Bridges between deterministic and probabilistic models for binary data

Statistical Methodology

Volumn 7, Issue 3, 2010, Pages 187-209

  Gelman, Andrew ^a   Leenen, Iwin ^b   Mechelen, Iven Van ^b   Boeck, Paul De ^b   Poblome, Jeroen ^b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Binary data; Deterministic models; Guttman scaling; Implicit stochastic models; Metropolis Hastings algorithm; Parallelogram model; Psychometrics

Indexed keywords

EID: 77950916816     PISSN: 15723127     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.stamet.2009.08.005     Document Type: Article

References (35)

1. Agrawal R., Imielinski T., and Swami A.N. Mining association rules between sets of items in large databases. SIGMOD 22 (1993) 207-216
2. Andrich D. Hyperbolic cosine latent trait models for unfolding direct responses and pairwise preferences. Applied Psychological Measurement 19 (1995) 269-290
3. Arabie P., and Hubert L. Combinatorial data analysis. Annual Review of Psychology 43 (1992) 169-203
4. Clark P., and Niblett T. The CN2 induction algorithm. Machine Learning 3 (1989) 261-283
5. Coombs C.H. A Theory of Data (1964), Wiley, New York
6. Degeest R., Ottenburgs R., Viaene W., Kucha H., Laduron D., Bocquet A., and Waelkens M. Characterization of the common wares manufactured in Roman Sagalassos. An overview. In: Waelkens M., and Poblome J. (Eds). Sagalassos IV. Report on the Survey and Excavation Campaigns of 1994 and 1995. Acta Archaeologica Lovaniensia Monographiae, vol. 9 (1997), University Press, Leuven 519-531
7. In: Fischer G.H., and Molenaar I.W. (Eds). Rasch Models: Foundations, Recent Developments, and Applications (1995), Springer, New York
8. Fulkerson D.R., and Gross O.A. Incidence matrices and interval graphs. Pacific Journal of Mathematics 15 (1965) 835-855
9. Gelman A., and Bois F.Y. How can statistical theory help with statistical practice? Example of a Bayesian analysis in toxicokinetics. In: Minder C.E., and Friedl H. (Eds). Good Statistical Practice. Proceedings of the 12th International Workshop on Statistical Modelling (1997), Austrian Statistical Society, Wien 61-70
10. Gelman A., Carlin J.B., Stern H.S., and Rubin D.B. Bayesian Data Analysis (1995), Chapman and Hall, London
11. Gelman A., Meng X.L., and Stern H.S. Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Statistica Sinica 6 (1996) 733-807
12. Gelman A., and Rubin D.B. Inference from iterative simulation using multiple sequences (with discussion). Statistical Science 7 (1992) 457-511
13. Ghosh S.P. File organization: the consecutive retrieval property. Communication of the Association for Computing Machinery 9 (1972) 802-808
14. In: Gilks W.R., Richardson S., and Spiegelhalter D. (Eds). Practical Markov Chain Monte Carlo (1996), Chapman and Hall, London
15. Goldmann K. Some archaeological criteria for chronological seriation. In: Hodson F.R., Kendall D.G., and Ta ̌utu P. (Eds). Mathematics in the Archaeological and Historical Sciences: Proceedings of the Anglo-romanian Conference (1971), University Press, Edinburgh 202-208
16. Goodman L.A. Some statistical methods for scalogram analysis. Psychometrika 24 (1959) 29-43
17. Goodman L.A. A new model for scaling response patterns: An application of the quasi-independence concept. Journal of the American Statistical Association 70 (1975) 755-768
18. Guttman L. The basis for scalogram analysis. In: Stouffer S.A., et al. (Ed). Measurement and Prediction (1950), Princeton University Press, Princeton
19. Hoffman R.J. On testing a Guttman scale for significance. Educational and Psychological Measurement 39 (1979) 297-301
20. Hoijtink H. A latent trait model for dichotomous choice data. Psychometrika 55 (1990) 641-656
21. Kendall D.G. Incidence matrices, interval graphs and seriation in archaeology. Pacific Journal of Mathematics 28 (1969) 565-570
22. Kotsiantis S., and Kanellopoulos D. Association rules mining: A recent overview. GESTS International Transactions on Computer Science and Engineering 32 (2006) 71-82
23. I. Leenen, I. Van Mechelen, A conjunctive parallelogram model for pick any/n data. 1999. Manuscript submitted for publication
24. I. Leenen, I. Van Mechelen, P. De Boeck, Models for ordinal hierarchical classes analysis. 1999. Manuscript submitted for publication
25. I. Leenen, I. Van Mechelen, A. Gelman, Bayesian probabilistic extensions of a deterministic classification model. Computational Statistics (2000) (in press)
26. Mitchell S., and Waelkens M. Cremna and Sagalassos 1987. Anatolian Studies 38 (1988) 53-64
27. Poblome J. Production and distribution of Sagalassos red slip ware. A dialogue with the Roman economy. In: Herfort-Koch M., Mandel U., and Schädler U. (Eds). Hellenistische und kaiserzeitliche Keramik des östlichen Mittelmeergebietes (1996), Imbescheidt KG, Frankfurt am Main 75-103
28. Poblome J. Sagalassos Red Slip Ware. Typology and Chronology. Studies in Eastern Mediterranean Archaeology, vol. 2 (1999), Brepols, Turnhout
29. Poblome J., Viaene W., Kucha H., Waelkens M., Laduron D., and Depuydt F. The clay raw materials of Sagalassos red slip ware. A chronological evaluation. In: Waelkens M., and Poblome J. (Eds). Sagalassos IV. Report on the Survey and Excavation Campaigns of 1994 and 1995. Acta Archaeologica Lovaniensia Monographiae, vol. 9 (1997), University Press, Leuven 507-518
30. Proctor C.H. A probabilistic formulation and statistical analysis of Guttman scaling. Psychometrika 35 (1970) 73-78
31. Rubin D.B. Bayesianly justifiable and relevant frequency calculations for the applied statistician. Annals of Statistics 12 (1984) 1151-1172
32. Rubin D.B., and Stern H.S. Testing in latent class models using a posterior predictive check distribution. In: von Eye A., and Clogg C. (Eds). Latent Variable Analysis: Applications for Developmental Research (1994), Sage, Thousand Oaks, Calif. 420-438
33. Torgerson W.S. Theory and Methods of Scaling (1962), Wiley, New York
34. Van Mechelen I., and Van Damme G. A latent criteria model for choice data. Acta Psychologica 87 (1994) 85-94
35. Waelkens M., and the Sagalassos team. Interdisciplinarity in classical archaeology. A case study: The sagalassos archaeological research project (southwest Turkey). In: Waelkens M., and Poblome J. (Eds). Sagalassos IV. Report on the Survey and Excavation Campaigns of 1994 and 1995. Acta Archaeologica Lovaniensia Monographiae, vol. 9 (1997), University Press, Leuven 225-252