Beta Regression Model Research Articles

Developing prediction models for symptom severity around the time of discharge from a tertiary-care program for treatment-resistant psychosis.

Antipsychotics are the only therapeutic class indicated in the symptomatic management of psychotic disorders. However, individuals diagnosed with schizophrenia or schizoaffective disorder may not always benefit from these first-line agents. This refractoriness to conventional treatment can be difficult to address in most clinical settings. Therefore, a referral to a tertiary-care program that is better able to deliver specialized care in excess of the needs of most individuals may be necessary. The average outcome following a period of treatment at these programs tends to be one of improvement. Nonetheless, accurate prognostication of individual-level responses may be useful in identifying those who are unlikely to improve despite receiving specialized care. Thus, the main objective of this study was to predict symptom severity around the time of discharge from the Refractory Psychosis Program in British Columbia, Canada using only clinicodemographic information and prescription drug data available at the time of admission. To this end, a different boosted beta regression model was trained to predict the total score on each of the five factors of the Positive and Negative Syndrome Scale (PANSS) using a data set composed of 320 hospital admissions. Internal validation of these prediction models was then accomplished by nested cross-validation. Insofar as it is possible to make comparisons of model performance across different outcomes, the correlation between predictions and observations tended to be higher for the negative and disorganized factors than the positive, excited, and depressed factors on internal validation. Past scores had the greatest effect on the prediction of future scores across all 5 factors. The results of this study serve as a proof of concept for the prediction of symptom severity using this specific approach.

Increasing numbers and complexity of Staphylococcus aureus bloodstream infection—14 years of prospective evaluation at a German tertiary care centre with multi-centre validation of findings

ObjectivesStaphylococcus aureus bloodstream infection (SAB) is a common and severe infection. This study aims to describe temporal trends in numbers, epidemiological characteristics, clinical manifestations, and outcomes of SAB. MethodsWe performed a post-hoc analysis of three prospective SAB cohorts at the University Medical Centre Freiburg between 2006 and 2019. We validated our findings in a large German multi-centre cohort of five tertiary care centres (R-Net consortium, 2017–2019). Time-dependent trends were estimated using Poisson or beta regression models. ResultsWe included 1797 patients in the mono-centric and 2336 patients in the multi-centric analysis. Overall, we observed an increasing number of SAB cases over 14 years (6.4%/year and 1000 patient days, 95% CI: 5.1% to 7.7%), paralleled by an increase in the proportion of community-acquired SAB (4.9%/year [95% CI: 2.1% to 7.8%]) and a decrease in the rate of methicillin-resistant-SAB (−8.5%/year [95% CI: −11.2% to −5.6%]). All of these findings were confirmed in the multi-centre validation cohort (6.2% cases per 1000 patient cases/year [95% CI: −0.6% to 12.6%], community-acquired-SAB 8.7% [95% CI: −1.2% to 19.6%], methicillin-resistant S. aureus-SAB −18.6% [95% CI: −30.6 to −5.8%]). Moreover, we found an increasing proportion of patients with multiple risk factors for complicated/difficult-to-treat SAB (8.5%/year, 95% CI: 3.6% to 13.5%, p < 0.001), alongside an overall higher level of comorbidities (Charlson comorbidity score 0.23 points/year, 95% CI: 0.09 to 0.37, p 0.005). At the same time, the rate of deep-seated foci such as osteomyelitis or deep-seated abscesses significantly increased (6.7%, 95% CI: 3.9% to 9.6%, p < 0.001). A reduction of in-hospital mortality by 0.6% per year (95% CI: 0.08% to 1%) was observed in the subgroup of patients with infectious diseases consultations. DiscussionWe found an increasing number of SAB combined with a significant increase in comorbidities and complicating factors in tertiary care centres. The resulting challenges in securing adequate SAB management in the face of high patient turnover will become an important task for physicians.

The beta Liu-type estimator: simulation and application

The Beta Regression Model (BRM) is commonly used while analyzing data where the dependent variable is restricted to the interval $[0,1]$ for example proportion or probability. The Maximum Likelihood Estimator (MLE) is used to estimate the regression coefficients of BRMs. But in the presence of multicollinearity, MLE is very sensitive to high correlation among the explanatory variables. For this reason, we introduce a new biased estimator called the Beta Liu-Type Estimator (BLTE) to overcome the multicollinearity problem in the case that dependent variable follows a Beta distribution. The proposed estimator is a general estimator which includes other biased estimators, such as the Ridge Estimator, Liu Estimator, and the estimators with two biasing parameters as special cases in BRM. The performance of the proposed new estimator is compared to the MLE and other biased estimators in terms of the Estimated Mean Squared Error (EMSE) criterion by conducting a simulation study. Finally, a numerical example is given to show the benefit of the proposed estimator over existing estimators.

