Performance Of Model Selection Criteria Research Articles

Clustering sparse binary data with hierarchical Bayesian Bernoulli mixture model

Sparsity in features presents a big technical challenge to existing clustering methods for categorical data. Hierarchical Bayesian Bernoulli mixture model (HBBMM) incorporates constrained empirical Bayes priors for model parameters, so the resulting Expectation Maximization (EM) algorithm of estimator searching is confined in a proper region. The EM algorithm enables to obtain the maximum a posterior (MAP) estimation, in which cluster labels are simultaneously assigned. Three criteria are proposed to identify defining features of individual clusters, leading to understanding of the underlying data structures. Information based model selection criterion is applied to determine the number of clusters. Estimation consistency and performance of model selection criteria are investigated. Two real-world sparse categorical datasets are analyzed with the proposed method.

Assessment of the number of components in Gaussian mixture models in the presence of multiple local maximizers

Gaussian mixtures are very flexible in representing the underlying structure in the data. However, the likelihood inference for Gaussian mixtures with unrestricted covariance matrices is theoretically and practically challenging because the likelihood function is unbounded and often has multiple local maximizers. As shown in the numerical studies of this paper, the presence of multiple local maximizers including spurious local maximizers affects the performances of model selection criteria used to choose the number of components. In this paper we propose a new type of likelihood-based estimator, a gradient-based k-deleted maximum likelihood estimator, for Gaussian mixture models. The proposed estimator is designed to avoid spurious local maximizers and choose a statistically desirable local maximizer in the presence of multiple local maximizers. We first prove the consistency of the proposed estimator and then examine, by a real-data example and simulation studies, the performance of the proposed method in the likelihood-based model selection criteria commonly used to assess the number of components in Gaussian mixture models.

Model selection criteria for reduced rank multivariate time series: a simulation study

The main focus of our paper is to compare the performance of different model selection criteria used for multivariate reduced rank time series. We consider one of the most commonly used reduced rank model, that is, the reduced rank vector autoregression (RRVAR (p, r)) introduced by Velu et al. [Reduced rank models for multiple time series. Biometrika. 1986;7(31):105–118]. In our study, the most popular model selection criteria are included. The criteria are divided into two groups, that is, simultaneous selection and two-step selection criteria, accordingly. Methods from the former group select both an autoregressive order p and a rank r simultaneously, while in the case of two-step criteria, first an optimal order p is chosen (using model selection criteria intended for the unrestricted VAR model) and then an optimal rank r of coefficient matrices is selected (e.g. by means of sequential testing). Considered model selection criteria include well-known information criteria (such as Akaike information criterion, Schwarz criterion, Hannan–Quinn criterion, etc.) as well as widely used sequential tests (e.g. the Bartlett test) and the bootstrap method. An extensive simulation study is carried out in order to investigate the efficiency of all model selection criteria included in our study. The analysis takes into account 34 methods, including 6 simultaneous methods and 28 two-step approaches, accordingly. In order to carefully analyse how different factors affect performance of model selection criteria, we consider over 150 simulation settings. In particular, we investigate the influence of the following factors: time series dimension, different covariance structure, different level of correlation among components and different level of noise (variance). Moreover, we analyse the prediction accuracy concerned with the application of the RRVAR model and compare it with results obtained for the unrestricted vector autoregression. In this paper, we also present a real data application of model selection criteria for the RRVAR model using the Polish macroeconomic time series data observed in the period 1997–2007.

The Impact of Varied Discrimination Parameters on Mixed-Format Item Response Theory Model Selection

Whittaker, Chang, and Dodd compared the performance of model selection criteria when selecting among mixed-format IRT models and found that the criteria did not perform adequately when selecting the more parameterized models. It was suggested by M. S. Johnson that the problems when selecting the more parameterized models may be because of the low variance of the discrimination parameters used to generate the data. This simulation study reproduced the Whittaker et al. study by incorporating more variability in the discrimination parameter estimates used to generate the data. The results indicated that the majority of the criteria performed more accurately when selecting the more parameterized models. Differences among the criteria performance under certain conditions and implications for model selection practice are discussed.

Performances of Bayesian model selection criteria for generalized linear models with non-ignorably missing covariates

This article deals with model comparison as an essential part of generalized linear modelling in the presence of covariates missing not at random (MNAR). We provide an evaluation of the performances of some of the popular model selection criteria, particularly of deviance information criterion (DIC) and weighted L (WL) measure, for comparison among a set of candidate MNAR models. In addition, we seek to provide deviance and quadratic loss-based model selection criteria with alternative penalty terms targeting directly the MNAR models. This work is motivated by the need in the literature to understand the performances of these important model selection criteria for comparison among a set of MNAR models. A Monte Carlo simulation experiment is designed to assess the finite sample performances of these model selection criteria in the context of interest under different scenarios for missingness amounts. Some naturally driven DIC and WL extensions are also discussed and evaluated.

Ecological niche modeling in Maxent: the importance of model complexity and the performance of model selection criteria

Maxent, one of the most commonly used methods for inferring species distributions and environmental tolerances from occurrence data, allows users to fit models of arbitrary complexity. Model complexity is typically constrained via a process known as L1 regularization, but at present little guidance is available for setting the appropriate level of regularization, and the effects of inappropriately complex or simple models are largely unknown. In this study, we demonstrate the use of information criterion approaches to setting regularization in Maxent, and we compare models selected using information criteria to models selected using other criteria that are common in the literature. We evaluate model performance using occurrence data generated from a known "true" initial Maxent model, using several different metrics for model quality and transferability. We demonstrate that models that are inappropriately complex or inappropriately simple show reduced ability to infer habitat quality, reduced ability to infer the relative importance of variables in constraining species' distributions, and reduced transferability to other time periods. We also demonstrate that information criteria may offer significant advantages over the methods commonly used in the literature.

Model selection for nonlinear time series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.