Response to Sobel

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From SobePs comments, some readers might infer that I propose the independence model (a model that never fits mobility data) as the terminus for mobility analysis. That is not so. I propose it as the point of departure for deriving a quantitative model that does fit the data and whose parameter estimates can therefore be interpreted as adequately reproducing the observed mobility flows. However, in practice I find quantification indices helpful in suggesting such models. That said, the aims of my earlier comments were to defend the independence model as an appropriate baseline from which to assess patterns of association and dissociation between generations, to defend Hope's definition of structural mobility, and to suggest that the examples given by Sobel in criticism of Yasuda's index were inadequate. Sobel now goes even further in his criticism of the independence model: '... the independence model is no longer useful even as a null hypothesis, for both social theory and all available experience indicate that it is not a plausible representation of the mobility process'. Indeed, according to Sobel, '... the independence model ... has no role in mobility research'. But to pit the independence model and quantification indices against the parametrically based approach that Sobel advocates is simply to set up a false opposition. Description and explanation are not mutually exclusive. Hope advocates a structured modelling approach to mobility analysis, and I suspect (but am not sure) that that is the real target of Sobel's criticism. Hope fits a priori terms defined theoretically, terms applicable in principle to any mobility table. He calculates progressive reductions in what he terms mobility variance (which encompasses structural differences as well as association) achieved by fitting these theoretically defined terms in a defined order. Sobel, on the other hand, is interested only in the parameter estimates of some final model that is accepted as adequately reproducing the observed counts in a mobility table. I occupy an intermediate position. I support Hope's diffuse conception of structural mobility as a factor exogenous to stratification processes, more narrowly defined as 'association' between origin and destinations, and I have some sympathy with the logic underlying his structured approach. I also think that descriptive indices based on the concept of independence (such as the Yasuda index) can assist in the formulation of well-fitting log linear models, as I demonstrate below and elsewhere (Jones, 1985). But before that I must respond to Sobel's challenge and show that his formal proof, that Hope's definition of structural mobility is incorrect, is itself incorrect.