James Stein Estimator for the Beta Regression Model with Application to Heat-Treating Test and Body Fat Datasets

The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in the interval (0, 1), such as rates, proportions, percentages and fractions. Generally, the parameters of the BRM are estimated by the method of maximum likelihood estimation (MLE). However, the MLE does not offer accurate and reliable estimates when the explanatory variables in the BRM are correlated. To solve this problem, the ridge and Liu estimators for the BRM were proposed by different authors. In the current study, the James Stein Estimator (JSE) for the BRM is proposed. The matrix mean squared error (MSE) and the scalar MSE properties are derived and then compared to the available ridge estimator, Liu estimator and MLE. The performance of the proposed estimator is evaluated by conducting a simulation experiment and analyzing two real-life applications. The MSE of the estimators is considered as a performance evaluation criterion. The findings of the simulation experiment and applications indicate the superiority of the suggested estimator over the competitive estimators for estimating the parameters of the BRM.

The Interplay of Perceived Risks and Benefits in Deciding to Become Vaccinated against COVID-19 While Pregnant or Breastfeeding: A Cross-Sectional Study in Italy.

The present study examined the role of the perception of risks and benefits for the mother and her babies in deciding about the COVID-19 vaccination. In this cross-sectional study, five hypotheses were tested using data from a convenience sample of Italian pregnant and/or breastfeeding women (N = 1104, July-September 2021). A logistic regression model estimated the influence of the predictors on the reported behavior, and a beta regression model was used to evaluate which factors influenced the willingness to become vaccinated among unvaccinated women. The COVID-19 vaccination overall risks/benefits tradeoff was highly predictive of both behavior and intention. Ceteris paribus, an increase in the perception of risks for the baby weighed more against vaccination than a similar increase in the perception of risks for the mother. Additionally, pregnant women resulted in being less likely (or willing) to be vaccinated in their status than breastfeeding women, but they were equally accepting of vaccination if they were not pregnant. COVID-19 risk perception predicted intention to become vaccinated, but not behavior. In conclusion, the overall risks/benefits tradeoff is key in predicting vaccination behavior and intention, but the concerns for the baby weigh more than those for the mother in the decision, shedding light on this previously neglected aspect.

Universal robust regression via maximum mean discrepancy

Abstract Many modern datasets are collected automatically and are thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models, or generalized linear models, and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on maximum mean discrepancy minimization. We build two estimators that are both proven to be robust to Huber-type contamination. For one of them, we obtain a non-asymptotic error bound and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators, we derive new results on kernel conditional mean embedding of distributions that are of independent interest.

태풍에 따른 기상요소와 사과의 낙과 피해율 분석

Every year, direct and indirect damage to farms caused by natural disasters continues to occur. In particular, damage caused by typhoons appears to cause great damage. This study aims to identify and analyze the relationship between weather factors and damage rate in the event of a typhoon by utilizing the weather information provided by the Korea Meteorological Administration and the damage caused by crop accident insurance. Since the damage rate is proportional data with values between 0 and 1, it is not suitable to utilize standard statistical techniques that assume that the error term follows a normal distribution and has a constant variance. Therefore the analysis is conducted through the binomial regression and the beta regression model. As a result the adjusted R square of the beta regression model was higher than that of the binary regression model. And the minimum air pressure, maximum wind speed, and maximum humidity variables were significant among the weather variables. Through this analysis of the damage rate, it is expected that damage to farms can be reduced by preparing appropriate countermeasures in the event of a typhoon.

Mapping health assessment questionnaire disability index onto EQ-5D-5L in China.

This research aimed to develop the more accurate mapping algorithms from health assessment questionnaire disability index (HAQ-DI) onto EQ-5D-5L based on Chinese Rheumatoid Arthritis patients. The cross-sectional data of Chinese RA patients from 8 tertiary hospitals across four provincial capitals was used for constructing the mapping algorithms. Direct mapping using Ordinary least squares regression (OLS), the general linear regression model (GLM), MM-estimator model (MM), Tobit regression model (Tobit), Beta regression model (Beta) and the adjusted limited dependent variable mixture model (ALDVMM) and response mapping using Multivariate Ordered Probit regression model (MV-Probit) were carried out. HAQ-DI score, age, gender, BMI, DAS28-ESR and PtAAP were included as the explanatory variables. The bootstrap was used for validation of mapping algorithms. The average ranking of mean absolute error (MAE), root mean square error (RMSE), adjusted R 2 (adjR 2) and concordance correlation coefficient (CCC) were used to assess the predictive ability of the mapping algorithms. According to the average ranking of MAE, RMSE, adjR 2, and CCC, the mapping algorithm based on Beta performed the best. The mapping algorithm would perform better as the number of variables increasing. The mapping algorithms provided in this research can help researchers to obtain the health utility values more accurately. Researchers can choose the mapping algorithms under different combinations of variables based on the actual data.

