Latent Transition Analysis With a Mixture Item Response Theory Measurement Model

Cho, Sun‐Joo; Cohen, Allan S.; Kim, Seock-Ho; Bottge, Brian A.

doi:10.1177/0146621610362978

Cited by 24 publications

(32 citation statements)

References 38 publications

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“…Outcomes within class can mutually depend on continuously distributed latent factor(s) to accommodate associations among responses within class and represent systematic individual variability within class. This extension has appeared under separate names; for LPA it is called a factor mixture model (e.g., Lubke & Muthén, 2005;Yung, 1997); for GBT, a growth mixture model (e.g., Muthén & Shedden, 1999;Verbeke & Lesaffre, 1996); for LCA, a categorical-item factor mixture or IRT mixture model (Lubke & Neale, 2008;Mislevy & Verhelst, 1990;Muthén & Asparouhov, 2006;Rost, 1990); and for LTA, LTA with a categorical-item factor/IRT measurement model (Cho, Cohen, Kim, & Bottge, 2010;Nylund, 2007). Here we highlight the similarity of this extension across multivariate mixtures by reviewing the inclusion of one factor per class/state .q D 1/ in LPA, LCA, GBT, and LTA.…”

Section: Extension: Hybrid Mixture Modelsmentioning

confidence: 99%

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Understanding Linkages Among Mixture Models

Sterba

2013

Multivariate Behavioral Research

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The methodological literature on mixture modeling has rapidly expanded in the past 15 years, and mixture models are increasingly applied in practice. Nonetheless, this literature has historically been diffuse, with different notations, motivations, and parameterizations making mixture models appear disconnected. This pedagogical review facilitates an integrative understanding of mixture models. First, 5 prototypic mixture models are presented in a unified format with incremental complexity while highlighting their mutual reliance on familiar probability laws, common assumptions, and shared aspects of interpretation. Second, 2 recent extensionshybrid mixtures and parallel-process mixtures-are discussed. Both relax a key assumption of classic mixture models but do so in different ways. Similarities in construction and interpretation among hybrid mixtures and among parallel-process mixtures are emphasized. Third, the combination of both extensions is motivated and illustrated by means of an example on oppositional defiant and depressive symptoms. By clarifying how existing mixture models relate and can be combined, this article bridges past and current developments and provides a foundation for understanding new developments.

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Section: Extension: Hybrid Mixture Modelsmentioning

confidence: 99%

“…The approach to relaxing local independence from the LCA is used per timepoint in the LTA (Cho et al, 2010;Nylund, 2007). Equation (24) can be expanded to depend on˜1 i at Time 1 and Equation (25) can be expanded to depend oñ 2i at Time 2.…”

Section: Lta ! Lta With Categorical-item Factor Measurement Modelsmentioning

confidence: 99%

Understanding Linkages Among Mixture Models

Sterba

2013

Multivariate Behavioral Research

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“…These include classification of examinees into diagnostically useful groups [1], detection of differential item functioning [2][3][4][5][6], detection of differences in strategy use in problemsolving [7,8], modelling developmental stages in task solution [9], differential use of cognitive strategies [10][11][12], detection of speededness effects [1,13,14], personality assessment [15], and detection of response styles and faking in personality and organizational assessment [16]. With this increase in the number and application of MixIRT models has come a concurrent increase in the use of Markov chain Monte Carlo (MCMC) techniques for estimating the parameters of these models.…”

Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlo estimation of a mixture item response theory model

Cho

Cohen

Kim

2013

Journal of Statistical Computation and Simulation

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Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods.

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“…O. Muthén, , 2002. In this way, MSEM-RS is based on a more flexible measurement model than latent transition models (Collins & Wugalter, 1992), which are typically identified using categorical manifest variables (Cho, Cohen, Kim, & Bottge, 2010;Lanza, Patrick, & Maggs, 2010). In addition, in MSEM-RS, the emphasis may be placed on between-regime differences in how latent variables are implicated in a longitudinal change process.…”

Section: Discussionmentioning

confidence: 99%

Regime-Switching Bivariate Dual Change Score Model

Chow

Grimm

Filteau

et al. 2013

Multivariate Behavioral Research

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Mixture structural equation model with regime switching (MSEM-RS) provides one possible way of representing over-time heterogeneities in dynamic processes by allowing a system to manifest qualitatively or quantitatively distinct change processes conditional on the latent "regime" the system is in at a particular time point. Unlike standard mixture structural equation models such as growth mixture models, MSEM-RS allows individuals to transition between latent classes over time. This class of models, often referred to as regime-switching models in the time series and econometric applications, can be specified as regime-switching mixture structural equation models when the number of repeated measures involved is not large. We illustrate the empirical utility of such models using one special case-a regime-switching bivariate dual change score model in which two growth processes are allowed to manifest regime-dependent coupling relations with one another. The proposed model is illustrated using a set of longitudinal reading and arithmetic performance data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 study (ECLS-K; U.S. Department of Education, National Center for Education Statistics, 2010).

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Latent Transition Analysis With a Mixture Item Response Theory Measurement Model

Cited by 24 publications

References 38 publications

Understanding Linkages Among Mixture Models

Understanding Linkages Among Mixture Models

Markov chain Monte Carlo estimation of a mixture item response theory model

Regime-Switching Bivariate Dual Change Score Model

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