Beta Regression Model Research Articles

A new modified ridge-type estimator for the beta regression model: simulation and application

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

Modelling extreme precipitation: an application to two selected rainfall stations in Malaysia

Statistical models of rainfall have been applied in the understanding of the rainfall past trends, identifying for any anomalies, and making projections of future climate change in Malaysia. Herein, we analyse the rainfall data of 7-year period using the gamma and beta regression models to fit Malaysian extreme precipitation events of two stations, each in the West Coast region and the East Coast region, with extreme precipitation calendar date (in the angular form) as the predictor of the models. While the significance test as the p-value is much less than 0.05, it shows that there is a significant relationship between the climatology response variables. The deviance residual plot will be used to check the goodness of fit for diagnostic checking. The results show the models are useful in highlighting the latest trends and projections of climate change in Malaysia.

Residual and local influence analyses for unit gamma regressions

AbstractWe obtain local influence measures and residuals for the unit gamma regression model. In particular, we introduce four residuals that are based on Fisher's iterative scoring parameter estimation algorithm and develop local influence analysis based on several different perturbation schemes: cases weighting, response additive perturbation, and covariate(s) additive perturbation. An empirical application in which variables related to education and investment in research and development are used to explain the proportion of nonpoor people in a set of countries is presented and discussed. Residual and local influence analyses show that the unit gamma regression model yields a good fit to the data, even outperforming the beta regression model. The diagnostic analysis singles out countries whose data are worthy of further investigation. Our results reveal that lower poverty levels are associated with higher shares of investment in high technology. The statistical significance of such a relationship is not sensitive to atypical data points.

Antibody kinetics and exposure to Toxoplasma gondii in cats: a seroepidemiological study

Domestic cats are the most important definitive hosts for Toxoplasma gondii, the agent of an important global zoonosis. Serial sera from cats orally inoculated either withT. gondii tissue cysts (n = 3) or sporulated oocysts (n = 3) and from 65 client-owned cats, plus sera from 1,757 client-owned cats presented to veterinarians in Switzerland were analysed for an antibody response to T. gondii by ELISA. Risk factors for seropositivity and prevalence were estimated with a generalised linear and beta regression model. The first model examined the association of an OD405 value as the dependent variable, with gender, age, and outside access as possible independent variables. In the second model, we first analysed the data assuming a bimodal distribution representing two overlapping distributions of OD405 values from positive and negative cats, enabling the assignment of a probability of true infection status to each cat. Mean probabilities of true infection status across groups represent an estimate of true prevalence. These probabilities were then regressed against age, gender and outside access. Antibody kinetics in cats orally inoculated with tissue cysts, shedding oocysts, did not differ significantly from those of cats inoculated with sporulated oocysts without detectable oocyst excretion, suggesting extraintestinal parasite invasion and exposure to tachyzoites in both situations at an early stage of infection. Analysis of serial serum samples suggested a persisting long-term humoral immune response. Of the client-owned cats, 42.4% (95% confidence interval (CI): 40.1–44.6) had a positive true infection status. This was higher (56.3% (95% CI: 53.2–59.6)) in cats with outside access than in those without (22.1% (95% CI: 18.9–25.4)). In the first model, the factors age (P < 0.0001), gender (male: P = 0.046), and outside access (P < 0.0001) were independently associated with significantly higher OD405 values. In the second model, the probability of having a positive true infection status increased with age (P < 0.0001), was higher with outside access (P < 0.0001) and in outdoor male cats (P = 0.0006).

Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Background: Typically, modeling of health-related quality of life data is often troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. Objectives: In the present paper, we aim to investigate whether Bayesian beta regression is appropriate for analyzing the SF-6D health state utility scores and respondent characteristics. Methods: A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). Results: For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criteria used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (−1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Conclusions: Beta regression provides a flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged.

