Partially Ordered Mixed Hidden Markov Model for the Disablement Process of Older Adults

REFERENCES

• Agresti , A. 2002 . Categorical Data Analysis , New York : Wiley-Interscience .
   Google Scholar
• Allison , P. 1999 . Logistic Regression Using the SAS System: Theory and Application , Cary, NC: SAS Publishing .
   Google Scholar
• Altman , R. 2007 . “Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting,” . Journal of the American Statistical Association , 102 : 201 – 210 .
   Web of Science ®Google Scholar
• Bartolucci , F. and Farcomeni , A. 2009 . “A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure,” . Journal of American Statistical Association , 104 : 816 – 831 .
   Web of Science ®Google Scholar
• Baum , L. and Petrie , T. 1966 . “Statistical Inference for Probabilistic Functions of Finite State Markov Chains,” . The Annals of Mathematical Statistics , 37 : 1554 – 1563 .
   Google Scholar
• Beckett , L. , Brock , D. , Lemke , J. , de Leon , C. , Guralnik , J. , Fillenbaum , G. , Branch , L. , Wetle , T. and Evans , D. 1996 . “Analysis of Change in Self-Reported Physical Function Among Older Persons in Four Population Studies,” . American Journal of Epidemiology , 143 : 766 – 778 .
   PubMed Web of Science ®Google Scholar
• Cleveland , W. 1979 . “Robust Locally Weighted Regression and Smoothing Scatterplots,” . Journal of the American Statistical Association , 74 : 829 – 836 .
   Web of Science ®Google Scholar
• Crimmins , E. , Saito , Y. and Reynolds , S. 1997 . “Further Evidence on Recent Trends in the Prevalence and Incidence of Disability Among Older Americans From Two Sources: The LSOA and the NHIS,” . Journals of Gerontology, Series B , 52 : 59 – 71 .
   PubMed Web of Science ®Google Scholar
• Dempster , A. , Laird , N. and Rubin , D. 1977 . “Maximum Likelihood From Incomplete Data via the EM Algorithm,” . Journal of the Royal Statistical Society, Series B , 39 : 1 – 38 .
   Google Scholar
• Fahrmeir , L. and Tutz , G. 2001 . Multivariate Statistical Modelling Based on Generalized Linear Models , New York : Springer-Verlag .
   Google Scholar
• Fang , S. and Puthenpura , S. 1993 . Linear Optimization and Extensions: Theory and Algorithms , Upper Saddle River , NJ : Prentice-Hall, Inc .
   Google Scholar
• Freedman , V. , Martin , L. and Schoeni , R. 2002 . “Recent Trends in Disability and Functioning Among Older Adults in the United States: A Systematic Review,” . Journal of the American Medical Association , 288 : 3137 – 3146 .
   PubMed Web of Science ®Google Scholar
• Gill , T. , Gahbauer , E. , Allore , H. and Han , L. 2006 . “Transitions Between Frailty States Among Community-Living Older Persons,” . Archives of Internal Medicine , 166 : 418 – 423 .
   PubMed Web of Science ®Google Scholar
• Gill , T. and Kurland , B. 2003 . “The Burden and Patterns of Disability in Activities of Daily Living Among Community-Living Older Persons,” . Journals of Gerontology Series A: Biological and Medical Sciences , 58 : 70 – 75 .
   PubMed Web of Science ®Google Scholar
• Guilley , E. , Ghisletta , P. , Armi , F. , Berchtold , A. , d’Epinay , C. , Michel , J. and de Ribaupierre , A. 2008 . “Dynamics of Frailty and ADL Dependence in a Five-Year Longitudinal Study of Octogenarians,” . Research on Aging , 30 : 299 – 317 .
   Web of Science ®Google Scholar
• Hardy , S. , Dubin , J. , Holford , T. and Gill , T. 2005 . “Transitions Between States of Disability and Independence Among Older Persons,” . American Journal of Epidemiology , 161 : 575 – 584 .
   PubMed Web of Science ®Google Scholar
• Hardy , S. and Gill , T. 2004 . “Recovery From Disability Among Community-Dwelling Older Persons,” . Journal of the American Medical Association , 291 : 1596 – 1602 .
