Marker selection by Akaike information criterion and Bayesian information criterion

We carried out a discriminant analysis with identity by descent (IBD) at each marker as inputs, and the sib pair type (affected-affected versus affected-unaffected) as the output. Using simple logistic regression for this discriminant analysis, we illustrate the importance of comparing models with different number of parameters. Such model comparisons are best carried out using either the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). When AIC (or BIC) stepwise variable selection was applied to the German Asthma data set, a group of markers were selected which provide the best fit to the data (assuming an additive effect). Interestingly, these 25-26 markers were not identical to those with the highest (in magnitude) single-locus lod scores.

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

Using information criteria to select the correct variance–covariance structure for longitudinal data in ecology

1. Ecological data sets often use clustered measurements or use repeated sampling in a longitudinal design. Choosing the correct covariance structure is an important step in the analysis of such data, as the covariance describes the degree of similarity among the repeated observations. 2. Three methods for choosing the covariance are: the Akaike information criterion (AIC), the quasi-information criterion (QIC), and the deviance information criterion (DIC). We compared the methods using a simulation study and using a data set that explored effects of forest fragmentation on avian species richness over 15 years. 3. The overall success was 80.6% for the AIC, 29.4% for the QIC and 81.6% for the DIC. For the forest fragmentation study the AIC and DIC selected the unstructured covariance, whereas the QIC selected the simpler autoregressive covariance. Graphical diagnostics suggested that the unstructured covariance was probably correct. 4. We recommend using DIC for selecting the correct covariance structure.

Modified Information Criteria and Selection of Long Memory Time Series Models

The problem of model selection of a univariate long memory time series is investigated once a semi parametric estimator for the long memory parameter has been used. Standard information criteria are not consistent in this case. A Modified Information Criterion (MIC) that overcomes these difficulties is introduced and proofs that show its asymptotic validity are provided. The results are general and cover a wide range of short memory processes. Simulation evidence compares the new and existing methodologies and empirical applications in monthly inflation and daily realized volatility are presented.

Categorical data clustering using a minimum message length criterion

Research on cluster analysis for categorical data continues to develop, new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. We propose a new approach in which clustering and the estimation of the number of clusters is done simultaneously for categorical data. We assume that the data originate from a finite mixture of multinomial distributions and use a minimum message length criterion (MML) to select the number of clusters (Wallace and Bolton, 1986). For this purpose, we implement an EM-type algorithm (Silvestre et al., 2008) based on the (Figueiredo and Jain, 2002) approach. The novelty of the approach rests on the integration of the model estimation and selection of the number of clusters in a single algorithm, rather than selecting this number based on a set of pre-estimated candidate models. The performance of our approach is compared with the use of Bayesian Information Criterion (BIC) (Schwarz, 1978) and Integrated Completed Likelihood (ICL) (Biernacki et al., 2000) using synthetic data. The obtained results illustrate the capacity of the proposed algorithm to attain the true number of cluster while outperforming BIC and ICL since it is faster, which is especially relevant when dealing with large data sets.

Selecting from amongst non–nested conditional variance models: information criteria and portfolio determination

We consider the finite sample properties of model selection by information criteria in conditionally heteroscedastic models. Recent theoretical results show that certain popular criteria are consistent in that they will select the true model asymptotically with probability 1. To examine the empirical relevance of this property, Monte Carlo simulations are conducted for a set of non–nested data generating processes (DGPs) with the set of candidate models consisting of all types of model used as DGPs. In addition, not only is the best model considered but also those with similar values of the information criterion, called close competitors, thus forming a portfolio of eligible models. To supplement the simulations, the criteria are applied to a set of economic and financial series. In the simulations, the criteria are largely ineffective at identifying the correct model, either as best or a close competitor, the parsimonious GARCH(1, 1) model being preferred for most DGPs. In contrast, asymmetric models are generally selected to represent actual data. This leads to the conjecture that the properties of parameterizations of processes commonly used to model heteroscedastic data are more similar than may be imagined and that more attention needs to be paid to the behaviour of the standardized disturbances of such models, both in simulation exercises and in empirical modelling.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Mutual Information and Perplexity based Clustering of Dialogue Information for Dynamic Adaptation of Language Models

We present two approaches to cluster dialogue-based information obtained by the speech understanding module and the dialogue manager of a spoken dialogue system. The purpose is to estimate a language model related to each cluster, and use them to dynamically modify the model of the speech recognizer at each dialogue turn. In the first approach we build the cluster tree using local decisions based on a Maximum Normalized Mutual Information criterion. In the second one we take global decisions, based on the optimization of the global perplexity of the combination of the cluster-related LMs. Our experiments show a relative reduction of the word error rate of 15.17%, which helps to improve the performance of the understanding and the dialogue manager modules.

Mutual Information and Perplexity based Clustering of Dialogue Information for Dynamic Adaptation of Language Models

We present two approaches to cluster dialogue-based information obtained by the speech understanding module and the dialogue manager of a spoken dialogue system. The purpose is to estimate a language model related to each cluster, and use them to dynamically modify the model of the speech recognizer at each dialogue turn. In the first approach we build the cluster tree using local decisions based on a Maximum Normalized Mutual Information criterion. In the second one we take global decisions, based on the optimization of the global perplexity of the combination of the cluster-related LMs. Our experiments show a relative reduction of the word error rate of 15.17%, which helps to improve the performance of the understanding and the dialogue manager modules.

Bayesian latent trait modeling of migraine symptom data

Definition of disease phenotype is a necessary preliminary to research into genetic causes of a complex disease. Clinical diagnosis of migraine is currently based on diagnostic criteria developed by the International Headache Society. Previously, we examined the natural clustering of these diagnostic symptoms using latent class analysis (LCA) and found that a four-class model was preferred. However, the classes can be ordered such that all symptoms progressively intensify, suggesting that a single continuous variable representing disease severity may provide a better model. Here, we compare two models: item response theory and LCA, each constructed within a Bayesian context. A deviance information criterion is used to assess model fit. We phenotyped our population sample using these models, estimated heritability and conducted genome-wide linkage analysis using Merlin-qtl. LCA with four classes was again preferred. After transformation, phenotypic trait values derived from both models are highly correlated (correlation = 0.99) and consequently results from subsequent genetic analyses were similar. Heritability was estimated at 0.37, while multipoint linkage analysis produced genome-wide significant linkage to chromosome 7q31-q33 and suggestive linkage to chromosomes 1 and 2. We argue that such continuous measures are a powerful tool for identifying genes contributing to migraine susceptibility.

Bayes factor based speaker clustering for speaker diarization

This paper proposes the use of the Bayes Factor to replace the Bayesian Information Criterion (BIC) as a criterion for speaker clustering within a speaker diarization system. The BIC is one of the most popular decision criteria used in speaker diarization systems today. However, it will be shown in this paper that the BIC is only an approximation to the Bayes factor of marginal likelihoods of the data given each hypothesis. This paper uses the Bayes factor directly as a decision criterion for speaker clustering, thus removing the error introduced by the BIC approximation. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, leading to a 14.7% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.