Spatial patterns in Brazilian state legislative elections

In this paper we explore spatial patterns in voting behavior of the Brazilian electorate in the state legislative elections of 2014. With data aggregated at the municipality level, we employ a Beta regression model augmented with spatially correlated random effects to model the share of votes received by the three largest political parties: PMDB, PSDB, and PT. Results suggest PT is more preferred by the electorate in poorer and more densely populated areas, specially in states of the Northwest and South regions, while PSDB performs better in municipalities with relatively higher standards of living. Also, analysis of the spatial random effects indicates this component is especially important to account for the major stylized fact that is the simultaneous PSDB hegemony and relative lack of PMDB presence in the state of São Paulo.

How macronutrients and pancreatic enzyme supplements dose variability affect fat, protein and starch absorption in children with cystic fibrosis.

low evidence on the dose of enzymatic supplements used in pancreatic enzyme replacement therapy (PERT) is available. assessing if fat, protein and starch absorption could be related to the dose of the enzymatic supplement, the intra-patient variability in the dose and macronutrient intake. Four-day food records and 3-day faecal samples were prospectively collected in 69 children with cystic fibrosis. Pearson correlations between enzyme dose and macronutrient absorption, and beta regression models were applied to explain the results. the supply of protease units per protein intake (PU/g protein) in relation to lipase units per fat intake (LU/g fat) was low and the intra-patient variability in the dose of enzymes was ±1331 LU/g fat. Fat and starch absorption was >90% while for protein it was 81.5%. The coefficient of fat absorption was associated with an interaction between the dose of LU/g fat and its variability among different days. Lipid and protein intake were also determinants of the coefficient of fat absorption. the dose of PERT should be re-adjusted to the amount of dietary fat of every meal (constant LU/g fat) to minimize variability and increase fat absorption. Also, the supply of protease should be increased to prevent from protein malabsorption.

Mapping EQ5D utilities from forced vital capacity and diffusing capacity in fibrotic interstitial lung disease.

Fibrotic interstitial lung disease (ILD) includes a large group of conditions that lead to scarring of the lungs. The lack of available 5-level EuroQol 5D (EQ5D) data has limited the ability to conduct economic evaluations in ILD. The purpose of this study was to develop and validate a mapping algorithm that predicts EQ5D utilities from commonly collected pulmonary function measurements (forced vital capacity [FVC] and diffusing capacity of the lung for carbon monoxide [DLCO]) in fibrotic ILDs. EQ5D utility and pulmonary function measurements from the Canadian Registry for Pulmonary Fibrosis were included. Ordinary least squares (OLS), beta regression, two-part, and tobit models were used to map EQ5D utilities from FVC or DLCO. Model performance was assessed by comparing the predicted and observed utilities. Subgroup analyses were also conducted to test how well models performed across different patient characteristics. The models were then externally validated in the Australian Idiopathic Pulmonary Fibrosis Registry. The OLS model performed as well as other more complex models (root mean squared error: 0.17 for FVC and 0.16 for DLCO). As with the other models, the OLS algorithm performed well across the different subgroups (except for EQ5D utilities < 0.5) and in the external validation cohort. We developed a mapping algorithm that predicts EQ5D utilities from FVC and DLCO, with the intent that this algorithm can be applied to clinical trial populations and real-world cohorts that have not prioritized collection of health-related utilities. The mapping algorithm can be used in future economic evaluations of potential ILD therapies.

Assessing the impact of local context and priorities regarding domestic disease outbreaks and imported risk on early pandemic response: Cross-continental comparisons.

