Latent Markov models: A review of a general framework for the analysis of longitudinal data with covariates

Test

Volumn 23, Issue 3, 2014, Pages 433-465

  Bartolucci, F ^a   Farcomeni, A ^b   Pennoni, F ^c  

^a UNIVERSITY OF PERUGIA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

Bayesian framework; EM algorithm; Forward Backward recursions; Hidden Markov models; Measurement errors; Panel data; Unobserved heterogeneity

Indexed keywords

EID: 84906821317     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11749-014-0381-7     Document Type: Article

References (103)

1. Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second international symposium on information theory. Akademiai Kiado, Budapest, pp 267-281.
2. Altman RM (2007) Mixed hidden Markov models: an extension of the hidden Markov model to the longitudinal data setting. J Am Stat Assoc 102: 201-210.
3. Anderson TW (1951) Probability models for analysing time changes in attitudes. In: Paul FL (ed) The use of mathematical models in the measurement of the attitudes, The RAND Research Memorandum No. 455.
4. Anderson TW (1954) Probability models for analysing time changes in attitudes. In: Paul FL (ed) Mathematical thinking in the social science. The Free press, IL.
5. Andersson S, Rydén T (2009) Subspace estimation and prediction methods for hidden Markov models. Ann Stat 37: 4131-4152.
6. Archer GEB, Titterington DM (2009) Parameter estimation for hidden Markov chains. J Stat Plann Inference 108: 365-390.
7. Bacci S, Pandolfi S, Pennoni F (2014) A comparison of some criteria for states selection in the latent Markov model for longitudinal data. Adv Data Anal Classif 8: 125-145.
8. Bartolucci F (2006) Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities. J R Stat Soc Ser B 68: 155-178.
9. Bartolucci F, Farcomeni A (2009) A multivariate extension of the dynamic logit model for longitudinal data based on a latent Markov heterogeneity structure. J Am Stat Assoc 104: 816-831.
10. Bartolucci F, Farcomeni A (2010) A note on the mixture transition distribution and hidden Markov models. J Time Ser Anal 31: 132-138.
11. Bartolucci F, Pandolfi S (2013) A new constant memory recursion for hidden Markov models. J Comput Biol (2014, in press).
12. Bartolucci F, Pennoni F (2007) A class of latent Markov models for capture-recapture data allowing for time, heterogeneity and behavior effects. Biometrics 63: 568-578.
13. Bartolucci F, Pennoni F, Francis B (2007) A latent Markov model for detecting patterns of criminal activity. J R Stat Soc Ser A 170: 151-132.
14. Bartolucci F, Lupparelli M, Montanari GE (2009) Latent Markov model for binary longitudinal data: an application to the performance evaluation of nursing homes. Ann Appl Stat 3: 611-636.
15. Bartolucci F, Pennoni F, Vittadini G (2011) Assessment of school performance through a multilevel latent Markov Rasch model. J Educ Behav Stat 36: 491-522.
16. Bartolucci F, Farcomeni A, Pennoni F (2013) Latent Markov models for longitudinal data. Chapman and Hall/CRC Press, Boca Raton.
17. Baum L, Petrie T (1966) Statistical inference for probabilistic functions of finite state Markov chains. Ann Math Stat 37: 1554-1563.
18. Baum L, Petrie T, Soules G, Weiss N (1970) A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann Math Stat 41: 164-171.
19. Berchtold A (2004) Optimization of mixture models: Comparison of different strategies. Comput Stat 19: 385-406.
20. Bernardo JM, Smith AFM (1994) Bayesian Theory. Wiley, Chichester.
21. Bickel PJ, Ritov Y, Rydén T (1998) Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models. Ann Stat 26: 1614-1635.
22. Bollen KA, Curran PJ (2006) Latent curve models: a structural equation perspective. Wiley, Hoboken.
23. Bonrmann L, Mutz R, Daniel HD (2008) Latent Markov modeling applied to grant peer review. J Informetr 2: 217-228.
24. Boucheron S, Gassiat E (2007) An information-theoretic perspective on order estimation. In: O Cappé TR E Moulines (ed) Inference in Hidden Markov models, Springer, Berlin, pp 565-602.
25. Bye BV, Schechter ES (1986) A latent Markov model approach to the estimation of response error in multiwave panel data. J Am Stat Assoc 81: 375-380.
26. Cappé O, Moulines E, Rydén T (2005) Inference in Hidden Markov models. Springer, New York.
27. Cheng RCH, Liu WB (2001) The consistency of estimators in finite mixture models. Scand J Stat 28: 603-616.
28. Chib S (1996) Calculating posterior distributions and modal estimates in Markov mixture models. J Econom 75: 79-97.
29. Collins LM, Wugalter SE (1992) Latent class models for stage-sequential dynamic latent variables. Multivar Behav Res 27: 131-157.
30. Colombi R, Forcina A (2001) Marginal regression models for the analysis of positive association of ordinal response variables. Biometrika 88: 1007-1019.
31. Congdon P (2006) Bayesian model choice based on Monte Carlo estimates of posterior model probabilities. Comput Stat Data Anal 50: 346-357.
32. Cowles MK, Carlin BP (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. J Am Stat Assoc 91: 883-904.
33. Dannemann J (2012) Semiparametric hidden Markov models. J Comput Graphical Stat 21: 677-692.
34. Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge.
35. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J R Stat Soc Ser B 39: 1-38.
36. Dias JG, Vermunt JK (2007) Latent class modeling of website users' search patterns: Implications for online market segmentation. J Retailing Consum Serv 14: 359-368.
37. Elliot DS, Huizinga D, Menard S (1989) Multiple problem youth: delinquency, substance use, and mental health problems. Springer, New York.
38. Farcomeni A (2011) Hidden Markov partition models. Stat Probab Lett 81: 1766-1770.
39. Farcomeni A (2012) Quantile regression for longitudinal data based on latent Markov subject-specific parameters. Stat Comput 22: 141-152.
40. Farcomeni A, Arima S (2012) A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data. Stat Appl Genetics Mol Biol 11(4): article 3.
41. Feng Z, McCulloch CE (1996) Using bootstrap likelihood ratios in finite mixture models. J R Stat Soc Ser B 58: 609-617.
42. Fitzmaurice G, Davidian M, Verbeke G, G M, (eds) (2009) Longitudinal data analysis. Chapman and Hall, CRC, London.
43. Frühwirth-Schnatter S (2001) Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. J Am Stat Assoc 96: 194-209.
44. García-Escudero L, Gordaliza A, Mayo-Iscar A (2013) A constrained robust proposal for mixture modeling avoiding spurious solutions. Adv Data Anal Classif 1-17: doi: 10. 1007/s11634-013-0153-3.
45. Ghahramani Z, Jordan MI (1997) Factorial hidden Markov models. Mach Learn 29: 245-273.
46. Glonek GFV, McCullagh P (1995) Multivariate logistic models. J R Stat Soc B 57: 533-546.
47. Goodman LA (1961) Statistical methods for the mover-stayer model. J Am Stat Assoc 56: 841-868.
48. Goodman LA (1974) Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61: 215-231.
49. Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82: 711-732.
50. Hambleton RK, Swaminathan H (1985) Item response theory: principles and applications. Kluwer Nijhoff, Boston.
51. Hoffmann L, Lehrke M, Todt E (1985) Development and changes in pupils' interest in physics (grade 5 to 10): design of a longitudinal study. In: Lehrke M, Hoffmann L, Gardner PL (eds) Interest in science and technology education. IPN, Kiel, pp 71-80.
52. Juang B, Rabiner L (1991) Hidden Markov models for speech recognition. Technometrics 33: 251-272.
53. Kaplan D (2008) An overview of Markov chain methods for the study of stage-sequential developmental processes. Dev Psychol 44: 457-467.
54. Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90: 773-795.
55. Khreich W, Granger E, Miri A, Sabourin R (2010) On the memory complexity of the forward-backward algorithm. Pattern Recognit Lett 31: 91-99.
56. Koski T (2001) Hidden Markov models for bioinformatics. Kluwer, Dordrecht.
57. Künsch HR (2005) State space and hidden Markov models. In: Barndorff-Nielsen OE, Cox DR, Klüppelberg C (eds) Complex stochastic systems. Chapman and Hall/CRC, Boca Raton, FL, pp 109-173.
58. Langeheine R (1988) New development in latent class theory. In: Langeheine R, Rost J (eds) Latent trait and latent class models. Plenum Press, New York, pp 77-108.
59. Langeheine R (1994) Latent variables Markov models. In: von Eye A, Clogg C (eds) Latent variables analysis: applications for developmental research. Sage, Thousand Oaks, CA, pp 373-395.
60. Langeheine R, van de Pol F (1994) Discrete-time mixed Markov latent class models. In: Dale A, Davies R (eds) Analyzing social and political change: a casebook of methods. Sage Publications, London, pp 171-197.
61. Lazarsfeld PF (1950) The logical and mathematical foundation of latent structure analysis. In: Stouffer SA, Guttman L, Suchman EA (ed) Measurement and prediction. Princeton University Press, New York.
62. Lazarsfeld PF, Henry NW (1968) Latent structure analysis. Houghton Mifflin, Boston.
63. Leonard T (1975) Bayesian estimation methods for two-way contingency tables. J R Stat Soc Ser B 37: 23-37.
64. Leroux BG, Puterman ML (1992) Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 48: 545-558.
65. Levinson SE, Rabiner LR, Sondhi MM (1983) An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition. Bell Syst Tech J 62: 1035-1074.
66. Louis T (1982) Finding the observed information matrix when using the EM algorithm. J R Stat Soc Ser B 44: 226-233.
67. Lystig TC, Hughes J (2002) Exact computation of the observed information matrix for hidden Markov models. J Comput Graphical Stat 11: 678-689.
68. MacDonald IL, Zucchini W (1997) Hidden Markov and other models for discrete-valued time series. Chapman and Hall, London.
