Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T17:33:15.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive causal models

Part of: Special processes Parametric inference

Published online by Cambridge University Press:  09 April 2009

Harri Kiiveri ,
T. P. Speed  and
J. B. Carlin
Harri Kiiveri
Affiliation:
Department of Mathematics University of Western AustraliaNedlands, W.A. 6009, Australia
T. P. Speed
Affiliation:
CSIRO Division of Mathematics and Statistics P.O. Box 1965, Canberra City ACT 2601, Australia
J. B. Carlin
Affiliation:
Department of Statistics Oxford Street Harvard UniversityCambridge, Massachusetts 02138, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The notion of a recursive causal graph is introduced, hopefully capturing the essential aspects of the path diagrams usually associated with recursive causal models. We describe the conditional independence constraints which such graphs are meant to embody and prove a theorem relating the fulfilment of these constraints by a probability distribution to a particular sort of factorisation. The relation of our results to the usual linear structural equations on the one hand, and to log-linear models, on the other, is also explained

Keywords

causal modelspath analysisconditional independencelog-linear models.

MSC classification

Secondary: 62F99: None of the above, but in this section 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 1 , February 1984 , pp. 30 - 52
Copyright
Copyright © Australian Mathematical Society 1984

References

Blalock, H. M. Jr, (1962), ‘Four-variable causal models and partial correlations’, Amer. J. Sociology 68, 182–194. Reprinted as Chapter 2 in Blalock (1971).CrossRefGoogle Scholar
Blalock, H. M. Jr, (1971), Causal models in the social sciences (Macmillan Press Ltd., London).Google Scholar
Boudon, R. (1965), ‘A method of linear causal analysis: dependence analysis’, Amer. Sociological Rev. 30, 365–374.CrossRefGoogle Scholar
Carlin, J. B. (1977), Causal models: an attempt at a unified approach (Honours thesis, Department of Mathematics, University of Western Australia).Google Scholar
Darroch, J. N., Lauritzen, S. L. and Speed, T. P. (1980), ‘Log-linear models for contingency tables and Markov fields over graphs’, Ann. Statist. 8, 522–539.CrossRefGoogle Scholar
Duncan, O. D. (1966), ‘Path analysis: sociological examples’, Amer. J. Sociology 72, 1–16. Reprinted as Chapter 7 in Blalock (1971).CrossRefGoogle Scholar
Duncan, O. D. (1975), Introduction to structural equation models (Academic Press, New York).Google Scholar
Fienberg, S. E. (1977), The analysis of cross classified categorical data (MIT Press, Cambridge, Massachusetts).Google Scholar
Goldberger, A. S. and Duncan, O. D. (1973), Structural equation models in the social sciences (Seminar Press, New York).Google Scholar
Goodman, L. A. (1972), ‘A general model for the analysis of surveys’, Amer. J. Sociology 77, 1035–1086.CrossRefGoogle Scholar
Goodman, L. A. (1973a), ‘The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach’, Biometrika 60, 179–192.CrossRefGoogle Scholar
Goodman, L. A. (1973b), ‘Causal analysis of data from panel studies and other kinds of surveys’, Amer. J. Sociology 78, 1135–1191.CrossRefGoogle Scholar
Goodman, L. A. (1974a), ‘Exploratory latent structure analysis using both identifiable and unidentifiable models’, Biometrika 61, 215–231.CrossRefGoogle Scholar
Goodman, L. A. (1974b), ‘The analysis of systems of qualitative variables when some of the variables are unobservable, Part I—a modified latent structure approach’, Amer. J. Sociology 79, 1179–1259.CrossRefGoogle Scholar
Heise, D. R. (1975), Causal analysis (John Wiley & Sons, New York).Google Scholar
Jöreskog, K. G. (1977), ‘Structural equation models in the social sciences: Specification, estimation and testing’, Applications of statistics, pp. 265–287, edited by Krishnaiah, P. R. (North-Holland Publishing Co.).Google Scholar
Kang, K. M. and Seneta, E. (1980), ‘Path analysis: an exposition’, Developments in statistics 3, pp. 217–246, edited by Krishnaiah, P. R. (Academic Press).Google Scholar
Kiiveri, H. (1982), A unified theory of causal models (Ph.D. thesis, in preparation).Google Scholar
Kiiveri, H. and Speed, T. P. (1982), ‘The structural analysis of multivariate data: a review’, Sociological Methodology, to appear.CrossRefGoogle Scholar
Moran, P. A. P. (1961), ‘Path coefficients reconsidered’, Austral. J. Statist. 3, 87–93.CrossRefGoogle Scholar
Simon, H. A. (1953), ‘Causal ordering and identifiability’, Studies in econometric method, Chapter 3, edited by William, C. Hood and Tjalling, C. Koupmans. Cowles Commission for Research in Economics (John Wiley & Sons, New York). Reprinted in Simon (1957).Google Scholar
Simon, H. A. (1954), ‘Spurious correlation: a causal interpretation’, J. Amer. Statist. Assoc. 49, 467–479. Reprinted in Simon (1957).Google Scholar
Speed, T. P. (1978), ‘Relations between models for spatial data, contingency tables and Markov fields on graphs’, Proceedings of the conference on spatial patterns and processes, edited by Tweedie, R. L., Supplement to Advances in Applied Probability.Google Scholar
Speed, T. P. (1978a), Graphical methods in the analysis of data (Lecture notes issued at the University of Copenhagen Institute of Mathematical Statistics, 111 pp.).Google Scholar
Speed, T. P. (1979), ‘A note on nearest-neighbour Gibbs and Markov probability’, Sankhyā Ser. A 41, 184–197.Google Scholar
Wermuth, N. (1980), ‘Linear recursive equations, covariance selection and path analysis’, J. Amer. Statist. Assoc. 75, 963–972.CrossRefGoogle Scholar
Wright, S. (1921), ‘Correlation and causation’, J. Agric. Research 20, 557–585.Google Scholar
Wright, S. (1934), ‘The method of path coefficients’, Ann. Math. Statist. 5, 161–215.CrossRefGoogle Scholar