IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v16y2022i2d10.1007_s11634-021-00446-7.html
   My bibliography  Save this article

Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models

Author

Listed:
  • Giorgio Eduardo Montanari

    (University of Perugia)

  • Marco Doretti

    (University of Perugia)

  • Maria Francesca Marino

    (University of Florence)

Abstract

In this paper, an ordinal multilevel latent Markov model based on separate random effects is proposed. In detail, two distinct second-level discrete effects are considered in the model, one affecting the initial probability vector and the other affecting the transition probability matrix of the first-level ordinal latent Markov process. To model these separate effects, we consider a bi-dimensional mixture specification that allows to avoid unverifiable assumptions on the random effect distribution and to derive a two-way clustering of second-level units. Starting from a general model where the two random effects are dependent, we also obtain the independence model as a special case. The proposal is applied to data on the physical health status of a sample of elderly residents grouped into nursing homes. A simulation study assessing the performance of the proposal is also included.

Suggested Citation

  • Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 457-485, June.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00446-7
    DOI: 10.1007/s11634-021-00446-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-021-00446-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11634-021-00446-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Giorgio E. Montanari & Silvia Pandolfi, 2018. "Evaluation of long-term health care services through a latent Markov model with covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 151-173, March.
    2. Bakk, Zsuzsa & Kuha, Jouni, 2018. "Two-step estimation of models between latent classes and external variables," LSE Research Online Documents on Economics 85161, London School of Economics and Political Science, LSE Library.
    3. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    4. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    5. Bartolucci, Francesco & Montanari, Giorgio E. & Pandolfi, Silvia, 2015. "Three-step estimation of latent Markov models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 287-301.
    6. Francesco Bartolucci & Monia Lupparelli, 2016. "Pairwise Likelihood Inference for Nested Hidden Markov Chain Models for Multilevel Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 216-228, March.
    7. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2011. "Assessment of School Performance Through a Multilevel Latent Markov Rasch Model," Journal of Educational and Behavioral Statistics, , vol. 36(4), pages 491-522, August.
    8. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    9. Altman, Rachel MacKay, 2007. "Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 201-210, March.
    10. Linzer, Drew A. & Lewis, Jeffrey B., 2011. "poLCA: An R Package for Polytomous Variable Latent Class Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i10).
    11. Zsuzsa Bakk & Jouni Kuha, 2018. "Two-Step Estimation of Models Between Latent Classes and External Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 871-892, December.
    12. Edward Ip & Qiang Zhang & Jack Rejeski & Tammy Harris & Stephen Kritchevsky, 2013. "Partially Ordered Mixed Hidden Markov Model for the Disablement Process of Older Adults," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 370-384, June.
    13. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    14. Giorgio E. Montanari & Marco Doretti, 2019. "Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 307-326, November.
    15. Marino, Maria Francesca & Alfó, Marco, 2016. "Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 193-209.
    16. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
    17. Sprangers, Mirjam A. G. & Schwartz, Carolyn E., 1999. "Integrating response shift into health-related quality of life research: a theoretical model," Social Science & Medicine, Elsevier, vol. 48(11), pages 1507-1515, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Montanari, Giorgio E. & Doretti, Marco & Bartolucci, Francesco, 2017. "A multilevel latent Markov model for the evaluation of nursing homes' performance," MPRA Paper 80691, University Library of Munich, Germany.
    2. Giorgio E. Montanari & Marco Doretti, 2019. "Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 307-326, November.
    3. Antonello Maruotti & Jan Bulla & Tanya Mark, 2019. "Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 19-42, April.
    4. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    5. Di Mari, Roberto & Bakk, Zsuzsa & Oser, Jennifer & Kuha, Jouni, 2023. "A two-step estimator for multilevel latent class analysis with covariates," LSE Research Online Documents on Economics 119994, London School of Economics and Political Science, LSE Library.
    6. Roberto Mari & Antonello Maruotti, 2022. "A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 273-300, June.
    7. Ruijin Lu & Tonja R. Nansel & Zhen Chen, 2023. "A Perception-Augmented Hidden Markov Model for Parent–Child Relations in Families of Youth with Type 1 Diabetes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 288-308, April.
    8. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2016. "Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 146-179, April.
    9. Keefe Murphy & T. Brendan Murphy & Raffaella Piccarreta & I. Claire Gormley, 2021. "Clustering longitudinal life‐course sequences using mixtures of exponential‐distance models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1414-1451, October.
    10. Catania, Leopoldo & Di Mari, Roberto, 2021. "Hierarchical Markov-switching models for multivariate integer-valued time-series," Journal of Econometrics, Elsevier, vol. 221(1), pages 118-137.
    11. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    12. Suh, Ellie, 2022. "Can't save or won't save: financial resilience and discretionary retirement saving among British adults in their thirties and forties," LSE Research Online Documents on Economics 110492, London School of Economics and Political Science, LSE Library.
    13. Lin, Yiqi & Song, Xinyuan, 2022. "Order selection for regression-based hidden Markov model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    14. Bakk, Zsuzsa & Kuha, Jouni, 2020. "Relating latent class membership to external variables: an overview," LSE Research Online Documents on Economics 107564, London School of Economics and Political Science, LSE Library.
    15. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Rejoinder on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 484-486, September.
    16. Jesse D. Raffa & Joel A. Dubin, 2015. "Multivariate longitudinal data analysis with mixed effects hidden Markov models," Biometrics, The International Biometric Society, vol. 71(3), pages 821-831, September.
    17. David Aristei & Silvia Bacci & Francesco Bartolucci & Silvia Pandolfi, 2021. "A bivariate finite mixture growth model with selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 759-793, September.
    18. Zhou, Jie & Song, Xinyuan & Sun, Liuquan, 2020. "Continuous time hidden Markov model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    19. Giorgio E. Montanari & Silvia Pandolfi, 2018. "Evaluation of long-term health care services through a latent Markov model with covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 151-173, March.
    20. Xia, Ye-Mao & Tang, Nian-Sheng, 2019. "Bayesian analysis for mixture of latent variable hidden Markov models with multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 190-211.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00446-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.