Polygenic risk score for Alzheimer’s disease and its association with eye movement performance

AbstractBackgroundMany neurodegenerative disorders are characterised by changes in specific eye movement (EM) outcomes. Individuals with Alzheimer’s disease (AD) make more antisaccade errors and correct a lower proportion of those errors compared to controls. EM impairments occur at an early stage of neuropathological changes and have, therefore, been discussed as a potential biomarker. Despite high test‐retest correlations for measures of EM performance and an estimated heritability of &gt;40% for antisaccade performance, genetic association studies identified only a few single‐nucleotide polymorphisms (SNPs) related to EM performance. Polygenic risk scores (PRSs) are advantageous as they summarize the effects of many SNPs into a single score. Therefore, we assessed whether higher genetic risk for AD in healthy participants was associated with higher antisaccade error rate and lower correction rate of antisaccade errors.MethodThe analyses were based on data of the first 2,000 participants (aged 30‐95) of the Rhineland Study, a community‐based prospective cohort study in Bonn, Germany. Genotyping was performed on Omni 2.5 exome arrays. We created PRS for AD by including all SNPs that reached genome‐wide significance at a threshold of p=5x10‐7in stage one of the GWAS of the “IGAP consortium”. Missing SNPs were imputed using the 1000 Genomes reference panel. We examined the association between genetic risk for AD and antisaccade error rate using multivariable regression with PRS as predictor and antisaccade error rate as outcome variables. For antisaccade correction rate we used a one‐inflated beta regression model as the residuals were severely skewed. Ancestry, age, age2, sex, visual acuity and education were added as covariates in both regression models.ResultPolygenic risk for AD was associated with neither antisaccade error rate nor the proportion of uncorrected errors in those who did not correct all of their errors. However, a higher PRS for AD was associated with a lower odds of correcting all mistakes (odds ratio=0.85 (95%‐CI:0.73‐1.00) per one standard deviation increase in PRS).ConclusionPolygenic risk for AD was associated with error correction rate in healthy individuals. Our findings suggest that eye movement performance may be a potential biomarker for early‐stage AD‐related neuropathological changes in the general population.

Post-Fire Vegetation Response in a Repeatedly Burned Low-Elevation Sagebrush Steppe Protected Area Provides Insights About Resilience and Invasion Resistance

Sagebrush steppe ecosystems are threatened by human land-use legacies, biological invasions, and altered fire and climate dynamics. Steppe protected areas are therefore of heightened conservation importance but are few and vulnerable to the same impacts broadly affecting sagebrush steppe. To address this problem, sagebrush steppe conservation science is increasingly emphasizing a focus on resilience to fire and resistance to non-native annual grass invasion as a decision framework. It is well-established that the positive feedback loop between fire and annual grass invasion is the driving process of most contemporary steppe degradation. We use a newly developed ordinal zero-augmented beta regression model fit to large-sample vegetation monitoring data from John Day Fossil Beds National Monument, USA, spanning 7 years to evaluate fire responses of two native perennial foundation bunchgrasses and two non-native invasive annual grasses in a repeatedly burned, historically grazed, and inherently low-resilient protected area. We structured our model hierarchically to support inferences about variation among ecological site types and over time after also accounting for growing-season water deficit, fine-scale topographic variation, and burn severity. We use a state-and-transition conceptual diagram and abundances of plants listed in ecological site reference conditions to formalize our hypothesis of fire-accelerated transition to ecologically novel annual grassland. Notably, big sagebrush (Artemisia tridentata) and other woody species were entirely removed by fire. The two perennial grasses, bluebunch wheatgrass (Pseudoroegneria spicata) and Thurber's needlegrass (Achnatherum thurberianum) exhibited fire resiliency, with no apparent trend after fire. The two annual grasses, cheatgrass (Bromus tectorum) and medusahead (Taeniatherum caput-medusae), increased in response to burn severity, most notably medusahead. Surprisingly, we found no variation in grass cover among ecological sites, suggesting fire-driven homogenization as shrubs were removed and annual grasses became dominant. We found contrasting responses among all four grass species along gradients of topography and water deficit, informative to protected-area conservation strategies. The fine-grained influence of topography was particularly important to variation in cover among species and provides a foothold for conservation in low-resilient, aridic steppe. Broadly, our study demonstrates how to operationalize resilience and resistance concepts for protected areas by integrating empirical data with conceptual and statistical models.

