Fuzzy clusterwise growth curve models via generalized estimating equations: An application to the antisocial behavior of children

Multivariate Behavioral Research

Volumn 42, Issue 2, 2007, Pages 233-259

  Hwang, Heungsun ^a   Takane, Yoshio ^a   DeSarbo, Wayne S ^b  

^a MCGILL UNIVERSITY   (Canada)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547417989     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1080/00273170701360332     Document Type: Article

References (72)

1. Arabie, P., Carroll, J. D., DeSarbo, W. S., & Wind, J. (1981). Overlapping clustering: A new method for product positioning. Journal of Marketing Research, 18, 310-317.
2. Arabie, P., & Hubert, L. (1994). Cluster analysis in marketing research. In R. P. Bagozzi (Ed.), Advanced methods of marketing research (pp. 160-189). Oxford: Blackwell.
3. Bagozzi, R. P. (1982). A field investigation of causal relations among cognition, affect, intensions, and behavior. Journal of Marketing Research, 19, 562-584.
4. Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for over-extraction of latent trajectory classes. Psychological Methods, 8, 338-363.
5. Bezdek, J. C. (1974a). Numerical taxonomy with fuzzy sets. Journal of Mathematical Biology, 1, 57-71.
6. Bezdek, J. C. (1974b). Cluster validity with fuzzy set. Journal of Cybernetics, 3, 58-72.
7. Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press.
8. Bezdek, J. C., Coray, C., Gunderson, R., & Watson, J. (1981). Detection and characteristics of cluster substructure. II. Fuzzy c-varieties and convex combinations thereof. SIAM Journal on Applied Mathematics, 40, 358-372.
9. Biesanz, J. C., Deeb-Sossa, N., Papadakis, A. A., Bollen, K. A., & Curran, P. J. (2004). The role of coding time in estimating and interpreting growth curve models. Psychological Methods, 9, 30-52.
10. Böckenholt, U., & Takane, Y. (1994). Linear constraints in correspondence analysis. In M. J. Greenacre & J. Blasius (Eds.), Correspondence analysis in social sciences (pp. 112-127). London: Academic Press.
11. Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models: Applications and data analysis methods. Newbury Park: Sage Publications.
12. Cheong, Y. F., Fotiu, R. P., & Raudenbush, S. W. (2001). Efficiency and robustness of alternative estimators for two- and three-level models: The case of NAEP. Journal of Educational and Behavioral Statistics, 26, 411-429.
13. Curran, P. J. (1998). Introduction to hierarchical linear models of individual growth: An applied example using the SAS data system. Paper presented at the first international institute on developmental science, University of North Carolina, Chapel Hill.
14. Curran, P. J., & Bollen, K. A. (1999). A hybrid latent trajectory model of stability and change: Applications in developmental psychology. Paper presented at the biennial meeting of the society for research on child development, Albuquerque, New Mexico.
15. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM-algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
16. DeSarbo, W. S., & Cron, W. L. (1988). A conditional mixture maximum likelihood methodology for clusterwise linear regression. Journal of Classification, 5, 249-289.
17. DeSarbo, W. S., Grewal, R., & Hwang, H. (2006). A clusterwise bilinear multidimensional scaling methodology for marketing research: An application to the estimation of strategic groups. Unpublished manuscript.
18. DeSarbo, W. S., Wedel, M., Vriens, M., & Ramaswamy, V. (1992). Latent class metric conjoint analysis. Marketing Letters, 3, 273-288.
19. Diggle, P. J., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data. Oxford: Oxford University Press.
20. Duncan, T. E., Duncan, S. C., Hops, H., & Stoolmiller, M. (1995). An analysis of the relationship between parent and adolescent marijuana use via generalized estimating equation methodology. Multivariate Behavioral Research, 30, 317-339.
21. Dunn, J. C. (1974). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Journal of Cybernetics, 3, 32-57.
22. th ed. London: Arnold Press.
23. Ghisletta, P., & Spini, D. (2004). An introduction to generalized estimating equations and an application to assess selectivity effects in a longitudinal study on very old individuals. Journal of Educational and Behavioral Statistics, 29, 412-437.
24. Goldstein, H. I. (1987). Multilevel models in educational and social research. London: Oxford University.
25. Gordon, A. D. (1999). Classification. London: Chapman & Hall/CRC.
26. Grizzle, J. E., & Allen, D. M. (1969). Analysis of growth and dose response curves. Biometrics, 25, 357-381.
27. Guttman, L. A. (1954). A new approach to factor analysis: The radix. In P. F. Lazarsfeld (Ed.), Mathematical thinking in the social sciences (pp. 3-22). New York: Columbia University Press.
28. Hathaway, R. J., & Bezdek, J. C. (1993). Switching regression models and fuzzy clutering. IEEE Transactions on Fuzzy Systems, 1, 195-204.
29. Hipp J. P., & Bauer, D. J. (2006). Local solutions in the estimation of growth mixture models. Psychological Methods, 11, 36-53.
30. Hong, S., Mitchell, S., & Harshman, R. A. (2006). Bootstrap scree tests: A Monte Carlo simulation and applications to published data. British Journal of Mathematical and Statistical Psychology, 59, 35-57.
