Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates

Journal of Educational and Behavioral Statistics

Volumn 24, Issue 2, 1999, Pages 179-207

  Vermunt, Jeroen K ^b   Langeheine, Rolf ^b   Bockenholt, Ulf ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b NONE

Author keywords

Categorical data; EM algorithm; Latent class analysis; Latent Markov models; Log linear models; Logit models; Measurement error; Modified lisrel approach; Modified path analysis approach; Panel analysis; Time varying covariates

Indexed keywords

EID: 0033419512     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986024002179     Document Type: Article

References (61)

1. Agresti, A. (1990). Categorical data analysis. New York: Wiley.
2. Baker, S. G., and Laird, N. M. (1988). Regression analysis for categorical variables with out-come subject to nonignorable response. Journal of the American Statistical Association, 83, 62-69.
3. Bartholomew, D. J. (1987). Latent variable models and factor analysis. London: Griffin.
4. Bassi, F., Croon, M., Hagenaars, J., and Vermunt, J. (1999). Estimating true changes when categorical panel data are affected by uncorrelated and correlated classification errors: an application to unemployment data. Unpublished manuscript, University of Tilburg.
5. Böckenholt, U., and Langeheine, R. (1996). Latent change in recurrent choice data. Psychometrika, 61, 285-302.
6. Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, Mass.: MIT Press.
7. Clogg, C. C. (1977). Unrestricted and restricted maximum likelihood latent structure analysis: A manual for users. University Park; PA: Working Paper 1977-09, Population Issues Research Center.
8. Clogg, C. C., and Goodman, L. A. (1984). Latent structure analysis of a set of multidimensional contingency tables. Journal of the American Statistical Association, 79, 762-771.
9. Clogg, C. C., Eliason, S. R., and Grego, J. M. (1990). Models for the analysis of change in discrete variables. In A. Von Eye (Ed.), Statistical methods in longitudinal research, Vol. II. (pp. 409-441). Boston: Academic Press.
10. Collins, L. M., and Wugalter, S. E. (1992). Latent class models for stage-sequential dynamic latent variables. Multivariate Behavioral Research, 27, 131-157.
11. Collins, L. M., Fidler, P. L., Wugalter, S. E., and Long, D. (1993). Goodness-of-fit testing for latent class models. Multivariate Behavioral Research, 28, 375-389.
12. Dayton, C. M., and Macready, G. B. (1988). Concomitant-variable latent-class models. Journal of the American Statistical Association, 83, 173-178.
13. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motiviation and self-determination in human behavior. New York: Plenum.
14. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Ser. B., 39, 1-38.
15. Fay, R. E. (1986). Causal models for patterns of nonresponse. Journal of the American Statistical Association, 81, 354-365.
16. Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data. Journal of the American Statistical Association, 87, 476-486.
17. Fuchs, C. (1982). Maximum likelihood estimation and model selection in contingency tables with missing data. Journal of the American Statistical Association, 77, 237-250.
18. Gardner, P. L. (1985). Students' attitudes to science and technology: An international overview. In M. Lehrke, L. Hoffmann, and P. L. Gardner (Eds.), Interests in science and technology education (pp. 15-34). Kiel: IPN.
19. Goodman, L. A. (1972). A modified multiple regression approach for the analysis of dichotomous variables. American Sociological Review, 37, 28-46.
20. Goodman, L. A. (1973). The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach. Biometrika, 60, 179-192.
21. Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215-231.
22. Goodman, L. A. (1979). Simple models for the analysis of association in cross-classifications having ordered categories. Journal of the American Statistical Association, 74, 537-552.
23. Haberman, S. J. (1977). Log-linear models and frequency tables with small expected cell counts. Annals of Statistics, 5, 1148-1169.
24. Haberman, S. J. (1978). Analysis of qualitative data, Vol. 1, Introductory topics. New York: Academic Press.
25. Haberman, S. J. (1979). Analysis of qualitative data, Vol. 2, New developments. New York: Academic Press.
26. Hagenaars, J. A. (1990). Categorical longitudinal data: Loglinear panel, trend and cohort analysis. Newbury Park: Sage.
27. Hagenaars, J. A. (1992). Exemplifying longitudinal loglinear analysis with latent variables. In P G. M. Van der Heijden, W. Jansen, B. Francis, and G. U. H. Seeber (Eds.), Statistical modelling, (pp. 105-120). Amsterdam: Elsevier Science Publishers B.V.
28. Hagenaars, J. A. (1993). Loglinear models with latent variables. Newbury Park: CA: Sage.
29. Häussler, P., and Hoffmann, L. (1995). Physikunterricht - an den Interessen von Mädchen und Jungen orientiert. Unterrichtswissenschaft, 23, 107-126.