How do Bookmakers Interpret Running Performance of Teams in Previous Games? Evidence From the Football Bundesliga

This study examines how running performance (intensive runs, total distance covered) of football teams in previous games impacts betting markets as it relates to expected win probability. Theoretically, bookmakers could interpret team’s running performance as effort or fatigue, with sports science studies suggesting that distance covered reflects effort and intensive runs signal fatigue. Using data from the 2011/12-2018/19 seasons of the German Bundesliga, beta regression models reveal that bookmakers interpret team’s running performance in previous games contrary to physiological explanations in sports sciences. Tests of market efficiency incorporating these findings do not find a profitable betting strategy for bettors.

Transport modes and tourism seasonality in Italy: By air or by road?

From the late 1990s, the European air transport deregulation has led to the increasing use of the plane to reach tourist destinations. This article investigates the impact of tourists’ changed traveling habits on Italy’s seasonal tourism demand pattern. The role of transportation on seasonality, indeed, has been almost neglected in empirical research. We analyze international monthly arrivals by transport modes from 1997 to 2018, and we use the Gini index as a measure of seasonality. The Gini’s decomposition allows us to evaluate the effects of the growth in the use of each transport mode (cars, planes, ships, trains) on seasonality. A beta regression model confirms that an increment in the proportion of tourist arrivals by airplane determines a reduction in Italy’s overall seasonality of international tourism demand. These results might be a starting point for policy makers in developing strategies to counteract seasonality.

Food preferences determine human–elephant coexistence in African woodlands

AbstractHuman–elephant coexistence remains a major conservation and livelihood challenge across elephantLoxodonta africanarange in Africa. This study investigates the extent of elephant crop damage on 66 farms in the Selous–Niassa corridor (Tanzania), to search for potential management solutions to this problem. We found that the relative abundance of highly preferred crops (area covered by preferred crops divided by the total area of each farm) was by far the most important factor determining crop damage by elephants. Eighteen crop types were ranked according to their preference by elephants. Sweet potatoes, bananas, peanuts, onions, pumpkins and maize were the most preferred crops, with maize the most common crop among those highly preferred. On average elephants damaged 25.7% of the cultivated farmland they entered. A beta regression model suggests that a reduction in the cultivation of preferred crops from 75 to 25% of the farmland area decreases elephant crop damage by 64%. Water availability (distance to the nearest waterhole) and the presence of private investors (mostly hunting tourism companies) were of lower importance in determining elephant crop damage. Thus, damage by elephants increased with shorter distances to waterholes and decreased in areas with private investors. However, further studies are required, particularly of the perceived costs and benefits of elephants to local communities. Farm aggregation and the use of non-preferred crops that also require less water would potentially reduce elephant damage but would be a major lifestyle change for some local communities.

The Effect of Forms’ Ratio of Conditioning on Word-Final /s/ Voicing in Mexican Spanish

There is mounting evidence that words that occur proportionately more often in contexts that condition a phonetically-motivated sound change end up changing more rapidly than other words. Support has been found in at least modern-day Spanish, Medieval Spanish, bilingual English-Spanish, and modern-day English. This study tests whether there is support for this idea with regards to the variable voicing of word-final /s/ in Spanish. An analysis of 1431 tokens of word-final /s/ spoken by 15 female speakers of Mexican Spanish living in Salinas, California, USA is performed. The response variable is the percentage of the /s/ segment that is voiced, and the effect of a handful of predictor variables shown in the literature to condition /s/ voicing is investigated. The variable of interest is forms’ ratio of conditioning (FRC), or the proportion of times with which word types occur in the context that conditions voicing of word-final /s/. The results of a series of 40 beta regression models indicate that FRC significantly conditions the percentage of voicing of word-final /s/ in these data. Also, the effect of manipulating two aspects of FRC operationalization is analyzed. This study adds to the growing body of literature documenting the importance of cumulative contextual information in the mental representation of words.

