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I propose a new model, ordered Beta regression, for continuous distributions with both lower and upper bounds, such as data arising from survey slider scales, visual analog scales, and dose–response relationships. This model employs the cut point technique popularized by ordered logit to fit a single linear model to both continuous (0,1) and degenerate [0,1] responses. The model can be estimated with or without observations at the bounds, and as such is a general solution for these types of data. Employing a Monte Carlo simulation, I show that the model is noticeably more efficient than ordinary least squares regression, zero-and-one-inflated Beta regression, rescaled Beta regression, and fractional logit while fully capturing nuances in the outcome. I apply the model to a replication of the Aidt and Jensen (2014, European Economic Review 72, 52–75) study of suffrage extensions in Europe. The model can be fit with the R package ordbetareg to facilitate hierarchical, dynamic, and multivariate modeling.

In this paper, we estimate the difference | E h ( Z n ) − E h ( Y ) | between the expectations of real finite Lipschitz function h of the sum Z n = ( X 1 + ⋯ + X n ) /B n , where B n 2 = E ( X 1 + ⋯ + X n ) 2 > 0, and a standard normal random variable Y , where real centered random variables X 1 ,X 2 , … satisfy the φ -mixing condition, defined between the “past” and “ future”, or are m -dependent. In particular cases, under the condition ∑ r = 1 ∞ r φ ( r ) < ∞ or ∑ r = 1 ∞ r φ 1 / 2 ( r ) < ∞ , the obtained upper bounds for φ -mixing random variables are of order O ( n − 1 / 2 ). In addition, we refine the previously known upper bounds of order O (( m + 1) 1+ δ L 2+ δ,n ), where L 2+ δ,n is the Lyapunov fraction of order 2 + δ , for m -dependent random variables, supplementing them with explicit constants. We also separately present the case of independent r.v.s.

Background In medical, social, and behavioral research we often encounter datasets with a multilevel structure and multiple correlated dependent variables. These data are frequently collected from a study population that distinguishes several subpopulations with different (i.e., heterogeneous) effects of an intervention. Despite the frequent occurrence of such data, methods to analyze them are less common and researchers often resort to either ignoring the multilevel and/or heterogeneous structure, analyzing only a single dependent variable, or a combination of these. These analysis strategies are suboptimal: Ignoring multilevel structures inflates Type I error rates, while neglecting the multivariate or heterogeneous structure masks detailed insights. Methods To analyze such data comprehensively, the current paper presents a novel Bayesian multilevel multivariate logistic regression model. The clustered structure of multilevel data is taken into account, such that posterior inferences can be made with accurate error rates. Further, the model shares information between different subpopulations in the estimation of average and conditional average multivariate treatment effects. To facilitate interpretation, multivariate logistic regression parameters are transformed to posterior success probabilities and differences between them. Results A numerical evaluation compared our framework to less comprehensive alternatives and highlighted the need to model the multilevel structure: Treatment comparisons based on the multilevel model had targeted Type I error rates, while single-level alternatives resulted in inflated Type I errors. Further, the multilevel model was more powerful than a single-level model when the number of clusters was higher. A re-analysis of the Third International Stroke Trial data illustrated how incorporating a multilevel structure, assessing treatment heterogeneity, and combining dependent variables contributed to an in-depth understanding of treatment effects. Further, we demonstrated how Bayes factors can aid in the selection of a suitable model. Conclusion The method is useful in prediction of treatment effects and decision-making within subpopulations from multiple clusters, while taking advantage of the size of the entire study sample and while properly incorporating the uncertainty in a principled probabilistic manner using the full posterior distribution.

An individualized dynamic risk prediction model that incorporates all available information collected over the follow-up can be used to choose an optimal treatment strategy in realtime, although existing methods have not been designed to handle competing risks. In this study, we developed a landmark proportional subdistribution hazard (PSH) model and a comprehensive supermodel for dynamic risk prediction with competing risks. Simulations showed that our proposed models perform satisfactorily (assessed by the time-dependent relative difference, Brier score and area under the receiver operating characteristics curve) under PSH or non-PSH settings. The models were used to predict the probabilities of developing a distant metastasis among breast cancer patients where death was treated as a competing risk. Prediction can be estimated by using standard statistical packages.

Let X i , Y i i = 1 n be a sequence of independent bivariate random vectors. In this paper, we establish a refined Cramér-type moderate deviation theorem for the general self-normalized sum ∑ i = 1 n X i / ∑ i = 1 n Y i 2 1 / 2 , which unifies and extends the classical Cramér (Actual. Sci. Ind. 736 (1938) 5–23) theorem and the self-normalized Cramér-type moderate deviation theorems by Jing, Shao and Wang (Ann. Probab. 31 (2003) 2167–2215) as well as the further refined version by Wang (J. Theoret. Probab. 24 (2011) 307–329). The advantage of our result is evidenced through successful applications to weakly dependent random variables and self-normalized winsorized mean. Specifically, by applying our new framework on general self-normalized sum, we significantly improve Cramér-type moderate deviation theorems for one-dependent random variables, geometrically β-mixing random variables and causal processes under geometrical moment contraction. As an additional application, we also derive the Cramér-type moderate deviation theorems for self-normalized winsorized mean.