31. Hruschka, H. (1986). Market definition and segmentation using fuzzy clustering methods. International Journal of Research in Marketing, 3, 117-134.
32. Hwang, H., & Takane, Y. (2004). A multivariate reduced-rank growth curve model with unbalanced data. Psychometrika, 69, 65-79.
33. Hwang, H., & Takane, Y. (2005). Estimation of growth curve models with structured error covariances by generalized estimating equations. Behaviormetrika, 32, 141-153.
34. Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997). Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16, 39-59.
35. Jöreskog, K. G. (1970). Estimation and testing of simplex models. British Journal of Mathematical and Statistical Psychology, 23, 121-145.
36. Kamakura, W. A., Kim, B., & Lee, J. (1996). Modeling preference and structural heterogeneity in consumer choice. Marketing Science, 15, 152-172.
37. Khatri, C. G. (1988). Robustness study for a linear growth model. Journal of Multivariate Analysis, 24, 66-87.
38. Khatri, C. G. (1966). A note on a MANOVA model applied to problems in growth curves. Annals of the Institute of Statistical Mathematics, 18, 75-86.
39. Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963-974.
40. Li, F., Duncan, T. E., & Duncan, S. C. (2001). Latent growth modeling of longitudinal data: A finite growth mixture modeling approach. Structural Equation Modeling, 8, 493-530.
41. Li, F., Maddalozzo, G. F., Harmer, P., & Duncan, T. E. (1998). Analysis of longitudinal data of repeated observations using generalized estimating equations methodology. Measurement in Physical Education and Exercise Science, 2, 93-113.
42. Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
43. MacCallum, R. C., Kim, C., Malarkey, W. B., & Kiecolt-Glaser, J. K. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32, 215-253.
44. McBratney, A. B., & Moore, A. W. (1985). Application of fuzzy sets to climatic classification. Agricultural and Forest Meteorology, 35, 165-185.
45. McCullagh, P. (1983). Quasi-likelihood functions. The Annals of Statistics, 11, 59-67.
46. McCullagh, P., & Neider, J. A. (1989). Generalized linear models. London: Chapman & Hall.
47. McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: John Wiley & Sons.
48. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
49. Moffitt, T. E. (1993). Adolescent-limited and life-course-persistent antisocial behavior: A developmental taxonomy. Psychological Review, 100, 674-701.
50. Mulaik, S. A. (1972). The foundations of factor analysis. New York: McGraw-Hill.
51. Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585.
52. Muthén, B. O., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.
53. Nagin, D. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4, 139-157.
54. Okeke, F., & Karnieli, A. (2006). Linear mixture model approach for selecting fuzzy exponent value in fuzzy c-means algorithm. Ecological Informatics, 1, 117-124.
55. Pan, W. (2001). Akaike's information criterion in generalized estimating equations. Biometrics, 57, 120-125.
56. Potthoff, R. F., & Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313-326.
57. Raudenbush, S. W. (1995). Reexaming, reaffirming, and improving application of hierarchical models. Journal of Educational and Behavioral Statistics, 20, 210-220.
58. Raudenbush, S. W. (2001). Comparing personal trajectories and drawing causal inferences from longitudinal data. Annual Review of Psychology, 52, 501-525.
59. Rao, C. R. (1965). The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika, 52, 447-458.
60. Reinsel, G. C., & Velu, R. P. (1998). Multivariate reduced-rank regression. Theory and application. New York: Springer.
61. Roubens, M. (1982). Fuzzy clustering algorithms and their cluster validity. European Journal of Operational Research, 10, 294-301.
62. Takane, Y., & Hunter, M. A. (2001). Constrained principal component analysis: A comprehensive theory. Applicable Algebra in Engineering, Communication, and Computing, 12, 391-419.
63. Takane, Y., Yanai, H., & Mayekawa, S. (1991). Relationships among several methods of linearly constrained correspondence analysis. Psychometrika, 56, 667-684.
64. Tucker, L. R. (1951). A method for synthesis of factor analysis studies (Personnel Research Section Report No. 984). Washington, D.C.: U.S. Department of the Army.
65. von Rosen, D. (1991). The growth curve model: A review. Communications in Statistics: Theory and Methods, 9, 2791-2822.
66. Vonesh, E. F., & Carter, R. L. (1987). Efficient inference for random-coefficient growth curve models with unbalanced data. Biometrics, 43, 617-628.
67. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439-447.
68. Wedel, M., & Kamakura, W. A. (1998). Market segmentation: Conceptual and methodological foundations. Boston: Kluwer Academic Publishers.
69. Wedel, M., & Steenkamp, J.-B. E. M. (1989). Fuzzy clusterwise regression approach to benefit segmentation. International Journal of Research in Marketing, 6, 241-258.
70. Wedel, M., & Steenkamp, J.-B. E. M. (1991). A clusterwise regression method for simultaneous fuzzy market structuring and benefit segmentation. Journal of Marketing Research, 28, 385-396.
71. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353.
72. Zeger, S. L., & Liang, K. Y. (1986). The analysis of discrete and continuous longitudinal data. Biometrics, 42, 121-130.