The effect of group size, reproductive condition and time period on sexual segregation patterns in three vespertilionid bat species

AbstractSexual segregation is widespread across the animal kingdom, yet there is limited consensus on the factors that shape this behavioural phenomenon. Many of the existing theories are based on study species with high levels of sexual size dimorphism. Insights from studies on species with minimal sexual size dimorphism, such as vespertilionid bats, provide an opportunity to study the factors associated with segregation irrespective of body size effects. Using long‐term data pooled from multiple bat box monitoring schemes across the U.K., we investigated segregation patterns in maternity roosts of three vespertilionid bat species, Bechstein’s bat, Myotis bechsteinii, Natterer’s bat, M. nattereri and brown long‐eared bat, Plecotus auritus. We used the Sexual Segregation and Aggregation Statistic (SSAS) to evaluate temporal trends of sexual segregation of roosts over the reproductive period (divided into pre‐parturition, lactation and post‐lactation periods). Additionally, we used generalized linear mixed models and beta regression models to investigate the effect of group size on segregation patterns. Our results showed that the size of the maternity group was an important covariate of inter‐ and intra‐sexual segregation, with males and non‐breeding females typically segregated from large maternity groups across all three periods. Additionally, we demonstrate that reproductive condition and period influence segregation patterns, with breeding females segregated from non‐breeding females and males during the lactation period. Although sexual segregation may be caused by multiple mechanisms, our results show that group size, female reproductive condition and time period are key factors associated with segregation within bat roosts. These findings make a valuable contribution to the understanding of inter‐ and intra‐sexual segregation in vespertilionid bats and complement existing research on segregation in other mammalian taxa, providing further evidence that sexual size dimorphism is not a prerequisite for sexual segregation.

An innovative method to estimate lifetime prevalence of carcinogenic occupational circumstances: the example of painters and workers of the rubber manufacturing industry in France.

Existing methods to estimate lifetime exposure to occupational carcinogenic agents could be improved. We propose a new method to estimate the lifetime prevalence of exposure to occupational carcinogens using the example of painters and workers of the rubber industry in France. From census, we calculated the proportion of painters and rubber industry workers using predefined occupational codes related to each occupation by sex and 10-year age group in 1982, 1990, 1999, 2007, and 2013. Using a beta-regression model, we obtained the yearly prevalence of exposure by 10-year age group over the period 1967-2007. We estimated the age- and sex-specific lifetime prevalence of exposure of the population in 2017 over 1967-2007, summing up the estimated prevalence of exposure for years 1967, 1977, 1987, 1997, and 2007 combined with a sex- and age-specific turnover factor. Corresponding population-attributable fractions were estimated for lung and bladder cancers in 2017. In 2017, we estimated that 5.6 and 0.2% of men in France had ever worked as a painter or in the rubber industry, respectively, during their working time. The lifetime prevalence of ever having worked as a painter or in the rubber industry was much lower in women: 1.8% and 0.1%, respectively. We estimated that 950 lung cancer and 40 bladder cancer cases were attributable to these occupations in 2017. Based on accurate data and taking into account evolution of specific jobs over time, the proposed method provides good estimates of lifetime prevalence of exposure to occupational carcinogens. It could be applied in any other country with similar data.

Adjusted R2 - type measures for beta regression model

R 2 measure, which named coefficient of determination, is usually used as tools for evaluation the predictive power of the regression models. However, this measure, which is based on deviance for generalized linear models, is sensitive to the small samples. Therefore, it is necessary to adjust R 2 measure according to the number of covariates. Beta regression model has received much attention in several science fields in modeling proportions or rates data. In this paper, several adjusted R 2 measures are proposed in beta regression models. The performance of the proposed measures is evaluated through simulation and real data application. Results demonstrate the superiority of the proposed measures compared to others.

