Rule following and rule use in the balance-scale task

Cognition

Volumn 103, Issue 3, 2007, Pages 460-472

  Shultz, Thomas R ^a   Takane, Yoshio ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Addition rule; Balance scale; Boundary estimates; Connectionism; Goodness of fit tests; Latent class analysis; Local independence assumption; Rule learning; Rule assessment method; Torque rule

Indexed keywords

ARTICLE; BALANCE SCALE TASK; COGNITION; COGNITIVE DEVELOPMENT; MODEL; PRIORITY JOURNAL; RATING SCALE; SIMULATION;

EID: 34047132715     PISSN: 00100277     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cognition.2006.12.004     Document Type: Note

References (45)

1. Aitkin M., Anderson D., and Hinde J. Statistical modelling of data on teaching styles. Journal of the Royal Statistical Society B, Series A 144 (1981) 419-461
2. Bartholomew D.J. Latent variable models and factor analysis (1987), Charles Griffin and Company, London
3. p contingency tables. British Journal of Mathematical and Statistical Psychology 55 (2002) 1-15
4. Boom J., Hoijtink H., and Kunnen S. Rules in the balance: Classes, strategies, or rules for the balance scale task. Cognitive Development 16 (2001) 717-735
5. Buckingham D., and Shultz T.R. The developmental course of distance, time, and velocity concepts: A generative connectionist model. Journal of Cognition and Development 1 (2000) 305-345
6. Cressie N., and Read T.R.C. Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society B 46 (1984) 440-464
7. Dijkstra T.K. On statistical inference with parameter estimates on the boundary of the parameter space. British Journal of Mathematical and Statistical Psychology 45 (1992) 289-309
8. Ferretti R.P., and Butterfield E.C. Are children's rule-assessment classifications invariant across instances of problem types?. Child Development 57 (1986) 1419-1428
9. Ferretti R.P., Butterfield E.C., Cahn A., and Kerkman D. The classification of children's knowledge: Development on the balance-scale and inclined-plane tasks. Journal of Experimental Child Psychology 9 (1985) 131-160
10. Hagenaars J.A. Categorical longitudinal data (1990), Sage, Newbury Park, CA
11. Hoijtink H. Constrained latent class analysis using Gibbs sampler and posterior predictive p-values: Applications to educational testing. Statistics Sinica 8 (1998) 691-711
12. Jansen B.R.J., and van der Maas H.L.J. Statistical test of the rule assessment methodology by latent class analysis. Developmental Review 17 (1997) 321-357
13. Jansen B.R.J., and van der Maas H.L.J. The development of children's rule use on the balance scale task. Journal of Experimental Child Psychology 81 (2002) 383-416
14. Langeheine R., Pannekoek J., and van de Pol F. Bootstrap goodness-of-fit measures in categorical data analysis. Sociological Methods and Research 24 (1996) 493-516
15. Langley P. A general theory of discrimination learning. In: Klahr D., Langley P., and Neches R. (Eds). Production systems models of learning and development (1987), MIT Press, Cambridge, MA 99-161
16. Mareschal D., and Shultz T.R. Development of children's seriation: A connectionist approach. Connection Science 11 (1999) 149-186
17. McClelland J.L. Parallel distributed processing: Implications for cognition and development. In: Morris R.G.M. (Ed). Parallel distributed processing: Implications for psychology and neurobiology (1989), Oxford University Press, Oxford 8-45
18. McCutcheon A.L. Latent class analysis (1987), Sage, Newbury Park, CA
19. Newell A. Unified theories of cognition (1990), Harvard University Press, Cambridge, MA
20. Normandeau S., Larivee S., Roulin J.L., and Longeot F. The balance-scale dilemma: Either the subject or the experimenter muddles through. Journal of Genetic Psychology 150 (1989) 237-250
21. Oshima-Takane Y., Takane Y., and Shultz T.R. The learning of first and second pronouns in English: Network models and analysis. Journal of Child Language 26 (1999) 545-575
