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Summary: Generalised linear mixed regression models are fundamental in statistics. Modelling random effects that are shared by individuals allows for correlation among those individuals. There are many methods and statistical packages available for analysing data using these models. Most require some form of numerical or analytic approximation because the likelihood function generally involves intractable integrals over the latents. The Bayesian approach avoids this issue by iteratively sampling the full conditional distributions for various blocks of parameters and latent random effects. Depending on the choice of the prior, some full conditionals are recognisable while others are not. In this paper we develop a novel normal approximation for the random effects full conditional, establish its asymptotic correctness and evaluate how well it performs. We make the case for hierarchical binomial and Poisson regression models with canonical link functions, for hierarchical gamma regression models with log link and for other cases. We also develop what we term a sufficient reduction (SR) approach to the Markov Chain Monte Carlo algorithm that allows for making inferences about all model parameters by replacing the full conditional for the latent variables with a considerably reduced dimensional function of the latents. We expect that this approximation could be quite useful in situations where there are a very large number of latent effects, which may be occurring in an increasingly 'Big Data' world. In the sequel, we compare our methods with INLA, which is a particularly popular method and which has been shown to be excellent in terms of speed and accuracy across a variety of settings. Our methods appear to be comparable to theirs in terms of accuracy, while INLA was faster, for the settings we considered. In addition, we note that our methods and those of others that involve Gibbs sampling trivially handle parameters that are functions of multiple parameters, while INLA approximations do not. Our primary illustration is for a three‐level hierarchical binomial regression model for data on health outcomes for patients who are clustered within physicians who are clustered within particular hospitals or hospital systems. [ABSTRACT FROM AUTHOR]

Abstract Background The impact of pre-pregnancy weight and the rate of gestational weight gain (GWG) together on the risk of early GDM (

The runoff threshold of a catchment is often reported in the literature as a measure used to evaluate the effectiveness of low‐impact development (LID) techniques and is oftentimes determined using linear regression. However, due to the heteroscedastic nature of precipitation and runoff data, linear regression analyses can result in invalid conclusions, so the use of a binomial regression model was investigated. Precipitation and runoff data collected from five studies were assessed for homoscedasticity and applied to four linear regression models for the evaluation of the linear regression runoff threshold (LRRT) and the associated 95% bootstrapping confidence intervals. Log‐transformation corrected the heteroscedasticity of two of the five precipitation and runoff datasets. While mixed‐effect linear models accounted for heteroscedasticity, these models often resulted in extremely large confidence intervals. A binomial regression model was created to determine the likelihood of runoff based on precipitation depth. For each catchment, the 10%–90% runoff probability range (p10–p90) is reported to provide the user with a more comprehensive understanding of when a catchment produces runoff than the LRRT. The p10–p90 range reflects the effects that environmental factors may have on runoff generation. For example, impervious catchments with limited interaction with the vegetation and soil produce a narrow p10–p90 range. Conversely, LID practices encourage the interaction of runoff with environmental factors and result in a wider p10–p90 range. Utilization of the binomial regression methodology presented herein is recommended for evaluation of the likelihood of runoff for each precipitation depth. [ABSTRACT FROM AUTHOR]

Background: The impact of pre-pregnancy weight and the rate of gestational weight gain (GWG) together on the risk of early GDM (< 24 weeks gestation; eGDM) has not been studied in the Indian context. We aimed to study the influence of (1) pre-pregnancy weight on the risk of eGDM diagnosed in two time intervals; and (2) in addition, the rate of GWG by 12 weeks on the risk of eGDM diagnosed in 19–24 weeks. Method: Our study utilized real-world clinical data on pregnant women routinely collected at an antenatal care clinic at a private tertiary hospital, in Pune, India. Women registering before 12 weeks of gestation (v1), with a singleton pregnancy, and having a follow-up visit between 19–24 weeks (v2) were included (n = 600). The oral glucose tolerance test was conducted universally as per Indian guidelines (DIPSI) at v1 and v2 for diagnosing eGDM. The data on the onset time of eGDM were interval censored; hence, we modeled the risk of eGDM using binomial regression to assess the influence of pre-pregnancy weight on the risk of eGDM in the two intervals. The rate of GWG by 12 weeks was added to assess its impact on the risk of eGDM diagnosed in v2. Result: Overall, 89 (14.8%) women (age 32 ± 4 years) were diagnosed with eGDM by 24 weeks, of which 59 (9.8%) were diagnosed before 12 weeks and 30 of 541 (5.5%) women were diagnosed between 19–24 weeks. Two-thirds (66%) of eGDM were diagnosed before 12 weeks of gestation. Women's pre-pregnancy weight was positively associated with the risk of GDM in both time intervals though the lower confidence limit was below zero in v1. The rate of GWG by 12 weeks was not observed to be associated with the risk of eGDM diagnosed between 19–24 weeks of gestation. These associations were independent of age, height, and parity. Conclusion: Health workers may focus on pre-pregnancy weight, a modifiable risk factor for eGDM. A larger community-based study measuring weight and GDM status more frequently may be warranted to deepen the understanding of the role of GWG as a risk factor for GDM. [ABSTRACT FROM AUTHOR]

The paper proposes a method to perform diagnostics of model-based trees for preference and evaluation data on the basis of surrogate residual analysis for ordinal data models. The discussion stems from the introduction of binomial regression trees and discusses how to perform local diagnostics of misspecification against alternative model extensions within the framework of mixture models with uncertainty. Three case studies concerning customer satisfaction and perceived trust for information sources illustrate usefulness and versatile applicative extent of the proposal. [ABSTRACT FROM AUTHOR]

The complementary log‐log link was originally introduced in 1922 to R. A. Fisher, long before the logit and probit links. While the last two links are symmetric, the complementary log‐log link is an asymmetrical link without a parameter associated with it. Several asymmetrical links with an extra parameter were proposed in the literature over last few years to deal with imbalanced data in binomial regression (when one of the classes is much smaller than the other); however, these do not necessarily have the cloglog link as a special case, with the exception of the link based on the generalized extreme value distribution. In this paper, we introduce flexible cloglog links for modeling binomial regression models that include an extra parameter associated with the link that explains some unbalancing for binomial outcomes. For all cases, the cloglog is a special case or the reciprocal version loglog link is obtained. A Bayesian Markov chain Monte Carlo inference approach is developed. Simulations study to evaluate the performance of the proposed algorithm is conducted and prior sensitivity analysis for the extra parameter shows that a uniform prior is the most convenient for all models. Additionally, two applications in medical data (age at menarche and pulmonary infection) illustrate the advantages of the proposed models. [ABSTRACT FROM AUTHOR]

Abstract Background Childhood stunting, wasting and underweight are significant public health challenges. There is a gap in knowledge of the coexistence of stunting, wasting, and underweight among children under five years (under-5) in Bangladesh. This study aims to (i) describe the prevalence of the coexistence of stunting, wasting, and underweight and ii) examine the risk factors for the coexistence of stunting, wasting, and underweight among children under-5 in Bangladesh. Methods This study included 6,610 and 7,357 under-5 children from Bangladesh Demographic Health Surveys (BDHS) 2014 and 2017/18, respectively. The associations between the coexistence of stunting, wasting, and underweight and independent variables were assessed using the Chi-square test of independence. The effects of associated independent variables were examined using negative binomial regression. Results The prevalence of coexistence of stunting, wasting, and underweight gradually declined from 5.2% in 2014 to 2.7% in 2017/18. Children born with low birth weight ((adjusted incidence rate ratios, aIRR) 2.31, 95% CI 1.64, 3.24)); children of age group 36–47 months (aIRR 2.26, 95% CI 1.67, 3.08); children from socio-economically poorest families (aIRR 2.02, 95% CI 1.36, 2.98); children of mothers with no formal education (aIRR 1.98, 95% CI 1.25, 3.15); and children of underweight mothers (aIRR 1.73, 95% CI 1.44, 2.08) were the most important risk factors. Further, lower incidence among children with the coexistence of stunting, wasting, and underweight was observed in the 2017–18 survey (aIRR 0.59, 95% CI 0.49, 0.70) compared to children in the 2014 survey. Conclusions One out of thirty-five under-5 children was identified to have coexistence of stunting, wasting, and underweight in Bangladesh. The burden of coexistence of stunting, wasting, and underweight was disproportionate among children born with low birth weight, socio-economically poorest, a mother with no formal education, and underweight mothers, indicating the need for individual, household, and societal-level interventions to reduce the consequences of coexistence of stunting, wasting, and underweight.

Confirmation of rights and collective trust (interpersonal and institutional) can act as primary factors for facilitating effective forest management and conservation. Collective forests are lands held collectively by either rural or indigenous communities based on a shared history, language, culture, or lineage. It is an institutional arrangement in which communities are involved wholly or partly in decision-making and contribute knowledge and labour to achieve healthy forests and social well-being. Based on the existing literature, the nature of collective forest rights and trust can be derived from social, rather than economic, prospects. Therefore, based on the institutional theory, this study constructs a theoretical framework to verify the impact of the confirmation of rights and trust on farmers' forestry management conservation behaviour. The empirical setup of the study was comprised of a data set of 682 collective forest farmers in Zhejiang and Jiangxi provinces, China. We utilized the negative binomial regression model to quantify the proposed framework. The main conclusions were as follows. Confirmation of rights and collective trust had a significant positive role in promoting farmers' forestry management and protection behaviour. Increasing the confirmation of rights and trusts by one unit increased the number of farmers' forest management and protection by 1.846 and 2.631 times, respectively. The interaction between confirmation and trust did not substantially affect farmers' behaviour. The diverse forest labour force, the total area of forest land, and the number of forest plots had a significant positive impact, while the head of the village and the number of migrant workers significantly and negatively impacted farmers' behaviour. Therefore, it is necessary to further improve the forestry land rights system and strengthen the trust mechanism so that it can become an effective institutional incentive for farmers to manage and protect forests. [ABSTRACT FROM AUTHOR]

Abstract Background There are handful hypothesis-driven ethnobotanical studies in Nepal. In this study, we tested the non-random medicinal plant selection hypothesis using national- and community-level datasets through three different types of regression: linear model with raw data, linear model with log-transformed data and negative binomial model. Methods For each of these model, we identified over-utilized families as those with highest positive Studentized residuals and underutilized families with highest negative Studentized residuals. The national-level data were collected from online databases and available literature while the community-level data were collected from Baitadi and Darchula districts. Results Both dataset showed larger variance (national dataset mean 6.51

Background: Childhood stunting, wasting and underweight are significant public health challenges. There is a gap in knowledge of the coexistence of stunting, wasting, and underweight among children under five years (under-5) in Bangladesh. This study aims to (i) describe the prevalence of the coexistence of stunting, wasting, and underweight and ii) examine the risk factors for the coexistence of stunting, wasting, and underweight among children under-5 in Bangladesh. Methods: This study included 6,610 and 7,357 under-5 children from Bangladesh Demographic Health Surveys (BDHS) 2014 and 2017/18, respectively. The associations between the coexistence of stunting, wasting, and underweight and independent variables were assessed using the Chi-square test of independence. The effects of associated independent variables were examined using negative binomial regression. Results: The prevalence of coexistence of stunting, wasting, and underweight gradually declined from 5.2% in 2014 to 2.7% in 2017/18. Children born with low birth weight ((adjusted incidence rate ratios, aIRR) 2.31, 95% CI 1.64, 3.24)); children of age group 36–47 months (aIRR 2.26, 95% CI 1.67, 3.08); children from socio-economically poorest families (aIRR 2.02, 95% CI 1.36, 2.98); children of mothers with no formal education (aIRR 1.98, 95% CI 1.25, 3.15); and children of underweight mothers (aIRR 1.73, 95% CI 1.44, 2.08) were the most important risk factors. Further, lower incidence among children with the coexistence of stunting, wasting, and underweight was observed in the 2017–18 survey (aIRR 0.59, 95% CI 0.49, 0.70) compared to children in the 2014 survey. Conclusions: One out of thirty-five under-5 children was identified to have coexistence of stunting, wasting, and underweight in Bangladesh. The burden of coexistence of stunting, wasting, and underweight was disproportionate among children born with low birth weight, socio-economically poorest, a mother with no formal education, and underweight mothers, indicating the need for individual, household, and societal-level interventions to reduce the consequences of coexistence of stunting, wasting, and underweight. [ABSTRACT FROM AUTHOR]

Recent European Union regulations aim at reducing the use of chemical pesticides in agriculture. In sunflower production in Serbia, the use of synthetic insecticides for soil and seed treatments has become a prevailing practice for wireworm (Coleoptera: Elateridae) control. However, a number of compounds efficiently used as seed treatments have been phased out. This work aimed at assessing the potential of an environmentally friendly "Attract and Kill" strategy (A&K) for controlling wireworms in sunflower in comparison to conventional insecticides. The experiments were carried out in 2018, 2019 and 2021 involving (a) soil treatments with ATTRACAP® and a Force 1.5 G; (b) seed treatments with Sonido, Force 20 CS, Lumiposa and Buteo Start 480 FS; (c) controls (i.e., untreated seeds). The efficacy of the treatments was assessed based on the plant density and emerging plant damage (%). A damage rating scale (levels 0–5) was created, aiming for a more reliable and concrete interpretation of the results. Data were processed using binomial and multinomial regressions, followed by modelling of the damage and calculating the odds of damage occurrence, depending on the applied insecticide. In all experimental years and at all localities, the Force 20 CS and/or Force 1.5 G treatments resulted in the highest plant density and the lowest percentage of plant damage. ATTRACAP® showed good effectiveness, since plant density and percentage of damaged plants were at the same level of significance as the commonly used conventional insecticides in sunflower production (Sonido for seed treatment and Force 1.5 G for soil treatment). Thus, the A&K strategy was efficient in controlling wireworms at conditions of low abundance, based on three-year experimental results. Although the damage rating scale enabled a clear differentiation of plant damage caused by wireworms responsible for reduced plant density, more reliable models were obtained by binomial regressions, classifying plants as damaged or undamaged. [ABSTRACT FROM AUTHOR]

We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject‐specific covariates available as predictors. The outcomes are not well characterized by simple parametric models, so we use a nonparametric approach with a binomial likelihood wherein the latent probabilities are drawn from a mixture with an arbitrary number of components, analogous to a Dirichlet process. We use a flexible probit stick‐breaking formulation for the component weights that allows for covariate dependence and clustering structure in the outcomes. The parameter space for this model is large and multiway: patients × tooth types × covariates × components. We reduce its effective dimensionality and account for the multiway structure, via low‐rank assumptions. We illustrate how this can improve performance and simplify interpretation while still providing sufficient flexibility. We describe a general and efficient Gibbs sampling algorithm for posterior computation. The resulting fit to the PD data outperforms competitors and is interpretable and well calibrated. An interactive visual of the predictive model is available at the website (https://ericfrazerlock.com/toothdata/ToothDisplay.html), and the code is available at the GitHub (https://github.com/lockEF/NonparametricMultiway). [ABSTRACT FROM AUTHOR]

Background: There are handful hypothesis-driven ethnobotanical studies in Nepal. In this study, we tested the non-random medicinal plant selection hypothesis using national- and community-level datasets through three different types of regression: linear model with raw data, linear model with log-transformed data and negative binomial model. Methods: For each of these model, we identified over-utilized families as those with highest positive Studentized residuals and underutilized families with highest negative Studentized residuals. The national-level data were collected from online databases and available literature while the community-level data were collected from Baitadi and Darchula districts. Results: Both dataset showed larger variance (national dataset mean 6.51 < variance 156.31, community dataset mean 1.16 < variance 2.38). All three types of regression were important to determine the medicinal plant species selection and use differences among the total plant families, although negative binomial regression was most useful. The negative binomial showed a positive nonlinear relationship between total plant family size and number of medicinal species per family for the national dataset (β1 = 0.0160 ± 0.0009, Z1 = 16.59, p < 0.00001, AIC1 = 1181), and with similar slope and stronger performance for the community dataset (β2 = 0.1747 ± 0.0199, Z2 = 8.76, p < 0.00001, AIC2 = 270.78). Moraceae and Euphorbiaceae were found over-utilized while Rosaceae, Cyperaceae and Caryophyllaceae were recorded as underutilized. Conclusions: As our datasets showed larger variance, negative binomial regression was found the most useful for testing non-random medicinal plant selection hypothesis. The predictions made by non-random selection of medicinal plants hypothesis holds true for community-level studies. The identification of over-utilized families is the first step toward sustainable conservation of plant resources and it provides a baseline for pharmacological research that might be leading to drug discovery. [ABSTRACT FROM AUTHOR]

Binary outcomes are extremely common in biomedical research. Despite its popularity, binomial regression often fails to model this kind of data accurately due to the overdispersion problem. Many alternatives can be found in the literature, the beta‐binomial (BB) regression model being one of the most popular. The additional parameter of this model enables a better fit to overdispersed data. It also exhibits an attractive interpretation in terms of the intraclass correlation coefficient. Nonetheless, in many real data applications, a single additional parameter cannot handle the entire excess of variability. In this study, we propose a new finite mixture distribution with BB components, namely, the flexible beta‐binomial (FBB), which is characterized by a richer parameterization. This allows us to enhance the variance structure to account for multiple causes of overdispersion while also preserving the intraclass correlation interpretation. The novel regression model, based on the FBB distribution, exploits the flexibility and large variety of the distribution's possible shapes (which includes bimodality and various tail behaviors). Thus, it succeeds in accounting for several (possibly concomitant) sources of overdispersion stemming from the presence of latent groups in the population, outliers, and excessive zero observations. Adopting a Bayesian approach to inference, we perform an intensive simulation study that shows the superiority of the new regression model over that of the existing ones. Its better performance is also confirmed by three applications to real datasets extensively studied in the biomedical literature, namely, bacteria data, atomic bomb radiation data, and control mice data. [ABSTRACT FROM AUTHOR]

The 2 × 2 crossover trial uses subjects as their own control to reduce the intersubject variability in the treatment comparison, and typically requires fewer subjects than a parallel design. The generalized estimating equations (GEE) methodology has been commonly used to analyze incomplete discrete outcomes from crossover trials. We propose a unified approach to the power and sample size determination for the Wald Z‐test and t‐test from GEE analysis of paired binary, ordinal and count outcomes in crossover trials. The proposed method allows misspecification of the variance and correlation of the outcomes, missing outcomes, and adjustment for the period effect. We demonstrate that misspecification of the working variance and correlation functions leads to no or minimal efficiency loss in GEE analysis of paired outcomes. In general, GEE requires the assumption of missing completely at random. For bivariate binary outcomes, we show by simulation that the GEE estimate is asymptotically unbiased or only minimally biased, and the proposed sample size method is suitable under missing at random (MAR) if the working correlation is correctly specified. The performance of the proposed method is illustrated with several numerical examples. Adaption of the method to other paired outcomes is discussed. [ABSTRACT FROM AUTHOR]

This study involves statistical analysis of reported cases of sexually transmitted diseases (STDs) of Chlamydia infection in the United States. The data are collected from 2007 to 2016. The research studies incidence of sexually transmitted diseases and survival among different age groups and gender and race factors which influence the incidence in the target population. In this work, log-binomial, logit model, probit model and complementary log–log model are used to establish a suitable model (using different criteria) that can predict the survival of infected people with STDs based on their age, gender and race. Here we have also focused on stratification: a statistical technique that allows to control for confounding by creating two or more categories. The Mantel–Haenszel formula allows to calculate an overall, unconfounded, that is adjusted, effect estimate for a specific outcome by combining (pooling) stratum-specific relative risks and odds ratios. Simulation is based on R-software.

The detailed study of the logit, probit and cloglog link functions is presented for the generalized linear model with binomial response in the presence of the problem of explanatory factors levels aggregation. Expressions are deduced for the estimators of the parameters and their variances, in general terms, which allows for finding the particular results for any link function chosen. The impact of the link function on the estimates is illustrated, concluding that the use of the appropriate variance in the levels aggregation is preferable, regardless of the link function to be used. [ABSTRACT FROM AUTHOR]

Recent European Union regulations aim at reducing the use of chemical pesticides in agriculture. In sunflower production in Serbia, the use of synthetic insecticides for soil and seed treatments has become a prevailing practice for wireworm (Coleoptera: Elateridae) control. However, a number of compounds efficiently used as seed treatments have been phased out. This work aimed at assessing the potential of an environmentally friendly “Attract and Kill” strategy (A&K) for controlling wireworms in sunflower in comparison to conventional insecticides. The experiments were carried out in 2018, 2019 and 2021 involving (a) soil treatments with ATTRACAP® and a Force 1.5 G; (b) seed treatments with Sonido, Force 20 CS, Lumiposa and Buteo Start 480 FS; (c) controls (i.e., untreated seeds). The efficacy of the treatments was assessed based on the plant density and emerging plant damage (%). A damage rating scale (levels 0–5) was created, aiming for a more reliable and concrete interpretation of the results. Data were processed using binomial and multinomial regressions, followed by modelling of the damage and calculating the odds of damage occurrence, depending on the applied insecticide. In all experimental years and at all localities, the Force 20 CS and/or Force 1.5 G treatments resulted in the highest plant density and the lowest percentage of plant damage. ATTRACAP® showed good effectiveness, since plant density and percentage of damaged plants were at the same level of significance as the commonly used conventional insecticides in sunflower production (Sonido for seed treatment and Force 1.5 G for soil treatment). Thus, the A&K strategy was efficient in controlling wireworms at conditions of low abundance, based on three-year experimental results. Although the damage rating scale enabled a clear differentiation of plant damage caused by wireworms responsible for reduced plant density, more reliable models were obtained by binomial regressions, classifying plants as damaged or undamaged.

We suggest a regression approach to estimate the excess cumulative incidence function (CIF) when matched data are available. In a competing risk setting, we define the excess risk as the difference between the CIF in the exposed group and the background CIF observed in the unexposed group. We show that the excess risk can be estimated through an extended binomial regression model that actively uses the matched structure of the data, avoiding further estimation of both the exposed and the unexposed CIFs. The method naturally deals with two time scales, age and time since exposure and simplifies how to deal with the left truncation on the age time-scale. The model makes it easy to predict individual excess risk scenarios and allows for a direct interpretation of the covariate effects on the cumulative incidence scale. After introducing the model and some theory to justify the approach, we show via simulations that our model works well in practice. We conclude by applying the excess risk model to data from the ALiCCS study to investigate the excess risk of late events in childhood cancer survivors. [ABSTRACT FROM AUTHOR]