Regression models with log-transformed dependent variables are widely used by social scientists to investigate nonlinear relationships between variables. Unfortunately, this transformation complicates the substantive interpretation of estimation results and often leads to incomplete and sometimes even misleading interpretations. We focus on one valuable but underused method, the presentation of quantities of interest such as expected values or first differences on the original scale of the dependent variable. The procedure to derive these quantities differs in seemingly minor but critical aspects from the well-known procedure based on standard linear models. To improve empirical practice, we explain the underlying problem and develop guidelines that help researchers to derive meaningful interpretations from regression results of models with log-transformed dependent variables.

Assuring the quantity and quality of groundwater resources is essential for the well-being of human and ecological health, society, and the economy. For the last few decades, groundwater vulnerability modeling techniques have become essential for groundwater protection and management. Groundwater contamination is highly dynamic due to its dependency on recharge, which is a function of time-dependent parameters such as precipitation and evapotranspiration. Therefore, it is necessary to consider the time-series analysis in the “approximation” process to model the dynamic vulnerability of groundwater contamination. This systematic literature review (SLR) aims to critically review the methods used to evaluate the spatiotemporal assessment of groundwater vulnerability. The PRISMA method was employed to search web platforms and refine the collected research articles by applying certain inclusion and exclusion criteria. Despite the enormous growth in this field in recent years, spatiotemporal variations in precipitation and evapotranspiration were not considered considerably. Groundwater contamination vulnerability assessment needs to integrate the multicriteria decision support tools for better analysis of the subsurface flow, residence time, and groundwater recharge. Holistic approaches need to be formulated to evaluate the groundwater contamination in changing climatic scenarios and uncertainties, which can provide knowledge and tools with which to prepare sustainable groundwater management strategies.

In this paper we extend results on reconstruction of probabilistic supports of independent and identically distributed random variables to supports of dependent stationary ${\\mathbb R}^d$ -valued random variables. All supports are assumed to be compact of positive reach in Euclidean space. Our main results involve the study of the convergence in the Hausdorff sense of a cloud of stationary dependent random vectors to their common support. A novel topological reconstruction result is stated, and a number of illustrative examples are presented. The example of the Möbius Markov chain on the circle is treated at the end with simulations.

Aims People with obesity are at risk for developing heart failure (HF), but little is known about the mechanistic pathways that link obesity with cardiac dysfunction. Methods and results We included 2030 participants from the Swedish Obese Subjects study who received conventional obesity treatment. First‐time detection of HF was obtained by cross‐checking the study population with the Swedish National Patient Register and the Swedish Cause of Death Register. We also examined if atrial fibrillation and myocardial infarction as time‐dependent variables could predict incident HF The mean age of the study cohort was 48.7 years, and 28% were men. The mean body mass index at baseline was 40.1 kg/m2 and remained stable during a median follow‐up of 20.1 years. First‐time diagnosis of HF occurred in 266 of patients and was related to male sex, increasing age, greater waist–hip ratio, hypertension, higher cholesterol, diabetes mellitus, and elevated free thyroxine in univariable analysis. Estimated glomerular filtration rate was negatively related to HF risk. In multivariable analysis, atrial fibrillation, which is related to HF with preserved ejection fraction (HFpEF), and myocardial infarction, which is linked to HF with reduced ejection fraction (HFrEF), were strongly associated with incident HF with sub‐hazard ratios 3.75 (95% confidence interval: 2.72–5.18, P < 0.001) and 3.68 (95% confidence interval: 2.55–5.30, P < 0.001), respectively. Conclusions Both atrial fibrillation and myocardial infarction as time‐dependent variables were independently and strongly related to incident HF in people with excess body fat, suggesting two main obesity‐related mechanistic pathways leading to either HFpEF or HFrEF.

This study introduces a simultaneous multiscale data assimilation method by implementing model space spatial scale‐dependent localization (SDL) and variable‐dependent localization (VDL) within an ensemble variational system. This method updates all resolved scales by assimilating all observations at once. The impact of such an approach is examined by a series of radar data assimilation experiments. Single‐observation experiments show that SDL concurrently and more properly updates the storm and its ambient environments compared to a traditional single scale localization (SSL) for radar data assimilation. Including VDL on top of SDL (SDLVDL) realistically decreases the spatial coverage and intensity of moisture increments compared to SDL. Comparisons are then performed on the analyses and forecasts of the 8 May 2003 Oklahoma City supercell storm. Results show that SDL improves the analyses and forecasts during the data assimilation cycling by producing more realistic enhanced low‐level convergences than SSL. SDLVDL obtains more accurate analyses and subsequent forecasts for moisture than SDL. SDLVDL yields the best performance in reflectivity forecasts and storm maintenance. Compared to SSL, SDL has higher forecast skills before 2230 UTC and produces degraded forecasts in the later lead time. Plain Language Summary Convection‐allowing numerical weather prediction models resolve atmospheric flows at a wide range of scales. Therefore an effective data assimilation method is required to properly update all resolved scales. This study introduces and describes an ensemble based simultaneous multiscale data assimilation method by utilizing a scale‐dependent and variable‐dependent localization (VDL) method in the model state space. This approach corrects storms and corresponding larger scale environments concurrently. Results and diagnostics from a tornadic supercell case study assimilating radar observations show that the proposed multiscale approach improves the analyses and the earlier forecasts compared to the traditional single‐scale method. Further applying a VDL method in the multiscale approach yields the best forecast performance during the entire forecast period. Key Points This study introduces a simultaneous multiscale data assimilation method using spatial scale‐dependent and variable‐dependent localization (VDL) The scale‐dependent method concurrently updates storm and its ambient environments compared to a traditional single scale method Further applying VDL is beneficial in the analysis and forecast of a tornadic supercell