Prioritizing Management of Non-Native Eurasian Watermilfoil Using Species Occurrence and Abundance Predictions

Prioritizing the prevention and control of non-native invasive species requires understanding where introductions are likely to occur and cause harm. We developed predictive models for Eurasian watermilfoil (EWM) (Myriophyllum spicatum L.) occurrence and abundance to produce a smart prioritization tool for EWM management. We used generalized linear models (GLMs) to predict species occurrence and extended beta regression models to predict abundance from data collected on 657 Wisconsin lakes. Species occurrence was positively related to the nearby density of vehicle roads, maximum air temperature, lake surface area, and maximum lake depth. Species occurrence was negatively related to near-surface lithological calcium oxide content, annual air temperature range, and average distance to all known source populations. EWM abundance was positively associated with conductivity, maximum air temperature, mean distance to source, and soil erodibility, and negatively related to % surface rock calcium oxide content and annual temperature range. We extended the models to generate occurrence and predictions for all lakes in Wisconsin greater than 1 ha (N = 9825), then prioritized prevention and management, placing highest priority on lakes likely to experience EWM introductions and support abundant populations. This modelling effort revealed that, although EWM has been present for several decades, many lakes are still vulnerable to introduction.

The beta and simplex regression models to explain homicides in state capitals of Brazil

The intentional killing of one human being by its own kind is considered the worst of the crimes. Therefore, homicide prevention is a major concern for policy makers in both developing and developed countries. We propose regression modeling for the homicide rates in Brazil along with appropriately chosen distributions for these responses that are in agreement with the restriction of values to the unit interval. We adopt the beta and simplex regression models with systematic components for the mean and dispersion parameters to explain the homicide rates in 27 state capitals of Brazil from the following explanatory variables: time, Gini coefficient, municipal human development index (MHDI), illiteracy and poverty rates. We employ standard likelihood techniques, perform influence and residual analysis and calculate goodness-of-fit statistics to select the best regression to explain homicides rates in these capitals. We perform the computations in the R package. The main results suggest the following: the mean homicide rate is increasing over time; there is a negative correlation between MHDI and murder rate; the poverty has a quite small negative impact on the mean homicide rates in the beta regression. The Gini coefficient and the illiteracy and poverty rates explain the dispersion of the homicide rates.

Livelihood Vulnerabilities Among Women in Small-Scale Fisheries in Ghana

Women play essential role in the fisheries sector of Ghana, particularly their involvement in post-harvest activities. However, several factors make them vulnerable to livelihood insecurity. This paper investigates the livelihood vulnerabilities of women in small-scale fisheries in the Gomoa, West District of Ghana by constructing a multi-dimensional livelihood vulnerability index for women fish processors-traders and identifying the factors that make them vulnerable. The Alkire-Foster multi-dimensional measure was used to quantify livelihood vulnerability based on the capital assets identified in the Sustainable Livelihood Framework and alternative livelihood options explored. A beta regression model was used to further examine the effect of other socio-economic characteristics on their vulnerability. The results show that 70 per cent of the women surveyed were multi-dimensionally vulnerable to livelihood insecurity and were deprived in 80 percent of the indicators. The results of the beta regression revealed that differences in multi-dimensional vulnerability are explained by age, household size, household head, access to remittances, and post-harvest losses (fish spoilage). The paper provides valuable insights on how to build resilience of women in small-scale fisheries in Ghana. To sustain and enhance the livelihoods of women in the sector, policy interventions should focus on improving their access to livelihood resources, particularly social capital, as well as building human and institutional capacity.

