From: Ian Wright (iwright@GMAIL.COM)
Date: Sun Sep 19 2004 - 23:34:51 EDT
Hi Allin > > In the social relations model the distribution can be approximated > > by a parameter-mix of ratios of normal variates with means and > > variances distributed according to a power-law. This is a > > 7-parameter distribution... > > Gak! Doesn't that sound like over-fitting? Does Occam approve? This distribution is derived from the dynamics of the model, given some simplifying assumptions. The distribution hasn't been arbitrarily picked to fit a set of data. But I know that some of the 7 parameters have functional relations between them. If I could analytically determine those relations I think the number of parameters could be reduced. But I haven't been able to do that as yet. The parameters, however, have explicit semantics as they have been deduced from the model, which would not be the case if a 7-parameter distribution had simply been fitted to the data. For example, the parameters are things like the mean value-added per worker, the mean cost per worker, the size of the employed workforce, the Pareto exponent of the firm size distribution, and so forth. In principle, these can be obtained from empirical data. But this is work in progress, and I am concerned to square all this with Julian's empirical and theoretical work. More generally, if Occam's principle is viewed as an optimisation principle, i.e. minimise model complexity under the constraint of reproducing the known data, then we can't really say that n parameters are "too much". It depends also on the complexity of the data. -Ian.
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