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.

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.

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.

Severity of driver injury and vehicle damage in traffic crashes at intersections: A Bayesian hierarchical analysis

Most crash severity studies ignored severity correlations between driver-vehicle units involved in the same crashes. Models without accounting for these within-crash correlations will result in biased estimates in the factor effects. This study developed a Bayesian hierarchical binomial logistic model to identify the significant factors affecting the severity level of driver injury and vehicle damage in traffic crashes at signalized intersections. Crash data in Singapore were employed to calibrate the model. Model fitness assessment and comparison using Intra-class Correlation Coefficient (ICC) and Deviance Information Criterion (DIC) ensured the suitability of introducing the crash-level random effects. Crashes occurring in peak time, in good street lighting condition, involving pedestrian injuries are associated with a lower severity, while those in night time, at T/Y type intersections, on right-most lane, and installed with red light camera have larger odds of being severe. Moreover, heavy vehicles have a better resistance on severe crash, while crashes involving two-wheel vehicles, young or aged drivers, and the involvement of offending party are more likely to result in severe injuries.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

Effect of temperature and precipitation on salmonellosis cases in South-East Queensland, Australia: An observational study

Objective Foodborne illnesses in Australia, including salmonellosis, are estimated to cost over $A1.25 billion annually. The weather has been identified as being influential on salmonellosis incidence, as cases increase during summer, however time series modelling of salmonellosis is challenging because outbreaks cause strong autocorrelation. This study assesses whether switching models is an improved method of estimating weather–salmonellosis associations. Design We analysed weather and salmonellosis in South-East Queensland between 2004 and 2013 using 2 common regression models and a switching model, each with 21-day lags for temperature and precipitation. Results The switching model best fit the data, as judged by its substantial improvement in deviance information criterion over the regression models, less autocorrelated residuals and control of seasonality. The switching model estimated a 5°C increase in mean temperature and 10 mm precipitation were associated with increases in salmonellosis cases of 45.4% (95% CrI 40.4%, 50.5%) and 24.1% (95% CrI 17.0%, 31.6%), respectively. Conclusions Switching models improve on traditional time series models in quantifying weather–salmonellosis associations. A better understanding of how temperature and precipitation influence salmonellosis may identify where interventions can be made to lower the health and economic costs of salmonellosis.

Modélisation des bi-grappes et sélection des variables pour des données de grande dimension : application aux données d’expression génétique

Les simulations ont été implémentées avec le programme Java.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Joint data assimilation of satellite reflectance and net ecosystem exchange data constrains ecosystem carbon fluxes at a high-elevation subalpine forest

We utilized an ecosystem process model (SIPNET, simplified photosynthesis and evapotranspiration model) to estimate carbon fluxes of gross primary productivity and total ecosystem respiration of a high-elevation coniferous forest. The data assimilation routine incorporated aggregated twice-daily measurements of the net ecosystem exchange of CO2 (NEE) and satellite-based reflectance measurements of the fraction of absorbed photosynthetically active radiation (fAPAR) on an eight-day timescale. From these data we conducted a data assimilation experiment with fifteen different combinations of available data using twice-daily NEE, aggregated annual NEE, eight-day f AP AR, and average annual fAPAR. Model parameters were conditioned on three years of NEE and fAPAR data and results were evaluated to determine the information content from the different combinations of data streams. Across the data assimilation experiments conducted, model selection metrics such as the Bayesian Information Criterion and Deviance Information Criterion obtained minimum values when assimilating average annual fAPAR and twice-daily NEE data. Application of wavelet coherence analyses showed higher correlations between measured and modeled fAPAR on longer timescales ranging from 9 to 12 months. There were strong correlations between measured and modeled NEE (R2, coefficient of determination, 0.86), but correlations between measured and modeled eight-day fAPAR were quite poor (R2 = −0.94). We conclude that this inability to determine fAPAR on eight-day timescale would improve with the considerations of the radiative transfer through the plant canopy. Modeled fluxes when assimilating average annual fAPAR and annual NEE were comparable to corresponding results when assimilating twice-daily NEE, albeit at a greater uncertainty. Our results support the conclusion that for this coniferous forest twice-daily NEE data are a critical measurement stream for the data assimilation. The results from this modeling exercise indicate that for this coniferous forest, average annuals for satellite-based fAPAR measurements paired with annual NEE estimates may provide spatial detail to components of ecosystem carbon fluxes in proximity of eddy covariance towers. Inclusion of other independent data streams in the assimilation will also reduce uncertainty on modeled values.