Safety and functional enrichment of gut microbiome in healthy subjects consuming a multi-strain fermented milk product: a randomised controlled trial

Many clinical studies have evaluated the effect of probiotics, but only a few have assessed their dose effects on gut microbiota and host. We conducted a randomized, double-blind, controlled intervention clinical trial to assess the safety (primary endpoint) of and gut microbiota response (secondary endpoint) to the daily ingestion for 4 weeks of two doses (1 or 3 bottles/day) of a fermented milk product (Test) in 96 healthy adults. The Test product is a multi-strain fermented milk product, combining yogurt strains and probiotic candidate strains Lactobacillus paracasei subsp. paracasei CNCM I-1518 and CNCM I-3689 and Lactobacillus rhamnosus CNCM I-3690. We assessed the safety of the Test product on the following parameters: adverse events, vital signs, hematological and metabolic profile, hepatic, kidney or thyroid function, inflammatory markers, bowel habits and digestive symptoms. We explored the longitudinal gut microbiota response to product consumption and dose, by 16S rRNA gene sequencing and functional contribution by shotgun metagenomics. Safety results did not show any significant difference between the Test and Control products whatever the parameters assessed, at the two doses ingested daily over a 4-week-period. Probiotic candidate strains were detected only during consumption period, and at a significantly higher level for the three strains in subjects who consumed 3 products bottles/day. The global structure of the gut microbiota as assessed by alpha and beta-diversity, was not altered by consumption of the product for four weeks. A zero-inflated beta regression model with random effects (ZIBR) identified a few bacterial genera with differential responses to test product consumption dose compared to control. Shotgun metagenomics analysis revealed a functional contribution to the gut microbiome of probiotic candidates.

Unit-Lindley mixed-effect model for proportion data

Recently, unit-Lindley distribution and its associated regression models have been developed as an alternative to Beta regression model for which continuous outcome in the unit interval . Proportion data usually occur in clinical trials, economics and social studies with hierarchical structures. In this study, unit-Lindley mixed-effect model is proposed and the appropriate likelihood analysis methods for parameter estimation are investigated. In the case of clustered or longitudinal proportion data in mixed-effect models, the full-likelihood function does not have a closed form. Parameter estimations of unit-Lindley mixed-effect model are obtained with Laplace and adaptive Gaussian quadrature approximation methods in this study. We analyzed a dataset on the proportion of households with insufficient water supply and sewage with some sociodemographic variables in the cities of Brazil by using unit-Lindley mixed-effect model including a random intercept as federative states of Brazil. Analysis results indicate that the proposed unit-Lindley mixed-effect model provides better fit than unit-Lindley regression model and beta mixed model. Also, in the simulation study the accuracy of the estimates of approximation methods are evaluated and compared via Monte Carlo simulation study in terms of bias and mean square error.

Urban-regional patterns of food purchasing behaviour: a cross-sectional analysis of the 2015-2016 Australian Household Expenditure Survey.

In many high-income countries people living in regional (rural) areas have higher rates of chronic disease compared to people living in urban areas. Food purchasing behaviour provides a potential pathway linking residential location with dietary intake and health outcomes. This study examined the relationship between geographic location and food expenditure on a range of foods. Data from the 2015-2016 Australian Household Expenditure Survey (number of households = 9827) were used to examine weekly household food expenditure and proportion of total food expenditure on 14 categories of food items. Foods were classified using the Australian Guide to Healthy Eating. Two-part models and zero-one inflated beta regression models were used to assess the association between geographic area and food expenditure. Average proportion of total food expenditure on fruit was estimated to be more for households located in major cities compared to households located in inner and outer regional areas. Households located in inner and outer regional areas allocated less to fresh fruit, fish and meals out compared to households in major cities. Households located in inner regional areas allocated a greater proportion of their food budget to sweet cakes, biscuits, puddings, desserts, chocolate and ice-cream compared to households in major cities and outer regional areas. The geographic patterns in food purchasing suggest those in regional areas may be at risk of diets less aligned with healthy guidelines. Given the findings of this study suggesting geographic differences in food purchasing, further research is warranted to enhance contextual understanding of food purchasing behaviours in regional areas.