Notes

Categorising ultra-processed food in large-scale cohort reports: facts in the Nurses' Well being Research, medical Professionals Follow-up Study, along with the Growing Up Today Study.
One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance hyperparameters for estimating the treatment effect in a two-group randomized controlled trial. Assuming a random sample of treatment effect sizes is obtained from past studies, the hyper priors can be constructed based on the sampling distributions of the effect size mean and precision. The performance of the hierarchical Bayes approach was compared with the empirical Bayes approach (hyperparameters are fixed values or point estimates) and the ordinary least squares (OLS) method via simulation. The design factors for data generation included the sample treatment effect size, treatment/control group size ratio, and sample size. Each generated data set was analyzed using the hierarchical Bayes approach with three hyper priors, the empirical Bayes approach with twelve priors (including correct and inaccurate priors), and the OLS method. Results indicated that the proposed hierarchical Bayes approach generally outperformed the empirical Bayes approach and the OLS method, especially with small samples. When more sample effect sizes were available, the treatment effect was estimated more accurately regardless of the sample sizes. Practical implications and future research directions are discussed.The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels-one for the responses and one for the response times-that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a skew distribution with a support from zero to infinity. 1-Naphthyl PP1 cost Such a support is unrealistic as the solution process demands a minimal processing time that sets a response time threshold. Ignoring this response time threshold misspecifies the model and threatens the validity of model-based inferences. In this article, the response time model of van der Linden is replaced by a model that is based on the three-parameter lognormal distribution. The three-parameter lognormal distribution extends the lognormal distribution by an additional location parameter that bounds the support away from zero. Two different approaches to model fitting are proposed and evaluated with regard to parameter recovery in a simulation study. The extended model is applied to two data sets. In both data sets, the extension improves the fit of the hierarchical model.Bayesian structural equation modeling (BSEM) is a flexible tool for the exploration and estimation of sparse factor loading structures; that is, most cross-loading entries are zero and only a few important cross-loadings are nonzero. The current investigation was focused on the BSEM with small-variance normal distribution priors (BSEM-N) for both variable selection and model estimation. The prior sensitivity in BSEM-N was explored in factor analysis models with sparse loading structures through a simulation study (Study 1) and an empirical example (Study 2). Study 1 examined the prior sensitivity in BSEM-N based on the model fit, population model recovery, true and false positive rates, and parameter estimation. Seven shrinkage priors on cross-loadings and five noninformative/vague priors on other model parameters were examined. Study 2 provided a real data example to illustrate the impact of various priors on model fit and parameter selection and estimation. Results indicated that when the 95% credible intervals of shrinkage priors barely covered the population cross-loading values, it resulted in the best balance between true and false positives. If the goal is to perform variable selection, a sparse cross-loading structure is required, preferably with a minimal number of nontrivial cross-loadings and relatively high primary loading values. To improve parameter estimates, a relatively large prior variance is preferred. When cross-loadings are relatively large, BSEM-N with zero-mean priors is not recommended for the estimation of cross-loadings and factor correlations.The long-term accumulation of biodiversity has been punctuated by remarkable evolutionary transitions that allowed organisms to exploit new ecological opportunities. Mesozoic flying reptiles (the pterosaurs), which dominated the skies for more than 150 million years, were the product of one such transition. The ancestors of pterosaurs were small and probably bipedal early archosaurs1, which were certainly well-adapted to terrestrial locomotion. Pterosaurs diverged from dinosaur ancestors in the Early Triassic epoch (around 245 million years ago); however, the first fossils of pterosaurs are dated to 25 million years later, in the Late Triassic epoch. Therefore, in the absence of proto-pterosaur fossils, it is difficult to study how flight first evolved in this group. Here we describe the evolutionary dynamics of the adaptation of pterosaurs to a new method of locomotion. The earliest known pterosaurs took flight and subsequently appear to have become capable and efficient flyers. However, it seems clear that transitioning between forms of locomotion2,3-from terrestrial to volant-challenged early pterosaurs by imposing a high energetic burden, thus requiring flight to provide some offsetting fitness benefits. Using phylogenetic statistical methods and biophysical models combined with information from the fossil record, we detect an evolutionary signal of natural selection that acted to increase flight efficiency over millions of years. Our results show that there was still considerable room for improvement in terms of efficiency after the appearance of flight. However, in the Azhdarchoidea4, a clade that exhibits gigantism, we test the hypothesis that there was a decreased reliance on flight5-7 and find evidence for reduced selection on flight efficiency in this clade. Our approach offers a blueprint to objectively study functional and energetic changes through geological time at a more nuanced level than has previously been possible.
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