"What if Ingeborg Heinrich, my student at the Institute for Advanced Studies in Vienna in the fall of 1973, had succeeded in her project of teaching me how to use Rasch models? I could have started several years earlier on the studies that made up my work in the 1980s, and perhaps we would have had, that much sooner, the result reported by Hout, Duncan, and Sobel in 1987, that a Rasch model for a pair of polytomous variables implies that the cross-classification in the population is quasi-symmetric [QS]."
"Let {F_{ij}} (i=1,...,R; j=1,...,R) denote the expected [person] frequencies in the RxR contingency table [the cross-tabulation of two items, each with R categories]. We write QS as
where ß_{i}=ß_{j} if i=j, δ_{ij}=δ_{ij} if i<>j, δ_{ii}=1, i=1,...,R and πα_{j}=1" (Hout, Duncan, Sobel, 1987). This is close to a multiplicative form of the Rasch model for two polytomous items.
"And what if - now I am speculating about the future, so there is the bare possibility that the rumination will not be entirely fruitless - someone picks up on the amazing coincidence that QS is the key to these two apparently disparate conceptual domains [Rasch and mobility tables]? We are looking for a bright person with ten or twenty prime working years left. She could conceivably get her clue from my use of QS in testing the Rasch model for some Occupational Change in a Generation data deriving from Peter Blau's brilliant invention, the brother's education variable (Duncan 1990)."
"And what if - now it gets really wild - said investigator decides to take seriously the distinction between a scientific model and a mere statistical model? This distinction became salient to me in the paper Rogosa (1987) contributed ..."
"The critical distinction is between models that start with the individual process as opposed to models for relations among variables, of which path analysis, covariance structure analysis, and other causal modeling strategies are prominent examples. I see these models for relations among variables as statistical models without a substantive soul. Substantive processes happen to or act on individual units (persons), not to variables. And a useful model should be a representation of the relevant phenomena. Otherwise as Freedman finds with path analysis, `the technology tends to overwhelm common sense', and I feel that's because the technology has little or no link to common sense." (Rogosa, 1987)
"In what I had hoped would prove to be my last contribution to the sociological literature (Duncan and Stenbeck 1988), though not the last to be published, I mobilized every variety of rhetoric I knew to try to pound home this distinction and the absurd consequences of ignoring it."
"A statistical model may serve very well as a basis for inferences about multivariate population distributions. Unfortunately, the intellectual attractiveness of the problems of statistical inference that arise in working with complex cross-classifications makes it easy to mistake their solution for a contribution to scientific method. We feel it is time to re-establish the correct priorities. The design of investigations is the essential ingredient of scientific method, indeed, of empirical science itself. Data analysis by suitable statistical methods is a mere auxiliary to the central scientific task. It was the determination of what observations to make, under what conditions, that required the genius of a Tycho Brahe, a Galileo, a Mendel, or a Pasteur, all of whom could have made good use of statistical methods, had they been available, but none of whose discoveries could have been made by a platoon of statisticians." (Duncan and Stenbeck, 1988).
"The main point to emphasize here is that the postulate of probabilistic response must be clearly distinguished in both concept and research design from the stochastic variation of data that arises from random sampling of a heterogeneous population. The distinction is completely blurred in our conventional statistical training and practice of data analysis, wherein the stochastic aspects of the statistical model are most easily justified by the idea of sampling from a population distribution. We seldom stop to wonder if sampling is the only reason for making the model stochastic. The perverse consequence of doing good statistics is, therefore, to suppress curiosity about the actual processes that generate the data." (Duncan and Stenbeck, 1988)
"What if, in other words, some younger quantitative sociologist repudiates our Faustian bargain with statistics, the bargain which gave us instant, voluminous, and easy results - but results that often were mischievous or meaningless when they were not both?"
excerpted from Otis Dudley Duncan. 1992. What if? In Symposium: The American Occupational Structure: Reflections after Twenty-five Years. Contemporary Sociology, 21:5, 667-8.
Duncan, O.D. 1990. Family and Birth-Order Effects on Educational Attainment. pp. 167-77 in Structures of Power and Constraint: Papers in Honor of Peter M. Blau, edited by C. Calhoun, M.W. Meyer, and W.R. Scott. Cambridge: Cambridge University Press.
Duncan, O.D., Stenbeck, M. 1988. Panels and Cohorts: Design and Model in the Study of Voting Turnout. pp. 1-35 in Sociological Methodology 1988, edited by C. C. Clogg. Washington, DC: American Sociological Assoc.
Hout, M., Duncan, O.D., Sobel, M.E. 1987. Association and Heterogeneity: Structural Models of Similarities and Differences. pp. 146-84 in Sociological Methodology 1987, edited by C. C. Clogg. Washington, DC: American Sociological Association.
Rogosa, D. 1987. Casual [sic] Models Do Not Support Scientific Conclusions: A Comment in Support of Freedman. Journal of Educational Statistics 12:185-95.
Repudiating the Faustian bargain. Duncan O.D. … Rasch Measurement Transactions, 2000, 14:1 p.734
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