   PubMed Web of Science ®Google Scholar
• Harrell , F. 2001 . Regression Modeling Strategies , New York : Springer .
   Google Scholar
• Harris , T. , Visser , M. , Everhart , J. , Cauley , J. , Tylavsky , F. , Fyerst , T. , Zamboni , M. , Taaffe , D. , Resnick , H. , Scherzinger , A. and Nevitt , M. 2006 . “Waist Circumference and Sagittal Diameter Reflect Total Body Fat Better Than Visceral Fat in Older Men and Women: The Health, Aging and Body Composition Study,” . Annals of the New York Academy of Sciences , 904 : 462 – 473 .
   Google Scholar
• Hubbard , R. , Inoue , L. and Diehr , P. 2009 . “Joint Modeling of Self-Rated Health and Changes in Physical Functioning,” . Journal of the American Statistical Association , 104 : 912 – 928 .
   PubMed Web of Science ®Google Scholar
• Ip , E. , Snow-Jones , A. , Heckert , D. , Zhang , Q. and Gondolf , E. 2010 . “Latent Markov Model for Analyzing Temporal Configuration for Violence Profiles and Trajectories in a Sample of Batterers,” . Sociological Methods and Research , 39 : 222 – 255 .
   Web of Science ®Google Scholar
• Katz , S. 1983 . “Assessing Self-Maintenance: Activities of Daily Living, Mobility, and Instrumental Activities of Daily Living,” . Journal of the American Geriatrics Society , 31 : 721 – 27 .
   PubMed Web of Science ®Google Scholar
• Lauritzen , S. and Spiegelhalter , D. 1988 . “Local Computations With Probabilities on Graphical Structures and Their Application to Expert Systems,” . Journal of the Royal Statistical Society, Series B , 50 : 157 – 224 .
   Google Scholar
• Leveille , S. , Penninx , B. , Melzer , D. , Izmirlian , G. and Guralnik , J. 2000 . “Sex Differences in the Prevalence of Mobility Disability in Old Age: The Dynamics of Incidence, Recovery, and Mortality,” . Journals of Gerontology Series B: Psychological Sciences and Social Sciences , 55 : S41 – S50 .
   PubMed Web of Science ®Google Scholar
• MacDonald , I. and Zucchini , W. 1997 . Hidden Markov and Other Models for Discrete-Valued Time Series , Boca Raton, FL: CRC Press .
   Google Scholar
• McCullagh , P. 1980 . “Regression Models for Ordinal Data,” . Journal of the Royal Statistical Society, Series B , 42 : 109 – 142 .
   Google Scholar
• Meulders , M. , Ip , E. and De Boeck , P. 2005 . “Latent Variable Models for Partially Ordered Responses and Trajectory Analysis of Anger-Related Feelings,” . British Journal of Mathematical and Statistical Psychology , 58 : 117 – 143 .
   PubMedGoogle Scholar
• Peres , K. , Verret , C. , Alioum , A. and Barberger-Gateau , P. 2005 . “The Disablement Process: Factors Associated With Progression of Disability and Recovery in French Elderly People,” . Disability & Rehabilitation , 27 : 263 – 276 .
   PubMed Web of Science ®Google Scholar
• Rabiner , L. 1990 . “A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition,” . Readings in Speech Recognition , 53 : 267 – 296 .
   Google Scholar
• Rejeski , J. , Ip , E. , Bertoni , A. , Bray , G. , Evans , G. , Gregg , E. and Zhang , Q. 2012 . the Look AHEAD Research Group “Lifestyle Change and Mobility in Obese Adults With Type 2 Diabetes,” . New England Journal of Medicine , 366 : 1209 – 1217 .
   PubMed Web of Science ®Google Scholar
• Rejeski , W. , Ip , E. , Marsh , A. , Miller , M. and Farmer , D. 2008a . “Measuring Disability in Older Adults: The International Classification System of Functioning, Disability and Health (ICF) Framework,” . Geriatrics and Gerontology International , 8 : 48 – 54 .
