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The analysis of change, Newton's law of gravity and association models

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  • Mark de Rooij

Abstract

Summary. Newton's law of gravity states that the force between two objects in the universe is equal to the product of the masses of the two objects divided by the square of the distance between the two objects. In the first part of the paper it is shown that a model with a ‘law‐of‐gravity’ interpretation applies well to the analysis of longitudinal categorical data where the number of people changing their behaviour or choice from one category to another is a measure of force and the goal is to obtain estimates of mass for the two categories and an estimate of the distance between them. To provide a better description of the data dynamic masses and dynamic positions are introduced. It is shown that this generalized law of gravity is equivalent to Goodman's RC(M) association model. In the second part of the paper the model is generalized to two kinds of three‐way data. The first case is when there are multiple two‐way tables and in the second case we have change over three points of time. Conditional and partial association models are related to three‐way distance models, like the INDSCAL model, and triadic distance models respectively.

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  • Mark de Rooij, 2008. "The analysis of change, Newton's law of gravity and association models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 137-157, January.
    • Handle: RePEc:bla:jorssa:v:171:y:2008:i:1:p:137-157
    DOI: 10.1111/j.1467-985X.2007.00498.x
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    References listed on IDEAS

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    1. Mark De Rooij, 2001. "Distance Association Models for the Analysis of Repeated Transition Frequency Tables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(2), pages 157-181, July.
    2. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    3. PETER G. M. van der HEIJDEN & AB MOOIJAART, 1995. "Some New Log-Bilinear Models for the Analysis of Asymmetry in a Square Contingency Table," Sociological Methods & Research, , vol. 24(1), pages 7-29, August.
    4. A. G. Constantine & J. C. Gower, 1978. "Graphical Representation of Asymmetric Matrices," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 297-304, November.
    5. Raymond Sin-Kwok Wong, 2001. "Multidimensional Association Models," Sociological Methods & Research, , vol. 30(2), pages 197-240, November.
    6. Mark Rooij & Willem Heiser, 2005. "Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 99-122, March.
    7. John Daws, 1996. "The analysis of free-sorting data: Beyond pairwise cooccurrences," Journal of Classification, Springer;The Classification Society, vol. 13(1), pages 57-80, March.
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    Cited by:

    1. Fithian, William & Josse, Julie, 2017. "Multiple correspondence analysis and the multilogit bilinear model," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 87-102.

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