69. Magidson J, Vermunt JK (2001) Latent class factor and cluster models, bi-plots and related graphical displays. Sociol Methodol 31: 223-264.
70. Maruotti A (2011) Mixed hidden Markov models for longitudinal data: an overview. Int Stat Rev 79: 427-454.
71. McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman and Hall, CRC, London.
72. McHugh RB (1956) Efficient estimation and local identification in latent class analysis. Psychometrika 21: 331-347.
73. McLachlan G, Peel D (2000) Finite mixture models. Wiley, New York.
74. Muthén B (2004) Latent variable analysis: growth mixture modeling and related techniques for longitudinal data. In: Kaplan D (ed) Handbook of quantitative methodology for the social sciences. Sage Publications, Newbury Park, pp 345-368.
75. Nagin D (1999) Analyzing developmental trajectories: a semi-parametric, group-based approach. Psychol Methods 4: 139-157.
76. Nazaret W (1987) Bayesian log-linear estimates for three-way contingency tables. Biometrika 74: 401-410.
77. Oakes D (1999) Direct calculation of the information matrix via the EM algorithm. J R Stat Soc Ser B 61: 479-482.
78. Paas LJ, Vermunt JK, Bijlmolt THA (2009) Discrete time, discrete state latent Markov modelling for assessing and predicting household acquisitions of financial products. J R Stat Soc Ser A 170: 955-974.
79. van de Pol F, Langeheine R (1990) Mixed Markov latent class models. Sociol Method 20: 213-247.
80. Rijmen F, Vansteelandt K, De Boeck P (2007) Latent class models for diary methods data: parameter estimation by local computations. Psychometrika 73: 167-182.
81. Robert C, Ryden T, Titterington D (2000) Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method. J R Stat Soc Ser B 62: 57-75.
82. Robert CP, Casella G (2010) Monte Carlo statistical methods, 2nd edn. Springer, New York.
83. Robert CP, RydÉn T, Titterington D (1999) Convergence controls for MCMC algorithms, with applications to hidden Markov chains. J Stat Comput Simul 64: 327-355.
84. Roeder K, Lynch KG, Nagin DS (1999) Modeling uncertainty in latent class membership: a case study in criminology. J Am Stat Assoc 94: 766-776.
85. Rost J (2002) Mixed and latent Markov models as item response models. Methods of psychological research online, Special Issue, pp 53-70.
86. Rusakov D, Geiger D (2002) Asymptotic model selection for naive Bayesian networks. In: Proceedings of the eighteenth conference on uncertainty in artificial intelligence, Morgan Kaufmann Publishers Inc., pp 438-455.
87. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6: 461-464.
88. Scott SL (2002) Bayesian methods for hidden Markov models: recursive computing in the 21st century. J Am Stat Assoc 97: 337-351.
89. Seidel W, Ševčíková H (2004) Types of likelihood maxima in mixture models and their implication on the performance of tests. Ann Inst Stat Math 56: 631-654.
90. Spezia L (2010) Bayesian analysis of multivariate Gaussian hidden Markov models with an unknown number of regimes. J Time Ser Anal 31: 1-11.
91. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc Ser B 64: 583-639.
92. Turner R (2008) Direct maximization of the likelihood of a hidden Markov model. Comput Stat Data Anal 52: 4147-4160.
93. Turner TR, Cameron MA, Thomson PJ (1998) Hidden Markov chains in generalized linear models. Can J Stat 26: 107-125.
94. Tuyl F, Gerlach R, Mengersen K (2009) Posterior predictive arguments in favor of the Bayes-Laplace prior as the consensus prior for binomial and multinomial parameters. Bayesian Anal 4: 151-158.
95. Vansteelandt K, Rijmen F, Pieters G, Vanderlinden J (2007) Drive for thinness, affect regulation and physical activity in eating disorders: a daily life study. Behav Res Ther 45: 1717-1734.
96. Vermunt J (2010) Longitudinal research with latent variables. In: van Montfort K, Oud J, Satorra A (eds) Handbook of advanced multilevel analysis. Springer, Heidelberg, pp 119-152.
97. Vermunt JK, Langeheine R, Böckenholt U (1999) Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. J Educ Behav Stat 24: 179-207.
98. Viterbi A (1967) Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans Inform Theory 13: 260-269.
99. Welch LR (2003) Hidden Markov models and the Baum-Welch algorithm. IEEE Inform Theory Soc Newsl 53: 1-13.
100. Wiggins L (1955) Mathematical models for the analysis of multi-wave panels. In: University C (ed) Ph. D. Dissertation, University microfilms, Ann Arbor.
101. Wiggins L (1973) Panel analysis: latent probability models for attitude and behaviour processes. Elsevier, Amsterdam.
102. Yau C, Papaspiliopoulos O, Roberts G, Holmes C (2011) Bayesian nonparametric hidden Markov models with application to the analysis of copy-number-variation in mammalian genomes. J R Stat Soc Ser B 73: 37-57.
103. Zucchini W, MacDonald IL (2009) Hidden Markov Models for time series: an introduction using R. Springer, New York.