02 November 2008

Matrix unloaded

Interesting lecture* on Thursday evening, hosted by BRILLE at UWE and delivered by Stephen J Ball of the IoE. My thanks to Matt Davis, without whose suggestion I would never have been there, and to Adèle Evans whose perceptive comments sent me squirreling off along the lines of possibility afterwards.

The actual content reflected Ball's recent and current work (particularly a Political studies article*), but there was a lot of lateral detail added by the context and more drawn in by questions afterwards. The "geography" of mechanisms which replace bureaucracy with influence networks was well demonstrated. At a time when the nation state is clearly on its last legs and in a process of unvolution, these network maps hint at the underlying skeleton of what will replace it. Lots of important collateral issues too, such as the end user and involuntary donor impacts of philanthropic action.

What mostly hooked me, though, as a dabbler in network structured analyses myself, were technical aspects of the methodology. There were a number of questions I was itching to ask, in that direction, but wouldn't have been appropriate ... and, besides, I'll get more out of them by trying to resolve them myself. Some of them Professor Ball raised; others were implicit.

One of the issues which he mentioned was "the problem of fitting it on the page" – the scale and complexity of the networks being modelled. All of his diagrams, he repeatedly made clear, were partial and fragmentary, the reality of the whole existing only in their interpenetration.

He mentioned block modelling, but suggested that his models are not at a level of complexity or scale to justify its application; I'm not sure I see that, though I concede that I lack the knowledge of his study to contest it. In any case, it was very clear that both macro and micro structures are equally important: any method of integration must not sacrifice detail.

The lecture was illustrated using descriptive diagrams produced in SmartDraw. Professor Ball's networks are descriptive models – visualised forms of conceptual linkage structures to aid exploration – rather than active simulations of behaviour. The "nature of discourse through the arcs, and the nature of nodal influence thus enabled" (Professor Ball's words, but my emphasis), is the focus of study, not its measure. Linkages are qualitative, or even nominative, not quantitative, concerning directionality of influences and the public/private formal/informal weak/strong competitive/collaborative ways in which they shape one another. With my different perspective, I was itching to see them transferred into Simile (or some other active modelling tool) – though I'm not sure how it would be done. Considering that "how" is one of the things now occupying my attention in spare moments.

A question which Professor Ball highlighted early on, and emphasised, was how to define a measure that proves a policy result. In a very real sense, these networks can only be said to exist if there is such a result. Validation depends on establishing such measures which, to someone with my cast of mind, means quantising the model – though other methods exist, such as seeking a prediction from action at input to change of state at output.

Unlike most of the networks with which I play, the predominant active potential lies not in the interconnective arcs but in the nodes themselves. Some way would have to be found of translating that into arc actions – presumably, at first sight, in the form of equation systems associated with those nodes and hidden away in submodels. Then each arc would gain much of its quantitative value from interaction of those nodal systems – but there would also be value assignments inherent in some arcs, as well. A friendship between industrialist "X" and influential academic "Y" (both of whom are nodes) would find its quantitative expression(s) through interaction of their submodels with each other and also (some system of weighting becomes necessary here, related to closeness of association) with mutual acquaintances and to a lesser extent with other nodes in the network or beyond. ("Beyond" because some nodes have no interconnection, existing in separate networks, but two networks themselves impact on the environmental state within which both operate.)

Then there is the question of effect persistence. One arc in a particular diagram represented a grant from one node (a foundation) to a single element in another (a researcher in a think tank); that would be quite a short term linkage, perhaps as short as a year or even less. Another was a degree of common membership between two nodes – two or three partners in the same merchant bank who are also founding trustees of the same charity, for example – which will tend to greater longevity. Links between influential individuals who attended the same school and university will be longer lasting still (though even more difficult to quantify). A network diagram containing these linkages is a snapshot at one moment in time, its complete validity limited by the shortest linkage duration within it.

Any quantisation of such a snapshot would have to restrict itself to seeking dynamics and rest states within the network at that moment. Study of effects over time would require longitudinal linkage between successive snapshots.

All my instincts are towards modelling a whole network as a pyramid of substructures. At the base would be the system of equations for each node – or, preferably, just one system of equations, with a different table of variable values for each. Node inputs and outputs would link to impact matrices (fairly complex ones) which, in turn, would be expressed as arc effects. That would allow both tuning and examination to be focussed at any desired level (each level being a network in its own right), temporarily ignoring the others. That would correspond pretty well to real life experience, too. Longitudinal linkages would then reflect temporal process between time sliced variants of the same network, much simpler lateral ones (the effect of one discrete network on others in the same policy environment – and on the environment itself.

It's a wonderful playground to imagine ... but an immense one. Anybody got spare high performance computing capacity, and a few years funding, that they don't know what to do with?

  • BRILLE first keynote lecture in an educational policy research series: Policy Networks, Policy Analysis and Post-Neo-­liberal Governance. Led by Professor Stephen Ball, Thursday 30th October 2008, 18.00 - 19.30, Frenchay campus, UWE.
  • Stephen J Ball, "New Philanthropy, New Networks and New Governance in Education" in Political Studies, 2008. click here for 2collab bookmark
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