A latent markov model for the analysis of longitudinal data collected in continuous time: States, durations, and transitions

Psychological Methods

Volumn 10, Issue 1, 2005, Pages 65-83

  Böckenholt, Ulf ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Item response theory; Latent markov model; Stochastic processes

Indexed keywords

ARTICLE; HUMAN; METHODOLOGY; PROBABILITY; PSYCHOLOGY; STATISTICS; TIME;

HUMANS; MARKOV CHAINS; PSYCHOLOGY; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 17444375651     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.10.1.65     Document Type: Article

References (65)

1. Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks, CA: Sage.
2. Bartholomew, D. J. (1982). Stochastic models for social processes (3rd ed.). Chichester, England: Wiley.
3. Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88, 588-606.
4. Bhattacharya, R. N., & Waymire, E. (1992). Stochastic processes with applications. New York: Wiley.
5. Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.
6. Böckenholt, U. (1999). Measuring change: Mixed Markov models for ordinal panel data. British Journal of Mathematical and Statistical Psychology, 52, 125-136.
7. Böckenholt, U., & Langeheine, R. (1996). Latent change in recurrent choice data. Psychometrika, 61, 285-301.
8. Bolger, N., Davis, A., & Rafaeli, E. (2003). Diary methods: Capturing life as it is lived. Annual Review of Psychology, 54, 579-616.
9. Claridge, G., & Davis, C. (2001). What's the use of neuroticism? Personality and Individual Differences, 31, 383-400.
10. Coleman, J. S. (1964). Models of change and response uncertainty. Englewood Cliffs, NJ: Prentice-Hall.
11. Coleman, J. S. (1981). Longitudinal data analysis. New York: Basic Books.
12. Collins, L. M., & Sayer, A. G. (Eds.). (2001). New methods for the analysis of change. Washington, DC: American Psychological Association.
13. Collins, L. M., & Wugalter, S. E. (1992). Latent class models for stage-sequential dynamic latent variables. Multivariate Behavioral Research, 27, 131-157.
14. Costa, P. T. (1987). Influence of the normal personality dimension of neuroticism on chest pain symptoms and coronary artery disease. American Journal of Cardiology, 60, 201-261.
15. Cox, D. R., & Lewis, P. A. W. (1978). The statistical analysis of series of events. London: Chapman & Hall.
16. Cox, D. R., & Miller, H. D. (1965). The theory of stochastic processes. London: Methuen.
17. Csikszentmihalyi, M., & Larson, R. (1992). Validity and reliability of the experience sampling method. The Journal of Nervous and Mental Disease, 175, 526-536.
18. Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects models for repeated measures data. Psychological Methods, 7, 41-63.
19. Eid, M., & Langeheine, R. (1999). Measuring consistency and occasion specificity with latent class models: A new model and its application to the measurement of affect. Psychological Methods, 4, 100-116.
20. Embretson, S. (1994). Applications of cognitive design systems to test development. In C. R. Reynolds (Ed.), Cognitive assessment: A multidisciplinary perspective (pp. 107-135). New York: Plenum.
21. Feng, Z. D., & McCulloch, C. E. (1996). Using Bootstrap likelihood ratios in finite mixture models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 58, 609-617.
22. Fischer, G. H., & Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of change. Psychometrika, 56, 637-651.
23. Goldberg, L. (1997). A broad-bandwidth, public domain, personality inventory measuring the lower-level facets of several five-factor models. Retrieved February 10, 2005, from http://www.ipip.ori.org/ipip/
24. Gunthert, K., Cohen, L. H., & Armeli, S. (1999). The role of neuroticism in daily stress and coping. Journal of Personality and Social Psychology, 77, 1087-1100.
25. Hedeker, D., & Gibbons, R. (1996). MIXOR: A computer program for mixed-effects ordinal regression analysis. Computer Methods and Programs in Biomedicine, 49, 157-176.
26. Hemenover, S. H. (2003). Individual differences in rate of affect change: Studies in affective chronometry. Journal of Personality and Social Psychology, 85, 121-131.
27. Hope, A. C. A. (1968). A simplified Monte Carlo significance procedure. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 30, 582-598.
28. Jennrich, R. I., & Bright, P. B. (1976). Fitting systems of linear differential equations using computer generated exact derivatives. Technometrics, 18, 385-392.
29. Kahneman, D., Diener, E., & Schwarz, N. (1999). Well-being: The foundations of hedonic psychology. New York: Russell Sage Foundation.
30. Kalbfleisch, J. D., & Lawless, J. F. (1985). The analysis of panel data under a Markov assumption. Journal of the American Statistical Association, 80, 863-871.
31. Katz, R. W. (1981). On some criteria for estimating the order of a Markov chain. Technometrics, 23, 243-249.
