Detecting parameter redundancy

Catchpole, Edward A.; Morgan, Byron J. T.

doi:10.1093/biomet/84.1.187

Cited by 192 publications

(212 citation statements)

References 12 publications

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“…Although we do not investigate the sufficient conditions required for the model to be identifiability in this paper, we rely on the more general methodology of detecting parameter redundancy [19,20].…”

Section: Current Status Datamentioning

confidence: 99%

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Hens

Wienke

Aerts

et al. 2009

Statistics in Medicine

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SUMMARYFrailty models are often used to study the individual heterogeneity in multivariate survival analysis. Whereas the shared frailty model is widely applied, the correlated frailty model has gained attention because it elevates the restriction of unobserved factors to act similar within clusters. Estimating frailty models is not straightforward due to various types of censoring. In this paper, we study the behavior of the bivariate-correlated gamma frailty model for type I interval-censored data, better known as current status data. We show that applying a shared rather than a correlated frailty model to cross-sectionally collected serological data on hepatitis A and B leads to biased estimates for the baseline hazard and variance parameters.

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Section: Current Status Datamentioning

confidence: 99%

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Hens

Wienke

Aerts

et al. 2009

Statistics in Medicine

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“…It does require symbolic calculations, but these can be carried out readily using computer algebra software. Catchpole and colleagues (e.g., Catchpole & Morgan, 1997Catchpole, Morgan, & Freeman, 1998;Catchpole, Morgan, & Viallefont, 2002) developed this method in a series of articles for capture-recapture models. They also considered the problem of deriving identifying constraints, given an unidentified model.…”

Section: Identificationmentioning

confidence: 99%

“…Based on the experimental design, for example, in the case of multiple within-and/or between-participant conditions, the observations may be separated into K disjoint 2001; Catchpole & Morgan, 1997;Catchpole et al, 1998;Catchpole et al, 2002) emphasized its role in detecting parameter redundancy. Catchpole and Morgan (1997) distinguished two hierarchically ordered kinds of locally identified models: essentially and conditionally full rank models.…”

Section: Mpt Modelsmentioning

confidence: 99%

“…The required calculations to establish global identification can become intractable in complex models. We show how to establish local identification in multinomial processing tree models, based on formal methods independently proposed by Catchpole and Morgan (1997) and by Bekker, Merckens, and Wansbeek (1994). This approach is illustrated with multinomial processing tree models for the source-monitoring paradigm in memory research.…”

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confidence: 99%

“…expressed as a function of fewer than the original number of parameters (Catchpole & Morgan, 1997). If a model is not parameter redundant, it is locally, and possibly even globally, identified; we go into the details of local and global identification in terms of MPT models below.…”

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confidence: 99%

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Parameter identification in multinomial processing tree models

Schmittmann

Dolan

Raijmakers

et al. 2010

Behavior Research Methods

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Multinomial processing tree (MPT) models form an increasingly popular class of stochastic models for categorical data that have applications in a variety of research areas in cognitive, differential, and social psychology (e.g., Batchelder & Riefer, 1999Erdfelder et al., 2009;Stahl, 2006). For example, Batchelder and Riefer (1999) discussed over 80 applications of MPT models in various areas of psychology, including memory, perception, and reasoning. The statistical theory of MPT models, including maximum likelihood (ML) parameter estimation, overall model testing, and tests of specific hypotheses within models, has been discussed by Hu and Batchelder (1994) and by Riefer and Batchelder (1988). Flexible software to fit MPT models by means of ML estimation has been developed by Hu and Phillips (1999), Moshagen (2010), Rothkegel (1999), and Stahl and Klauer (2007. MPT models entail a reparameterization of the cell probabilities of the multinomial or product-multinomial distribution (Andersen, 1980;Bishop, Fienberg, & Holland, 1975) in terms of parameters assumed to represent the probabilities of underlying cognitive processes. The underlying cognitive architecture is represented as a rooted tree, in which each branch represents a processing sequence leading to an observable categorical response. More than one branch may terminate in a given response.In MPT models, as in all statistical models, global model identification (the ability to infer unique parameter values from data) is an important issue. A common cause of nonidentifiability of a model is parameter redundancy, in which case the likelihood of the model can be expressed as a function of fewer than the original number of parameters (Catchpole & Morgan, 1997). If a model is not parameter redundant, it is locally, and possibly even globally, identified; we go into the details of local and global identification in terms of MPT models below.In an MPT model, there is a function f ( ) that maps the model's parameter space into the set of possible multinomial probability distributions. Global identification can be established by proving that inequality of two parameter vectors implies inequality of the modeled multi nomial cell probability vectors f ( ) f ( ) for all parameter vectors and in the parameter space Meiser, 2005;Riefer & Batchelder, 1988; see also Bishop et al., 1975, p. 510). The required calculations for establishing global identification can become tedious, and even intractable, in complex models. In this case, the next best thing is to establish local identification; that is, implies f ( ) f ( ) for all in an open neighborhood around . One can empirically investigate local identification at a specific point G in the parameter space by fitting the generating MPT model to artificial (simulated) data generated by G , or to exact summary statistics-that is, the expected cell counts, derived from the probabilities f ( G ) implied by the generating MPT model. Obtaining parameter estimates sufficiently close to the true values G (in the case of simulated...

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