Containment and closure policies are effective measures used in the early stages of a highly transmissible global pandemic such as COVID-19 to mitigate the spread and reduce transmissions. However, these policies can have negative impacts on the economy and personal freedom. Governments must carefully consider the necessity of increasing their stringency. Local contexts and priorities regarding domestic disease outbreaks and the risk of imported cases from other countries may vary among different countries, and could influence the decision to increase containment measures. Thus, this study aimed to differentiate the impacts of these affecting factors on the stringency of governmental containment measures through cross-continental comparisons. This study utilized a zero/one inflated beta (ZOIB) regression model to investigate how domestic epidemic, imported risk, and local context affect government responses to a pandemic. We used a country's weekly confirmed case and death numbers as a measure of its domestic threat. The imported risk was measured using a combination of weekly new cases in each country and the air passenger traffic between countries. The findings indicate that domestic case numbers are a primary concern for governments when deciding to increase policy stringency. Countries with higher development levels tend to implement stricter policies as they can better handle the negative impacts. Additionally, there is an interaction between case numbers and development level, with countries at the second or third highest development level focusing more on domestic outbreaks than imported risks, while those at the highest level have similar concerns for both. We concluded that most countries adjust policies' stringency majorly based on the variation of domestic case number rather than the other pandemic factors and the countries with a high development level tend to implement strict policies since their socio-economical condition could afford such policies. These insights can aid policymakers in improving containment and closure policies for future pandemics.

Model selection uncertainty and stability in beta regression models: A study of bootstrap-based model averaging with an empirical application to clickstream data

Statistical model development is a central feature of many scientific investigations with a vast methodological landscape. However, uncertainty in the model development process has received less attention and is frequently resolved nonrigorously through beliefs about generalizability, practical usefulness, and computational ease. This is particularly problematic in settings of abundant data, such as clickstream data, as model selection routinely admits multiple models and imposes a source of uncertainty, unacknowledged and unknown by many, on all postselection conclusions. Regression models, based on the beta distribution, are a class of nonlinear models, attractive because of their great flexibility and potential explanatory power, but have not been investigated from the standpoint of multimodel uncertainty and model averaging. For this reason a formalized tool that can combine model selection uncertainty and beta regression modeling is presented in this work. The tool combines bootstrap model averaging, model selection, and asymptotic theory to yield a procedure that can perform joint modeling of the mean and precision parameters, capture sources of variability in the data, and achieve more accurate claims of estimate precision, variable importance, generalization performance, and model stability. Practical utility of the tool is demonstrated through a study of model selection consistency and variable importance in average exit and bounce rate statistical models. This work emphasizes the necessity of a departure from the all-too-common practice of ignoring model selection uncertainty and introduces an accessible technique to handle frequently neglected aspects of the modeling pipeline.

Modified Jackknife Ridge Estimator for Beta Regression Model With Application to Chemical Data

The linear regression model is not applicable when the response variable's value comes in percentages, proportions, and rates, which are restricted to the interval (0, 1). In this situation, we applied the beta regression model (BRM) popularly used to model chemical, environmental and biological data. The parameters in the model are often estimated using the conventional method of maximum likelihood. However, this estimator is unreliable and inefficient when the explanatory variables are linearly correlated- a condition known as multicollinearity. Thus, we developed the Jackknife Beta ridge and the modified Jackknife Beta ridge estimator to estimate the regression coefficient when multicollinearity exists efficiently. The properties of the new estimators were derived. We compared the estimator's performance with the existing estimators theoretically using the mean squared error criterion. Furthermore, we conducted a simulation study and chemical data to evaluate the new estimators’ performance. The theoretical comparison, simulation, and real-life application results established the dominance of the proposed methods.

Are social media data and survey data consistent in measuring park visitation, park satisfaction, and their influencing factors? A case study in Shanghai

Given the importance of urban parks for recreation, it is critical to understand how they are used and perceived. Currently, relatively few studies have examined the public’s activities and preferences at the same time. Social media data are increasingly recognized as a promising data source to study these two aspects. However, little is known regarding the utility and representativeness of social media data for urban parks. In particular, a lack of understanding exists on the comparability of research results measured by bottom-up social media data and top-down official survey data in urban park studies. This research used social media data from Ctrip and Dianping and survey data from the local government agency with park visits statistics and park satisfaction surveys to understand the public’s visitation and satisfaction of 102 urban parks in central Shanghai. We first assessed the similarities between the social media data and survey data by correlation analysis. We then used the negative binomial regression model and beta regression model to examine the matches and mismatches of the different data sources in investigating factors influencing park visitation and park satisfaction. Our correlation results showed that the social media data significantly correlated with the survey data and that social media data performed better in more frequently visited parks. Our regression results showed that the water bodies, recreational facilities, and surrounding commercial facilities were the common influencing factors of park visitation and park satisfaction for all parks. While significant correlations were noticed between these two data sources, we found that the surrounding population density was negatively associated with park visitation measured by social media data but positively associated with park visitation measured by survey data. This study provides a comparative perspective to study park visitation and park satisfaction by combining social media data and official survey data. Clarifying the consistencies and inconsistencies between the social media data and official survey data is important because it could help us to understand the representativeness and potential biases of the social media data when used in visitation monitoring and satisfaction monitoring.

