Fast computation of the deviance information criterion for latent variable models

Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.

Bayesian Criterion Based Variable Selection

Bayesian approaches for criterion based selection include the marginal likelihood based highest posterior model (HPM) and the deviance information criterion (DIC). The DIC is popular in practice as it can often be estimated from sampling based methods with relative ease and DIC is readily available in various Bayesian software. We find that sensitivity of DIC based selection can be high, in the range of 90 - 100%. However, correct selection by DIC can be in the range of 0 - 2%. These performances persist consistently with increase in sample size. We establish that both marginal likelihood and DIC asymptotically disfavor under-fitted models, explaining the high sensitivities of both criteria. However, mis-selection probability of DIC remains bounded below by a positive constant in linear models with g -priors whereas mis-selection probability by marginal likelihood converges to 0 under certain conditions. A consequence of our results is that not only the DIC cannot asymptotically differentiate between the data-generating and an over-fitted model, but, in fact, it cannot asymptotically differentiate between two over-fitted models as well. We illustrate these results in multiple simulation studies and in a biomarker selection problem on cancer cachexia of non-small cell lung cancer patients. We further study performances of HPM and DIC in generalized linear model as practitioners often choose to use DIC that is readily available in software in such non-conjugate settings.

Predictors of stunting among children age 6-59 months in Ethiopia using Bayesian multi-level analysis

In developing countries including Ethiopia stunting remained a major public health burden. It is associated with adverse health consequences, thus, investigating predictors of childhood stunting is crucial to design appropriate strategies to intervene the problem stunting. The study uses data from the Ethiopian Demographic and Health Survey (EDHS) conducted from January 18 to June 27, 2016 in Ethiopia. A total of 8117 children aged 6-59 months were included in the study with a stratified two stage cluster sampling technique. A Bayesian multilevel logistic regression was fitted using Win BUGS version 1.4.3 software to identify predictors of stunting among children age 6-59 months. Adjusted odds ratio (AOR) with 95% credible intervals was used to ascertain the strength and direction of association. In this study, increasing child's age (AOR = 1.022; 95% CrI 1.018-1.026), being a male child (AOR = 1.16; 95%CrI 1.05-1.29), a twin (AOR = 2.55; 95% CrI 1.78-3.56), having fever (AOR = 1.23; 95%CrI 1.02-1.46), having no formal education (AOR = 1.99; 95%CrI 1.28-2.96) and primary education (AOR = 83; 95%CrI 1.19-2.73), birth interval less than 24 months (AOR = 1.40; 95% CrI 1.20-1.61), increasing maternal BMI (AOR = 0.95; 95% CrI 0.93-0.97), and poorest household wealth status (AOR = 1.78; 95% CrI 1.35-2.30) were predictors of childhood stunting at individual level. Similarly, region and type of toilet facility were predictors of childhood stunting at community level. The current study revealed that both individual and community level factors were predictors of childhood stunting in Ethiopia. Thus, more emphasize should be given by the concerned bodies to intervene the problem stunting by improving maternal education, promotion of girl education, improving the economic status of households, promotion of context-specific child feeding practices, improving maternal nutrition education and counseling, and improving sanitation and hygiene practices.

Seemingly unrelated regression with measurement error: estimation via Markov Chain Monte Carlo and mean field variational Bayes approximation

Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a seemingly unrelated regression model with measurement error in the covariates and introduces two novel estimation methods: a pure Bayesian algorithm (based on Markov chain Monte Carlo techniques) and its mean field variational Bayes (MFVB) approximation. The MFVB method has the added advantage of being computationally fast and can handle big data. An issue pertinent to measurement error models is parameter identification, and this is resolved by employing a prior distribution on the measurement error variance. The methods are shown to perform well in multiple simulation studies, where we analyze the impact on posterior estimates for different values of reliability ratio or variance of the true unobserved quantity used in the data generating process. The paper further implements the proposed algorithms in an application drawn from the health literature and shows that modeling measurement error in the data can improve model fitting.

J, Mate BR. Fin whale movements in the Gulf of California, Mexico, from satellite telemetry

Fin whales (Balaenoptera physalus) have a global distribution, but the population inhabiting the Gulf of California (GoC) is thought to be geographically and genetically isolated. However, their distribution and movements are poorly known. The goal of this study was to describe fin whale movements for the first time from 11 Argos satellite tags deployed in the southwest GoC in March 2001. A Bayesian Switching State-Space Model was applied to obtain improved locations and to characterize movement behavior as either "area-restricted searching" (indicative of patch residence, ARS) or "transiting" (indicative of moving between patches). Model performance was assessed with convergence diagnostics and by examining the distribution of the deviance and the behavioral parameters from Markov Chain Monte Carlo models. ARS was the predominant mode behavior 83% of the time during both the cool (December-May) and warm seasons (June-November), with slower travel speeds (mean = 0.84 km/h) than during transiting mode (mean = 3.38 km/h). We suggest ARS mode indicates either foraging activities (year around) or reproductive activities during the winter (cool season). We tagged during the cool season, when the whales were located in the Loreto-La Paz Corridor in the southwestern GoC, close to the shoreline. As the season progressed, individuals moved northward to the Midriff Islands and the upper gulf for the warm season, much farther from shore. One tag lasted long enough to document a whale's return to Loreto the following cool season. One whale that was originally of undetermined sex, was tagged in the Bay of La Paz and was photographed 10 years later with a calf in the nearby San Jose Channel, suggesting seasonal site fidelity. The tagged whales moved along the western GoC to the upper gulf seasonally and did not transit to the eastern GoC south of the Midriff Islands. No tagged whales left the GoC, providing supporting evidence that these fin whales are a resident population.

Comparing hierarchical models via the marginalized deviance information criterion

Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent.