Maximum likelihood estimation of an extended latent Markov model for clustered binary panel data

Bartolucci, Francesco; Nigro, Valentina

doi:10.1016/j.csda.2006.11.030

Cited by 5 publications

(5 citation statements)

References 27 publications

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“…Finally, denote latent class transition probabilities by il t jl t 1 D Pr .L it D l t jL i.t 1/ D l t 1 / for moves from wave t 1 to an adjacent wave t . Here, there are two possible transition opportunities, so that the pair (t 1; t ) is either (1,2) or (2,3).…”

Section: Latent Class Transition Modelsmentioning

confidence: 99%

“…Panel data sets, for which the number of waves is small but the assessment interval is often large, are adept at handling complex dynamic behaviors, but they often suffer from missing data problems such as those due to death and drop-out [1]. Many longitudinal analyses of survey data assume a balanced panel design whereby either all subjects are observed across all waves or, if there are subjects with any missing data, they are removed from further consideration [2][3][4][5][6][7][8][9][10][11][12]. However, if a survey has late entrants or early drop-outs, these individuals may have different measurement profiles than those who are present across all waves, which may lead to biased findings if the probability of drop-out depends on the measurement process itself [13].…”

Section: Introductionmentioning

confidence: 99%

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Using group‐based latent class transition models to analyze chronic disability data from the National Long‐Term Care Survey 1984–2004

White

Erosheva

2013

Statistics in Medicine

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Latent class transition models track how individuals move among latent classes through time, traditionally assuming a complete set of observations for each individual. In this paper, we develop group-based latent class transition models that allow for staggered entry and exit, common in surveys with rolling enrollment designs. Such models are conceptually similar to, but structurally distinct from, pattern mixture models of the missing data literature. We employ group-based latent class transition modeling to conduct an in-depth data analysis of recent trends in chronic disability among the U.S. elderly population. Using activities of daily living data from the National Long-Term Care Survey (NLTCS), 1982-2004, we estimate model parameters using the expectation-maximization algorithm, implemented in SAS PROC IML. Our findings indicate that declines in chronic disability prevalence, observed in the 1980s and 1990s, did not continue in the early 2000s as previous NLTCS cross-sectional analyses have indicated.

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Section: Latent Class Transition Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Using group‐based latent class transition models to analyze chronic disability data from the National Long‐Term Care Survey 1984–2004

White

Erosheva

2013

Statistics in Medicine

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“…M 3 also contains many zero entries that correspond to transitions that are impossible by the definitions of the states.Because Equation A1 involves only observable states (i.e., actual data events), each parameter in the starting vector and transition matrix is an observable quantity. There are 5 + 2 j of these parameters, each of which is identifiable because, by Bernoulli’s theorem, a unique maximum-likelihood estimator is available in the form of the proportion of events in any experiment that exhibits that data state (e.g., Bartolucci & Nigro, 2007). Such estimators are obtained from the likelihood function where the π i range over the nonzero cells of W 3 and the θ ij range over the nonzero cells of M 3 .…”

Section: Identifiability Proof For Equationmentioning

confidence: 99%

“…There are 5 + 2j of these parameters, each of which is identifiable because, by Bernoulli's theorem, a unique maximum-likelihood estimator is available in the form of the proportion of events in any experiment that exhibits that data state (e.g., Bartolucci & Nigro, 2007). Such estimators are obtained from the likelihood function…”

Section: Final Word: a Unified Framework For Recognition And Recallmentioning

confidence: 99%

Trichotomous processes in early memory development, aging, and neurocognitive impairment: A unified theory.

Brainerd¹,

Reyna²,

Howe³

2009

Psychological Review

182

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link IN PRESS: Psychological Review AbstractOne of the most extensively investigated topics in the adult memory literature, dual memory processes, has had virtually no impact on the study of early memory development. We remove the key obstacles to such research by formulating a trichotomous theory of recall that combines the traditional dual processes of recollection and familiarity with a reconstruction process. The theory is then embedded in a hidden Markov model that measures all three processes with low-burden tasks that are appropriate for even young children. These techniques are applied to a large corpus of developmental studies of recall, yielding stable findings about the emergence of dual memory processes between childhood and young adulthood and generating tests of many theoretical predictions. The techniques are extended to the study of healthy aging and to the memory sequelae of common forms of cognitive impairment, resulting in a theoretical framework that is unified over four major domains of memory research: early development, mainstream adult research, aging, and cognitive impairment. The techniques are also extended to recognition, creating a unified dual-process framework for recall and recognition.Keywords: memory development, dual memory processes, aging, cognitive impairment, hidden Markov models Trichotomous Processes in Early Memory Development, Aging, and Cognitive Impairment:A Unified Theory This paper has three objectives. The first is to resolve a fundamental problem in memory development research; the second is to apply that solution to a large corpus of developmental studies of recall; and the third is to extend the solution to memory changes that occur during healthy aging and in certain forms of cognitive impairment. The problem in question is the scant impact that dual-process distinctions have had on the study of early (child-to-young-adult) memory development. The result is a dramatic disparity in knowledge about dual memory processes in adults, which is vast, versus knowledge about how those processes first evolve, which is thin and inconsistent. Our solution, as will be seen, is (a) to propose a trichotomous theory of recall that subsumes traditional dual-process distinctions, (b) to implement that theory in a low-burden family of tasks that are appropriate for even very young children, and (c) to show that a new mathematical model of those tasks can be used to measure the development of trichotomous memory processes and to test theoretical predictions about them. Concerning the second objective, we show that an attractive feature of this solution is that a developmental data base exists that can be analyzed with the model, thereby closing the gap in knowledge about early memory development. With respect to the third objective, unlike early development, the study of memory changes during aging and in cognitive impairment have been strong...

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“…There is also some authors' research based on models method. For example, Bartolucci [11] analyzed the binary panel data model; Zheng et al [9] applied the traditional clustering method to panel data analysis by constructing a panel data matrix. Ren et al [2] proposed a clustering method based on multi-index panel data by reestablishing the ward function based on the extended Frobenius criterion.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Estimation and Panel Data Clustering Analysis Based on D-Vine and C-Vine

Xie

Yang

et al. 2018

Mathematical Problems in Engineering

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This paper proposed a panel data clustering model based on D-vine and C-vine and supported a semiparametric estimation for parameters. These models include a two-step inference function for margins, two-step semiparameter estimation, and stepwise semiparametric estimation. In similarity measurement, similarity coefficients are constructed by a multivariate Hierarchical Nested Archimedean Copula (HNAC) model and compound PCC models, which are HNAC and D-vine compound model and HNAC and C-vine compound model. Estimation solutions and models evaluation are given for these models. In the case study, the clustering results of HNAC and D-vine compound model and HNAC and C-vine compound model are given, and the effect of different copula families on clustering results is also discussed. The result shows the models are effective and useful.

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Maximum likelihood estimation of an extended latent Markov model for clustered binary panel data

Cited by 5 publications

References 27 publications

Using group‐based latent class transition models to analyze chronic disability data from the National Long‐Term Care Survey 1984–2004

Using group‐based latent class transition models to analyze chronic disability data from the National Long‐Term Care Survey 1984–2004

Trichotomous processes in early memory development, aging, and neurocognitive impairment: A unified theory.

Semiparametric Estimation and Panel Data Clustering Analysis Based on D-Vine and C-Vine

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