22. Qu Y., Tan M., and Kutner M.H. Random effects model in latent class analysis for evaluating accuracy of diagnostic tests. Biometrics 52 (1996) 797-810
23. Quinlan, p., van der Mass, H., Jansen, B., Booij, O., & Rendell, M. (this issue). Re-thinking stages of cognitive development: An appraisal of connectionist models of the balance scale task. Cognition, doi:10.1016/j.cognition.2006.02.004.
24. Reiser M., and Lin Y. A goodness-of-fit test for the latent class model when expected frequencies are small. In: Sobel M., and Decker M. (Eds). Sociological methodology (1999), Blackwell, Boston 81-111
25. Schmidt W.C., and Ling C.X. A decision-tree model of balance scale development. Machine Learning 24 (1996) 203-229
26. Schmidt, W. C., & Shultz, T. R. (1991). A replication of McClelland's balance scale model (No. 91-10-18). Montreal: McGill Cognitive Science Centre, McGill University.
27. Shapiro A. Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints. Biometrika 72 (1985) 133-144
28. Shapiro A. Toward a unified theory of inequality constrained testing in multivariate analysis. International Statistical Review 56 (1988) 49-62
29. Shultz T.R. A computational analysis of conservation. Developmental Science 1 (1998) 103-126
30. Shultz T.R. Computational developmental psychology (2003), MIT Press, Cambridge, MA
31. Shultz T.R. Constructive learning in the modeling of psychological development. In: Munakata Y., and Johnson M.H. (Eds). Processes of change in brain and cognitive development: Attention and performance XXI (2006), Oxford University Press, Oxford 61-86
32. Shultz T.R., and Bale A.C. Neural network simulation of infant familiarization to artificial sentences: Rule-like behavior without explicit rules and variables. Infancy 2 (2001) 501-536
33. Shultz T.R., Buckingham D., and Oshima-Takane Y. A connectionist model of the learning of personal pronouns in English. In: Hanson S.J., Petsche T., Kearns M., and Rivest R.L. (Eds). Computational learning theory and natural learning systems: Intersection between theory and experiment Vol. 2 (1994), MIT Press, Cambridge, MA 347-362
34. Shultz T.R., and Cohen L.B. Modeling age differences in infant category learning. Infancy 5 (2004) 153-171
35. Shultz T.R., and Gerken L.A. A model of infant learning of word stress. Proceedings of the twenty-seventh annual conference of the cognitive science society (2005), Erlbaum, Mahwah, NJ 2015-2020
36. Shultz T.R., Mareschal D., and Schmidt W.C. Modeling cognitive development on balance scale phenomena. Machine Learning 16 (1994) 57-86
37. Shultz T.R., and Rivest F. Knowledge-based cascade-correlation: Using knowledge to speed learning. Connection Science 13 (2001) 1-30
38. Shultz T.R., and Vogel A. A connectionist model of the development of transitivity. Proceedings of the twenty-sixth annual conference of the cognitive science society (2004), Erlbaum, Mahwah, NJ 1243-1248
39. Siegler R.S., and Chen Z. Development of rules and strategies: Balancing the old and the new. Journal of Experimental Child Psychology 81 (2002) 446-457
40. Sirois S., and Shultz T.R. Neural network modeling of developmental effects in discrimination shifts. Journal of Experimental Child Psychology 71 (1998) 235-274
41. Sun R., Slusarz P., and Terry C. The interaction of the explicit and the implicit in skill learning: A dual-process approach. Psychological Review 112 (2005) 159-192
42. Thivierge, J. P., Dandurand, F., & Shultz, T. R. (2004). Transferring domain rules in a constructive network: Introducing RBCC. In Proceedings of the IEEE international joint conference on neural networks (pp. 1403-1409).
43. van Rijn H., van Someren M., and van der Maas H. Modeling developmental transitions on the balance scale task. Cognitive Science 27 (2003) 227-257
44. Vermunt J.K. LEM: A general program for the analysis of categorical data (1997), Department of Methodology and Statistics, Tilburg University, Netherlands
45. Wickens T.D. Multiway contingency tables analysis for the social sciences (1989), Erlbaum, Hillsdale, NJ