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Di Mari R, Bakk Z, Oser J, Kuha J. A two-step estimator for multilevel latent class analysis with covariates. PSYCHOMETRIKA 2023; 88:1144-1170. [PMID: 37544973 PMCID: PMC10656341 DOI: 10.1007/s11336-023-09929-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Indexed: 08/08/2023]
Abstract
We propose a two-step estimator for multilevel latent class analysis (LCA) with covariates. The measurement model for observed items is estimated in its first step, and in the second step covariates are added in the model, keeping the measurement model parameters fixed. We discuss model identification, and derive an Expectation Maximization algorithm for efficient implementation of the estimator. By means of an extensive simulation study we show that (1) this approach performs similarly to existing stepwise estimators for multilevel LCA but with much reduced computing time, and (2) it yields approximately unbiased parameter estimates with a negligible loss of efficiency compared to the one-step estimator. The proposal is illustrated with a cross-national analysis of predictors of citizenship norms.
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Affiliation(s)
- Roberto Di Mari
- Department of Economics and Business, University of Catania, Corso Italia 55, 95128, Catania, Italy.
| | - Zsuzsa Bakk
- Department of Methodology and Statistics, Leiden University, Leiden, The Netherlands
| | - Jennifer Oser
- Department of Politics and Government, Ben-Gurion University, Beer sheva, Israel
| | - Jouni Kuha
- Department of Statistics, London School of Economics and Political Science, London, UK
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2
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Ren B, Barnett I. Combining mixed effects hidden Markov models with latent alternating recurrent event processes to model diurnal active-rest cycles. Biometrics 2023; 79:3402-3417. [PMID: 37017074 DOI: 10.1111/biom.13865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 03/22/2023] [Indexed: 04/06/2023]
Abstract
Data collected from wearable devices can shed light on an individual's pattern of behavioral and circadian routine. Phone use can be modeled as alternating processes, between the state of active use and the state of being idle. Markov chains and alternating recurrent event models are commonly used to model state transitions in cases such as these, and the incorporation of random effects can be used to introduce diurnal effects. While state labels can be derived prior to modeling dynamics, this approach omits informative regression covariates that can influence state memberships. We instead propose an alternating recurrent event proportional hazards (PH) regression to model the transitions between latent states. We propose an expectation-maximization algorithm for imputing latent state labels and estimating parameters. We show that our E-step simplifies to the hidden Markov model (HMM) forward-backward algorithm, allowing us to recover an HMM with logistic regression transition probabilities. In addition, we show that PH modeling of discrete-time transitions implicitly penalizes the logistic regression likelihood and results in shrinkage estimators for the relative risk. This new estimator favors an extended stay in a state and is useful for modeling diurnal rhythms. We derive asymptotic distributions for our parameter estimates and compare our approach against competing methods through simulation as well as in a digital phenotyping study that followed smartphone use in a cohort of adolescents with mood disorders.
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Affiliation(s)
- Benny Ren
- Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, Pennsylvania, PA, USA
| | - Ian Barnett
- Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, Pennsylvania, PA, USA
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3
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Pandolfi S, Bartolucci F, Pennoni F. A hidden Markov model for continuous longitudinal data with missing responses and dropout. Biom J 2023; 65:e2200016. [PMID: 37035989 DOI: 10.1002/bimj.202200016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Revised: 01/04/2023] [Accepted: 01/10/2023] [Indexed: 04/11/2023]
Abstract
We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three different types of missing pattern: (I) partially missing outcomes at a given time occasion, (II) completely missing outcomes at a given time occasion (intermittent pattern), and (III) dropout before the end of the period of observation (monotone pattern). The missing-at-random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation-maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.
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Affiliation(s)
- Silvia Pandolfi
- Department of Economics, University of Perugia, Perugia, Italy
| | | | - Fulvia Pennoni
- Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy
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Brusa L, Bartolucci F, Pennoni F. Tempered expectation-maximization algorithm for the estimation of discrete latent variable models. Comput Stat 2022. [DOI: 10.1007/s00180-022-01276-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
AbstractMaximum likelihood estimation of discrete latent variable (DLV) models is usually performed by the expectation-maximization (EM) algorithm. A well-known drawback is related to the multimodality of the log-likelihood function so that the estimation algorithm can converge to a local maximum, not corresponding to the global one. We propose a tempered EM algorithm to explore the parameter space adequately for two main classes of DLV models, namely latent class and hidden Markov. We compare the proposal with the standard EM algorithm by an extensive Monte Carlo simulation study, evaluating both the ability to reach the global maximum and the computational time. We show the results of the analysis of discrete and continuous cross-sectional and longitudinal data referring to some applications of interest. All the results provide supporting evidence that the proposal outperforms the standard EM algorithm, and it significantly improves the chance to reach the global maximum. The advantage is relevant even considering the overall computing time.
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Tullio F, Bartolucci F. Causal inference for time-varying treatments in latent Markov models: An application to the effects of remittances on poverty dynamics. Ann Appl Stat 2022. [DOI: 10.1214/21-aoas1578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Federico Tullio
- Directorate General for Economics, Statistics and Research, Bank of Italy
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Merlo L, Maruotti A, Petrella L, Punzo A. Quantile hidden semi-Markov models for multivariate time series. STATISTICS AND COMPUTING 2022; 32:61. [PMID: 35968041 PMCID: PMC9360757 DOI: 10.1007/s11222-022-10130-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 07/24/2022] [Indexed: 06/15/2023]
Abstract
UNLABELLED This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states' sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s11222-022-10130-1.
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Affiliation(s)
- Luca Merlo
- Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro, 5, 00185 Rome, Italy
| | - Antonello Maruotti
- Department of Mathematics, University of Bergen, Bergen, Norway
- Department of Law, Economics, Political Sciences and Modern Languages, LUMSA University, Rome, Italy
| | - Lea Petrella
- MEMOTEF Department, Sapienza University of Rome, Rome, Italy
| | - Antonio Punzo
- Department of Economics and Business, University of Catania, Catania, Italy
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Haji-Maghsoudi S, Sadeghifar M, Roshanaei G, Mahjub H. Multivariate hidden semi-Markov models for longitudinal data: a dynamic regression modeling. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2021.2001529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Saiedeh Haji-Maghsoudi
- Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran
| | - Majid Sadeghifar
- Department of Statistics, Faculty of Basic Sciences, Bu-Ali Sina University, Hamadan, Iran
| | - Ghodratollah Roshanaei
- Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran
- Modeling of Noncommunicable Diseases Research Center, Hamadan University of Medical Sciences, Hamadan, Iran
| | - Hossein Mahjub
- Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran
- Research Center for Health Sciences, Hamadan University of Medical Sciences, Hamadan, Iran
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Di Mari R, Maruotti A. A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error. ADV DATA ANAL CLASSI 2021. [DOI: 10.1007/s11634-021-00473-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Asilkalkan A, Zhu X. Matrix‐variate time series modelling with hidden Markov models. Stat (Int Stat Inst) 2021. [DOI: 10.1002/sta4.409] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Abdullah Asilkalkan
- Department of Information Systems, Statistics, and Management Science The University of Alabama Tuscaloosa AL 35487 USA
| | - Xuwen Zhu
- Department of Information Systems, Statistics, and Management Science The University of Alabama Tuscaloosa AL 35487 USA
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10
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Maruotti A, Petrella L, Sposito L. Hidden semi-Markov-switching quantile regression for time series. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2021.107208] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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