Model Selection in Mixture Modeling
Model Selection in Mixture Modeling

Author: Emilie Shireman

Publisher:

Published: 2016

Total Pages: 72

ISBN-13:

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In the psychological sciences, mixture modeling (also referred to as latent class or latent profile analysis) is very commonly used to find sub-populations within a sample. However, the process by which researchers select a model (i.e., how many sub-populations and how many covariance parameters) is not standardized. Furthermore, many techniques that researchers use to select a model are ad hoc and have varied statistical theoretical support. This dissertation systematically examines three commonly used but not formally tested model selection heuristics for mixture modeling: (1) using several fit indices to collectively select a model, (2) using the difference in fit to differentiate "weak" versus "strong" evidence of one solution over another, and (3) examining the difficulty in convergence to indicate that a model is over-specified.

Methods for Model Selection in Applied Science and Engineering
Methods for Model Selection in Applied Science and Engineering

Author: Richard V. Field (Jr)

Publisher:

Published: 2004

Total Pages: 208

ISBN-13:

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Mathematical models are developed and used to study the properties of complex systems and/or modify these systems to satisfy some performance requirements in just about every area of applied science and engineering. A particular reason for developing a model, e.g., performance assessment or design, is referred to as the model use. Our objective is the development of a methodology for selecting a model that is sufficiently accurate for an intended use. Information on the system being modeled is, in general, incomplete, so that there may be two or more models consistent with the available information. The collection of these models is called the class of candidate models. Methods are developed for selecting the optimal member from a class of candidate models for the system. The optimal model depends on the available information, the selected class of candidate models, and the model use. Classical methods for model selection, including the method of maximum likelihood and Bayesian methods, as well as a method employing a decision-theoretic approach, are formulated to select the optimal model for numerous applications. There is no requirement that the candidate models be random. Classical methods for model selection ignore model use and require data to be available. Examples are used to show that these methods can be unreliable when data is limited. The decision-theoretic approach to model selection does not have these limitations, and model use is included through an appropriate utility function. This is especially important when modeling high risk systems, where the consequences of using an inappropriate model for the system can be disastrous. The decision-theoretic method for model selection is developed and applied for a series of complex and diverse applications. These include the selection of the: (1) optimal order of the polynomial chaos approximation for non-Gaussian random variables and stationary stochastic processes, (2) optimal pressure load model to be applied to a spacecraft during atmospheric re-entry, and (3) optimal design of a distributed sensor network for the purpose of vehicle tracking and identification.

Model Selection and Model Averaging
Model Selection and Model Averaging

Author: Gerda Claeskens

Publisher: Cambridge University Press

Published: 2008-07-28

Total Pages: 312

ISBN-13: 1139471805

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Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer? Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled, with discussions of frequentist and Bayesian methods; model averaging schemes are presented. Real-data examples are complemented by derivations providing deeper insight into the methodology, and instructive exercises build familiarity with the methods. The companion website features Data sets and R code.

Survey of Model Selection and Model Combination
Survey of Model Selection and Model Combination

Author: Mingyang Xu

Publisher:

Published: 2011

Total Pages: 0

ISBN-13:

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A general statistical modeling problem is that given a class of competing models and new data, how one can improve the overall model performance. In general, there exist two solutions for this problem, namely model selection and model combination. Model selection is to select a single best model while model combination builds a composite model by aggregating all available information. However, except for this difference model selection and model combination share the most important key elements such as model performance evaluation and are closely related to each other. A generalized flexible framework for designing predictive model performance evaluation method is put forward and possible choices for its two components, that is, model distance measure and generability estimation, are categorized and reviewed. After than, a unified framework is proposed to accommodate both model selection and model combination, in which model selection works as an extreme case of model combination. Finally, many model selection and combination methods in the literature, all of which can be fit into the unified framework, are reviewed.