The European honey bee species (Apis mellifera L.) is under increasing pressure from anthropogenic and other stressors. Winter mortality of entire colonies is generally attributed to biological, environmental, and management conditions. The rates of winter mortality can vary extremely from place to place. A landscape approach is used here to examine the dependency between spatially distributed winter mortality rates, environmental and biological conditions, and apiary management. The analysis was applied to data for the region of Wallonia in Belgium with winter mortality rates obtained from the European project EPILOBEE. Potential explanatory variables were spatially allocated based on GIS analysis, and subjected to binomial linear regression to identify the most predominant variables related to bee winter mortality. The results point to infestation with Varroa, the number of frost days, the potential flying hours, the connectivity of the natural landscape, and the use of plant protection products as most dominant causes for the region of Wallonia. The outcomes of this study will help focus beekeeping and environmental management to improve bee health and the effectiveness of apiary practices. The approach surpasses application to the problem of bee mortality and could be used to compare and rank the causes of other environmental problems by their significance, particularly when these are interdependent and spatially differentiated. [ABSTRACT FROM AUTHOR]

The treatment effect of a therapeutic product on a binary endpoint is often expressed as the difference in proportions of subjects with the outcome of interest between the treated and control groups of a clinical trial. Analysis of the proportional difference and construction of the associated confidence interval (CI) is often complicated due to the baseline covariate(s) being associated with the primary endpoint. Analysis adjusting for such baseline covariate(s) generally improves efficiency of hypothesis testing and precision of treatment effect estimation, and avoids possible bias caused by baseline covariate imbalances. Most existing literatures focus on constructing unadjusted or categorical covariate(s) adjusted only CI, which provides very limited advice on how different statistical methods perform and which method is optimal in terms of constructing both categorical and continuous baseline covariate(s) adjusted CI for proportional difference. We review and compare the performance of three commonly used model-based methods as well as the traditional nonparametric weighted-difference methods for the construction of covariate-adjusted CI for proportional difference via a real data application and simulations. The coverage of 95% CI, Type I error control, and power are examined. We also examine the factors leading to the model convergence failure in different scenarios via simulations. [ABSTRACT FROM AUTHOR]

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Many researchers want to report an |$R^{2}$| to measure the variance explained by a model. When the model includes correlation among data, such as phylogenetic models and mixed models, defining an |$R^{2}$| faces two conceptual problems. (i) It is unclear how to measure the variance explained by predictor (independent) variables when the model contains covariances. (ii) Researchers may want the |$R^{2}$| to include the variance explained by the covariances by asking questions such as "How much of the data is explained by phylogeny?" Here, I investigated three |$R^{2}$| s for phylogenetic and mixed models. |$R^{2}_{resid}$| is an extension of the ordinary least-squares |$R^{2}$| that weights residuals by variances and covariances estimated by the model; it is closely related to |$R^{2}_{glmm}$| presented by Nakagawa and Schielzeth (2013. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods Ecol. Evol. 4:133–142). |$R^{2}_{pred}$| is based on predicting each residual from the fitted model and computing the variance between observed and predicted values. |$R^{2}_{lik}$| is based on the likelihood of fitted models, and therefore, reflects the amount of information that the models contain. These three |$R^{2}$| s are formulated as partial |$R^{2}$| s, making it possible to compare the contributions of predictor variables and variance components (phylogenetic signal and random effects) to the fit of models. Because partial |$R^{2}$| s compare a full model with a reduced model without components of the full model, they are distinct from marginal |$R^{2}$| s that partition additive components of the variance. I assessed the properties of the |$R^{2}$| s for phylogenetic models using simulations for continuous and binary response data (phylogenetic generalized least squares and phylogenetic logistic regression). Because the |$R^{2}$| s are designed broadly for any model for correlated data, I also compared |$R^{2}$| s for linear mixed models and generalized linear mixed models. |$R^{2}_{resid}$|⁠, |$R^{2}_{pred}$|⁠, and |$R^{2}_{lik}$| all have similar performance in describing the variance explained by different components of models. However, |$R^{2}_{pred}$| gives the most direct answer to the question of how much variance in the data is explained by a model. |$R^{2}_{resid}$| is most appropriate for comparing models fit to different data sets, because it does not depend on sample sizes. And |$R^{2}_{lik}$| is most appropriate to assess the importance of different components within the same model applied to the same data, because it is most closely associated with statistical significance tests. [ABSTRACT FROM AUTHOR]