   PubMed Web of Science ®Google Scholar
• Rejeski , W. , Ip , E. , Marsh , A. , Zhang , Q. and Miller , M. 2008b . “Obesity Influences Transitional States of Disability in Older Adults With Knee Pain,” . Archives of Physical Medicine and Rehabilitation , 89 : 2102 – 2107 .
   PubMed Web of Science ®Google Scholar
• Schafer , J. 1997 . Analysis of Incomplete Multivariate Data , Boca Raton, FL: Chapman & Hall/CRC .
   Google Scholar
• Scott , S. 2002 . “Bayesian Methods for Hidden Markov Models,” . Journal of the American Statistical Association , 97 : 337 – 351 .
   Web of Science ®Google Scholar
• Scott , S. , James , G. and Sugar , C. 2005 . “Hidden Markov Models for Longitudinal Comparisons,” . Journal of the American Statistical Association , 100 : 359 – 370 .
   Web of Science ®Google Scholar
• Shirley , K. , Small , D. , Lynch , K. , Maisto , S. and Oslin , D. 2010 . “Hidden Markov Models for Alcoholism Treatment Trial Data,” . The Annals of Applied Statistics , 4 : 366 – 395 .
   Web of Science ®Google Scholar
• Smyth , P. 1997 . “Belief Networks, Hidden Markov Models, and Markov Random Fields: A Unifying View,” . Pattern Recognition Letters , 18 : 1261 – 1268 .
   Web of Science ®Google Scholar
• Smyth , P. 2000 . “Model Selection for Probabilistic Clustering Using Cross-Validated Likelihood,” . Statistics and Computing , 10 : 63 – 72 .
   Web of Science ®Google Scholar
• Stephens , M. 2000 . “Dealing With Label Switching in Mixture Models,” . Journal of the Royal Statistical Society, Series B , 62 : 795 – 809 .
   Google Scholar
• Thinggaard , M. , Jacobsen , R. , Jeune , B. , Martinussen , T. and Christensen , K. 2010 . “Is the Relationship Between BMI and Mortality Increasingly U-Shaped With Advancing Age? A 10-Year Follow-Up of Persons Aged 70–95 years,” . The Journals of Gerontology Series A: Biological Sciences and Medical Sciences , 65 : 526 – 531 .
   PubMed Web of Science ®Google Scholar
• Tutz , G. 1990 . “Sequential Item Response Models With an Ordered Response,” . British Journal of Mathematical and Statistical Psychology , 43 : 39 – 55 .
   Web of Science ®Google Scholar
• Verbrugge , L. and Jette , A. 1994 . “The Disablement Process,” . Social Science & Medicine , 38 : 1 – 14 .
   PubMed Web of Science ®Google Scholar
• Vermunt , J. , Langeheine , R. and Bockenholt , U. 1999 . “Discrete-Time Discrete-State Latent Markov Models With Time-Constant and Time-Varying Covariates,” . Journal of Educational and Behavioral Statistics , 24 : 179
   Web of Science ®Google Scholar
• Yang , Y. and George , L. 2005 . “Functional Disability, Disability Transitions, and Depressive Symptoms in Late Life,” . Journal of Aging and Health , 17 : 263 – 292 .
   PubMed Web of Science ®Google Scholar
• Zhang , Q. and Ip , E. H. 2010 . “Exact Computation of Standard Errors for Bayesian Networks with Discrete Hidden Variables.” Technical Report ” . Department of Biostatistical Sciences, Wake Forest School of Medicine .
   Google Scholar
• Zhang , Q. and Ip , E. H. 2011 . “Generalized Linear Model for Partially Ordered Data,” . Statistics in Medicine , 31 : 56 – 68 .
   PubMedGoogle Scholar
• Zhang , Q. , Snow Jones , A. , Rijmen , F. and Ip , E. 2010 . “Multivariate Discrete Hidden Markov Models for Domain-Based Measurements and Assessment of Risk Factors in Child Development,” . Journal of Computational and Graphical Statistics , 19 : 746 – 765 .
   PubMed Web of Science ®Google Scholar