32. Kim, J.-S., & Böckenholt, U. (2000). Modeling stage-sequential change in ordered categorical responses. Psychological Methods, 5, 380-400.
33. Langeheine, R., Pannekoek, J., & van de Pol, F. (1996). Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods and Research, 24, 492-516.
34. Langeheine, R., Stern, E., & van de Pol, F. (1994). State mastery learning: Dynamic models for longitudinal data. Applied Psychological Measurement, 18, 277-291.
35. Langeheine, R., & van de Pol, F. (1990). A unifying framework for Markov modelling in discrete space and discrete time. Sociological Methods and Research, 18, 416-441.
36. Langeheine, R., & van de Pol, F. (2002). Latent Markov chains. In J. Hagenaars & A. L. McCutcheon (Eds.), Applied Latent Class Analysis (pp. 304-344). New York: Cambridge University Press.
37. Larsen, R. J. (1992). Neuroticism and selective encoding and recall of symptoms: Evidence from a combined concurrent retrospective study. Journal of Personality and Social Psychology, 62, 480-488.
38. Levinson, S. E., Rabiner, L. R., & Sondhi, M. M. (1983). An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition. Bell System Technical Journal, 62, 1035-1074.
39. Lindsey, J. K. (1999). Models for repeated measurements (2nd ed.). Oxford, England: Oxford University Press.
40. MacDonald, I. L., & Zucchini, W. (1997). Hidden Markov and other models for discrete-valued time series. London: Chapman & Hall.
41. Macready, G. B., & Dayton, C. M. (1994). Latent class models for longitudinal assessment of trait acquisition. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 245-273). Thousand Oaks, CA: Sage.
42. McArdle, J. J. (1987). Latent growth curve models within developmental structural equation models. Child Development, 58, 110-133.
43. McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). London: Chapman & Hall.
44. Meiser, T., & Ohrt, B. (1996). Modeling structure and chance in transitions: Mixed latent partial Markov-chain models. Journal of Educational and Behavioral Statistics, 21, 91-109.
45. Molenaar, P. C. M. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181-202.
46. Morgan, T. M., Aneshensel, C. S., & Clark, V. A. (1983). Parameter estimation for mover-stayer models: Analyzing depression over time. Sociological Methods & Research, 11, 345-366.
47. Norris, J. E. (1998). Markov chains. Cambridge, England: Cambridge University Press.
48. Prochaska, J. O., DiClemente, C. C., & Norcross, J. C. (1992). In search of how people change: Applications to addictive behaviors. American Psychologist, 47, 1102-1114.
49. Raftery, A. E. (1986). A note on Bayes factors for loglinear contingency table models with vague prior information. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 48, 249-250.
50. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models. Newbury Park, CA: Sage.
51. Robinson, M. D., & Clore, G. L. (2002). Belief and feeling: Evidence for an accessibility model of emotional self-report. Psychological Bulletin, 128, 934-960.
52. Samejima, F. (1969). Estimation of ability using a response pattern of graded scores. Psychometric Monograph (No. 17).
53. Samejima, F. (1997). Graded response model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 85-100). New York: Springer-Verlag.
54. SAS Institute. (2004), SAS/IML 9.1 user's guide Volumes 1 and 2. Cary, NC: SAS.
55. Schimmack, U. (1997). Das Berliner-Alltagssprachliche-Stimmungsinventar (BASTI): Ein Vorschlag zur kontentvaliden erfassung von Stimmungen [The Berlin Everyday Language Mood Inventory: Toward a content valid mood assessment]. Diagnostica, 43, 150-173.
56. Schimmack, U. (2003). Affect measurement in experience sampling research. Journal of Happiness Studies, 4, 79-106.
57. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-466.
58. Singer, B., & Spilerman, S. (1976). The representation of social processes by Markov models. American Journal of Sociology, 82, 1-54.
59. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis. New York: Oxford University Press.
60. Snijders, A. B., & Bosker, R. J. (1999). Multilevel analysis: An introduction to basic and advanced multilevel modeling. Thousand Oaks, CA: Sage.
61. Stone, A. A., Shiffman, S. S., & DeVries, M. W. (1999). Ecological momentary assessment. In D. Kahneman, E. Diener, & N. Schwarz (Eds.), Well-being: The foundations of hedonic psychology (pp. 26-39). New York: Russell Sage Foundation.
62. Vermunt, J. K., Langeheine, R., & Böckenholt, U. (1999). Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. Journal of Educational and Behavioral Statistics, 24, 179-207.
63. West, S. G., & Hepworth, J. T. (1991). Statistical issues in the study of temporal data: Daily experiences. Journal of Personality, 59, 609-662.
64. Wickens, T. (1982). Models for behavior. San Francisco: Freeman.
65. Wilson, M. (1989). Saltus: A psychometric model of discontinuity in cognitive development. Psychological Bulletin, 105, 276-289.