A monotone single index model for missing-at-random longitudinal proportion data

Beta distributions are commonly used to model proportion valued response variables, often encountered in longitudinal studies. In this article, we develop semi-parametric Beta regression models for proportion valued responses, where the aggregate covariate effect is summarized and flexibly modeled, using a interpretable monotone time-varying single index transform of a linear combination of the potential covariates. We utilize the potential of single index models, which are effective dimension reduction tools and accommodate link function misspecification in generalized linear mixed models. Our Bayesian methodology incorporates the missing-at-random feature of the proportion response and utilize Hamiltonian Monte Carlo sampling to conduct inference. We explore finite-sample frequentist properties of our estimates and assess the robustness via detailed simulation studies. Finally, we illustrate our methodology via application to a motivating longitudinal dataset on obesity research recording proportion body fat.

Climate Change Impacts and Adaptation Strategies of Cassava Farmers in Ebonyi State, Nigeria

The study evaluated the climate change impacts and adaptation strategies of cassava farmers in Ebonyi State, Nigeria. Multi-stage sampling was used to select 419 cassava farmers who administered the questionnaire. Data were collected using primary and secondary means and were analysed using mean, frequency, percentage, beta regression model, and ordinary least squares multiple regression techniques. Factors influencing cassava production are meteorological information (95.7%), tradition and culture (94.5%), improved technology utilization (93.1%) and low access to credits (71.8%). Climate change effects on cassava production were reduced biodiversity (95.2%), increased crop failure (97.6%), decreased yield (100%) and increased soil salinity (92.6%). Cassava farmers adapted to various practices such as planting improved cassava varieties (95.9%), insurance (3.3%), planting different crops (96.9%), and livelihood diversification (94.9%). Age, education, household size, farm size and extension contacts were significant determinants of climate change adaptation strategies of cassava farmers. Variables such as temperature, rainfall, humidity and sunshine had both positive and negative impacts on cassava production. The study recommends cassava farmers seek early warning signals and information on climate change before embarking on their farming operations to avert possible negative consequences.

Modelling seabirds biodiversity through Bayesian Spatial Beta regression models: A proxy to inform marine protected areas in the Mediterranean Sea

Seabirds are bioindicators of marine ecosystems health and one of the world's most endangered avian groups. The creation of marine protected areas plays an important role in the conservation of marine environment and its biodiversity. The distributions of top predators, as seabirds, have been commonly used for the management and creation of these figures of protection.The main objective of this study is to investigate seabirds biodiversity distribution in the Mediterranean Sea through the use of Bayesian spatial Beta regression models. We used an extensive historical database of at-sea locations of 19 different seabird species as well as geophysical, climatology variables and cumulative anthropogenic threats to model species biodiversity. We found negative associations between seabirds biodiversity and distance to the coast as well as concavity of the seabed, and positive with chlorophyll and slope. Further, a positive association was found between seabirds biodiversity and coastal impact.In this study we define as hot spot of seabird biodiversity those areas with a posterior predictive mean over 0.50. We found potential hot spots in the Mediterranean Sea which do not overlap with the existing MPASs and marine IBAs. Specifically, our hot spots areas do not overlap with the 52.04% and 16.87% of the current MPAs and marine IBAs, respectively. Overall, our study highlights the need for the extension of spatial prioritization of conservation areas to seabirds biodiversity, addressing the challenges of establishing transboundary governance.

Using beta regression modeling in medical sciences: a comparative study

Beta regression (BR) models provide an adequate approach for modeling continuous outcomes of limited intervals (0, 1). The BR model assumes that the dependent variable follows a beta distribution and that its mean is affiliated to a set of exploratory variables through a linear predictor known as coefficients and link function. The BR model also includes a dispersion parameter. This paper describes the BR model along with its properties. Furthermore, the comparison between different link functions of the BR model is conducted through a medical real-life application to laparoscopic surgical operations aiming to widen congenital obstruction in the connection between the kidney and ureter, a condition called ureteropelvic junction obstruction (UJO).

μσ2-Beta and μσ2-Beta Binomial Regression Models

This paper proposes new parameterizations of the beta and beta binomial distributions as functions of the mean and variance parameters. From these new parameterizations, new beta and beta binomial linear regression models are formulated by assuming that appropriate real functions of the mean and variance follow linear regression structures. These models were fitted to real datasets by applying Bayesian methods, using the OpenBUGS software. The new beta regression models were fitted to the Dyslexia Reading Accuracy dataset and the new beta binomial regression models were applied to the School Absenteeism Dataset. In both cases, the results obtained by fitting these models were compared with those obtained by fitting the usual mean and dispersion beta regression models and the mean and dispersion beta binomial regression models, respectively.