30. Heinen, A. (1993). Discrete latent variable models Tilburg: Tilburg University Press.
31. Hoffman, L., and Lehrke, M. (1986). Eine Untersuchung über Schülerinteressen an Physik und Technik. Zeitschrift für Pädagogik, 32, 189-204.
32. Hoffmann, L., Lehrke, M., and Todt, E. (1985). Development and changes in pupils' interests in physics (grade 5 to 10): Design of a longitudinal study. In M. Lehrke, L. Hoffmann, and P. L. Gardner (Eds.), Interests in science and technology education (pp. 71-80). Kiel: IPN.
33. Kelton, C. M. L., and Smith, M. A. (1991). Statistical inference in nonstationary Markov models with embedded explanatory variables. Journal of Statistical Computing and Simulation, 38, 25-44.
34. Langeheine, R. (1991). Latente Markov-Modelle zur Evaluation von Stufentheorien der Entwicklung. Empirische Pädagogik, 5, 169-189.
35. Langeheine, R. (1994) Latent variables Markov models. In A. von Eye and C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 373-395). Thousand Oaks: Sage.
36. Langeheine, R., Pannekoek, J., and Van de Pol, F. (1996). Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods and Research, 24, 492-516.
37. Langeheine, R., and Van de Pol, F. (1993). Multiple indicator Markov models. In R. Steyer, K. F. Wender, and K. F. Widaman (Eds.), Proceedings of the 7th European Meeting of the Psychometric Society in Trier (pp. 248-252). Stuttgart: Fischer.
38. Langeheine, R., and Van de Pol (1994). Discrete-time mixed Markov latent class models. In A. Dale and R. B. Davies, (Eds.) Analyzing social and political change: A casebook of methods (pp. 170-197). London: Sage.
39. Lazarsfeld, P. F., and Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mill.
40. Little, R. J. A. (1982). Models for nonresponse in sample surveys. Journal of the American Statistical Association, 77, 237-250.
41. Little, R. J. A. (1985). Nonresponse adjustments in longitudinal surveys: Models for categorical data. Bulletin of the International Statistical Institute, 15, 1-15.
42. Little, R. J. A., and Rubin, D. B. (1987). Statistical analysis with missing data. New York: Wiley.
43. Meng, X. L., and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267-278.
44. Mooijaart, A., and Van der Heijden, P. G. M. (1992). The EM algorithm for latent class models with constraints. Psychometrika, 57, 261-271.
45. Muenz, L. R., and Rubinstein, L. V. (1985). Markov models for covariate dependence of binary sequences. Biometrics, 41, 91-101.
46. Omerod, M. B., and Duckworth, D. (1975). Pupils attitudes to science. A review of research. Windsor: NFER.
47. Poulsen, C. A. (1982). Latent structure analysis with choice modeling applications. Aarhus: Aarhus School of Business Administration and Economics.
48. Rindskopf, D. (1992). A general approach to categorical data analysis with missing data, using generalized linear models with composite links. Psychometrika, 57, 29-42.
49. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581-592.
50. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
51. Spilerman, D. (1972). The analysis of mobility processes by the introduction of independent variables into a Markov chain. American Sociological Review, 37, 277-294.
52. Van de Pol, F., and De Leeuw, J. (1986). A latent Markov model to correct for measurement error. Sociological Methods and Research, 15, 118-141.
53. Van de Pol, F., and Langeheine, R. (1990). Mixed Markov latent class models. In C. C. Clogg (Ed.), Sociological Methodology 1990 (pp. 213-247). Oxford: Blackwell.
54. Van de Pol, F., Langeheine, R., and De Jong, W. (1991). PANMARK user manual: Panel analysis using MARKov chains. Voorburg: Netherlands Central Bureau of Statistics.
55. Van der Heijden, P. G. M., Mooijaart, A., and De Leeuw, J. (1992). Constraint latent budget analysis. In P. Marsden (Ed.), Sociological Methodology 1992 (pp. 279-320). Oxford: Blackwell.
56. Vermunt, J. K. (1993). lem: Log-linear and event history analysis with missing data using the EM algorithm. WORC PAPER 93.09.015/7, Tilburg University.
57. Vermunt, J. K. (1996a). Causal log-linear modeling with latent variables and missing data. In U. Engel, and J. Reinecke (Eds.), Analysis of change: Advanced techniques in panel data analysis (pp. 35-60). Berlin: de Gruyter.
58. Vermunt, J. K. (1996b). Log-linear event history analysis: A general approach with missing data, latent variables, and unobserved heterogeneity. Tilburg: Tilburg University Press.
59. Westers, P. (1993). The solution-error response-error model: A method for the examination of test item bias. Doctoral dissertation, University of Twente, The Netherlands.
60. Wiggins, L. M. (1973). Panel analysis. Amsterdam: Elsevier.
61. Winship, C., and Mare, R. D. (1989). Loglinear models with missing data: A latent class approach. In C. C. Clogg (Ed.), Sociological Methodology, 1989 (pp. 331-367). Oxford: Blackwell.