Multilevel Latent Markov Models for Nested Longitudinal Discrete Data
Yu, Hsiu-Ting
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Permalink
https://hdl.handle.net/2142/82149
Description
Title
Multilevel Latent Markov Models for Nested Longitudinal Discrete Data
Author(s)
Yu, Hsiu-Ting
Issue Date
2007
Doctoral Committee Chair(s)
Anderson, Carolyn J.
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Tests and Measurements
Language
eng
Abstract
Multilevel longitudinal data are clustered both structurally and temporally. The hierarchically nested structure induces between-subject dependency because individuals in the same unit may share something in common. The longitudinal aspect of data induces within-subject dependency because observations are made on same subjects over time. Since both types of clustered structures contribute to the dependency in the data, both aspects need to be taken into account when modeling such data. Many developments for multilevel and longitudinal data have focused on continuous response or outcome variables, and less attention has been paid to data with discrete manifest and latent variables. The Multilevel Latent Markov Model (MLMM) extends the latent class model to simultaneously incorporate the temporal and structural dependency in a single model. The MLMM is a hybrid of random-effects and conditional models. The latent Markov model, one type of conditional model, is adopted to model the change between two occasions. The random-effects modeling approach is utilized to account for the effects due to the nested structure. The parameters of the proposed model are estimated by maximum likelihood approach with modified EM procedures. Simulation studies are conducted to investigate the estimation procedures. The effects of ignoring the multilevel data structure are also studied through simulations. The estimation procedures for the MLMM are implemented in MATLAB. The MLMM MATLAB Toolbox is available for estimating the MLMM and its component models (i.e., LCM, LMM, MLCM). An application using the Educational Longitudinal Study of 2002 (ELS:2002) illustrates the usefulness of the MLMM in describing the dynamics of change. Types of random effects and several technical issues in estimation are discussed. Future extensions include incorporating covariates, relaxing the model parameters, and developing graphical representations of models and results are also proposed. The MLMM provides conceptual models and estimation tools to model movements between latent states for nested longitudinal discrete data. An MLMM allows researchers to extend the focus from individual-level to higher-level while taking into account the effects of individuals' group membership. Analyzing data using an MLMM clearly has many advantages over traditional single-level models in terms of understanding the underlying structures and the dynamics of change.
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