duality: each cell of the metamatrix corresponds to a submatrix of the combined organizational structure formed by the union of all elements and relations. Thus, we can where useful move between the metamatrix and combined (or ``full'') adjacency matrix representations of the organization without loss of generality.
Given the above representational framework, the metamatrix approach to organizational analysis proceeds by examining the ways in which the requirements of the organization (e.g., its tasks and their relationships to inputs and each other) match (or fail to match) its capabilities (as embodied by relations among personnel, knowledge, resources, and external organizations). As one might expect, this leaves room for a wide variety of methods, many of which may depend on the context of the analysis itself. The software tools discussed here implement a variety of these techniques, and are designed so as to facilitate integration with traditional organization and network analytic methods.
Software ToolsCurrently, there are two independent implementations of the metamatrix approach, each of which lends itself to slightly different applications:
Research SupportThis work was supported in part by the Office of Naval Research (ONR), United States Navy Grant No. N00014-97-1-0037, NSF IGERT in CASOS, NSF IRI9633 662, NSF KDI IIS-9980109, and the Pennsylvania Infrastructure Technology Alliance, a partnership of Carnegie Mellon, Lehigh University, and the Commonwealth of Pennsylvania's Department of Economic and Community Development. Additional support was provided by ICES (the Institute for Complex Engineered Systems) and CASOS, the center for Computational Analysis of Social and Organizational Systems at Carnegie Mellon University (http://www.ices.cmu.edu/casos). |