Copyright of Investigación Administrativa is the property of ESCA Santo Tomas - IPN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study involves statistical analysis of reported cases of sexually transmitted diseases (STDs) of Chlamydia infection in the United States. The data are collected from 2007 to 2016. The research studies incidence of sexually transmitted diseases and survival among different age groups and gender and race factors which influence the incidence in the target population. In this work, log-binomial, logit model, probit model and complementary log-log model are used to establish a suitable model (using different criteria) that can predict the survival of infected people with STDs based on their age, gender and race. Here we have also focused on stratification: a statistical technique that allows to control for confounding by creating two or more categories. The Mantel-Haenszel formula allows to calculate an overall, unconfounded, that is adjusted, effect estimate for a specific outcome by combining (pooling) stratum-specific relative risks and odds ratios. Simulation is based on R-software. [ABSTRACT FROM AUTHOR]

In binomial regression, a link function is used to join the linear predictor variables and the expectation of the response variable. This paper proposes a flexible link function from a new class of generalized logistic distribution, namely a flexible generalized logit (glogit) link. This approach considers both symmetric and asymmetric models, including the cases of lighter and heavier tails, as compared to standard logistic. The glogit is created from the inverse cumulative distribution function of the exponentiated-exponential logistic (EEL) distribution. Using a Bayesian framework, we conduct a simulation study to investigate the model performance compared to the most commonly used link functions, e.g., logit, probit, and complementary log−log. Furthermore, we compared the proposed model with several other asymmetric models using two previously published datasets. The results show that the proposed model outperforms the existing ones and provides flexibility fitting the experimental dataset. Another attractive aspect of the model are analytically tractable and can be easily implemented under a Bayesian approach.

Intersexual and intrasexual selections are important driving forces that lead to diversification of sexual characteristics. Tetragnatha spiders have elongated chelicerae and sexual dimorphism in chelicera length whose magnitude varies among species. Because they use their chelicerae during copulation and as weapons in male–male competition, this divergence reflects repeated intersexual and intrasexual selection. To infer the causes of chelicera length diversity, we examined the roles of the elongated chelicerae in copulatory behavior of a Tetragnatha species and clarified the interspecific sexual dimorphism of chelicera length in 15 species. The longer chelicerae of female Tetragnatha allowed females to kill males, suggesting female rejection of mating using the elongated chelicerae. Comparisons based on independent contrasts showed that chelicera length was significantly positively correlated between the sexes across species, possibly reflecting sexually antagonistic coevolution of male and female chelicera lengths. However, some species showed male-biased sexual dimorphism, indicating that intrasexual selection (male competition) may be more important than intersexual competition in some species. Our results demonstrate that both intersexual and intrasexual selection led to interspecific variation in sexual dimorphism of chelicera length in this group. [ABSTRACT FROM AUTHOR]

A method for robustness in linear models is to assume that there is a mixture of standard and outlier observations with a different error variance for each class. For generalised linear models (GLMs) the mixture model approach is more difficult as the error variance for many distributions has a fixed relationship to the mean. This model is extended to GLMs by changing the classes to one where the standard class is a standard GLM and the outlier class which is an overdispersed GLM achieved by including a random effect term in the linear predictor. The advantages of this method are it can be extended to any model with a linear predictor, and outlier observations can be easily identified. Using simulation the model is compared to an M-estimator, and found to have improved bias and coverage. The method is demonstrated on three examples. [ABSTRACT FROM AUTHOR]