Modelling Interval Data with Random Intercepts: A Beta Regression Approach for Clustered and Longitudinal Structures

Eğitim, her birey ve bir bütün olarak toplum için ekonomik, sosyal ve kültürel gelişimin temelidir. Ülkemizde orta öğretim kurumlarına Milli Eğitim Bakanlığı tarafından yapılan lise giriş sınavı ile öğrenci kabul edilmektedir. Bu çalışmada, 2019 yılında Türkiye'nin 81 ilinde lise giriş sınavına giren öğrencilerin başarı oranları makine öğrenimi regresyon ve beta regresyon modeli ile ele alınmıştır. Bu makale, boşanma oranı, gayri safi yurtiçi hasıla, okuma yazma bilmeyenlerin sayısı ve yüksek öğretim nüfusu sayısı gibi değişkenleri kullanarak öğrencilerin başarı oranlarını modellemeyi, tahmin etmeyi ve açıklamayı amaçlamaktadır. Başarı oranlarını tahmin etmek için destek vektörü regresyon, rastgele orman, karar ağacı ve beta regresyon modeli uygulanmıştır. En yüksek R2 değerine sahip iki modelin beta regresyon ve rastgele orman modelleri olduğu bulunmuştur. Beta regresyon ve rastgele orman modelinin tahmin hataları incelendiğinde, başarı oranlarını tahmin etmede rastgele orman modelinin beta regresyon modeline göre nispeten üstün olduğu görülmektedir. Beta regresyon modeli Çanakkale ilinin başarı oranlarının en iyi yordayıcısı iken, rastgele orman modeli Ankara'nın başarı oranlarını iyi tahmin etmiştir. Ayrıca beta regresyon modelinde başarı oranları için anlamlı bulunan değişkenlerin rastgele orman modelinde de önemli olduğu görülmüştür. Öğrencilerin başarı oranlarını tahmin etmek için hem beta hem de rastgele orman modellerinin kullanılması önerilir.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

QuestionsPlant cover values in vegetation plot data are bounded between 0 and 1, and cover is typically recorded in discrete classes with non‐equal intervals. Consequently, cover data are skewed and heteroskedastic, which hampers the application of conventional regression methods. Recently developed ordinal beta regression models consider these statistical difficulties. Our primary question is whether we can detect species trends in vegetation plot time series data with this modelling approach. A second question is whether trends in cover have additional value compared to trends in occurrence, which are easier to assess for practitioners.LocationThe Netherlands, Western Europe.MethodsWe used vegetation plot data collected from 10,000 fixed plots which were surveyed once every four years during 1999–2022. We used the ordinal zero‐augmented beta regression (OZAB) model, a hierarchical model consisting of a logistic regression for presence and an ordinal beta regression for cover. We adapted the OZAB model for longitudinal data and produced estimates of cover and occurrence for each four‐year period. Thereafter we assessed trends in cover and in occurrence across all periods.ResultsWe found evidence of a trend in cover in 318 out of the 721 species (44%) with sufficient data. Most species showed similar directional trends in occurrence and percent cover. No trend in occurrence was detected for 64 species that had evidence of a trend in cover. Declining species had stronger relative changes in cover than in occurrence.ConclusionsOur model enables researchers to detect trends in cover using longitudinal vegetation plot data. Cover trends often corroborated trends in occurrence, but we also regularly found trends in cover even in the absence of evidence for trends in occurrence. Our approach thus contributes to a more complete picture of (changes in) vegetation composition based on large monitoring data sets.

Comparison of random regression and repeatability models to predict breeding values from test-day records of Norwegian goats

Although beta regression is a very useful tool to model the continuous bounded outcome variable with some explanatory variables, however, in the presence of multicollinearity, the performance of the maximum likelihood estimates for the estimation of the parameters is poor. In this paper, we propose improved shrinkage estimators via Liu estimator to obtain more efficient estimates. Therefore, we defined linear shrinkage, pretest, shrinkage pretest, Stein and positive part Stein estimators to estimate of the parameters in the beta regression model, when some of them have not a significant effect to predict the outcome variable so that a sub-model may be sufficient. We derived the asymptotic distributional biases, variances, and then we conducted extensive Monte Carlo simulation study to obtain the performance of the proposed estimation strategy. Our results showed a great benefit of the new methodologies for practitioners specifically in the applied sciences. We concluded the paper with two real data analysis from economics and education.

Data on rates, percentages, or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology, and several others. In this paper, we develop a robust inference procedure for the beta regression model, which is used to describe such response variables taking values in (0, 1) through some related explanatory variables. In relation to the beta regression model, the issue of robustness has been largely ignored in the literature so far. The existing maximum likelihood-based inference has serious lack of robustness against outliers in data and generate drastically different (erroneous) inference in the presence of data contamination. Here, we develop the robust minimum density power divergence estimator and a class of robust Wald-type tests for the beta regression model along with several applications. We derive their asymptotic properties and describe their robustness theoretically through the influence function analyses. Finite sample performances of the proposed estimators and tests are examined through suitable simulation studies and real data applications in the context of health care and psychology. Although we primarily focus on the beta regression models with a fixed dispersion parameter, some indications are also provided for extension to the variable dispersion beta regression models with an application.

An efficient and informative statistical method to analyze genotype-by-environment interaction (GxE) is needed in maize breeding programs. Thus, the objective of this study was to compare the effectiveness of multiple-trait models (MTM), random regression models (RRM), and compound symmetry models (CSM) in the analysis of multi-environment trials (MET) in maize breeding. For this, a data set with 84 maize hybrids evaluated across four environments for the trait grain yield (GY) was used. Variance components were estimated by restricted maximum likelihood (REML), and genetic values were predicted by best linear unbiased prediction (BLUP). The best fit MTM, RRM, and CSM were identified by the Akaike information criterion (AIC), and the significance of the genetic effects were tested using the likelihood ratio test (LRT). Genetic gains were predicted considering four selection intensities (5, 10, 15, and 20 hybrids). The selected MTM, RRM, and CSM models fit heterogeneous residuals. Moreover, for RRM the genetic effects were modeled by Legendre polynomials of order two. Genetic variability between maize hybrids were assessed for GY. In general, estimates of broad-sense heritability, selective accuracy, and predicted selection gains were slightly higher when obtained using MTM and RRM. Thus, considering the criterion of parsimony and the possibility of predicting genetic values of hybrids for untested environments, RRM is a preferential approach for analyzing MET in maize breeding.

Our objective was to develop a beta regression (BR) model to describe the longitudinal progression of the 11 item Alzheimer's disease (AD) assessment scale cognitive subscale (ADAS-cog) in AD patients in both natural history and randomized clinical trial settings, utilizing both individual patient and summary level literature data. Patient data from the coalition against major diseases database (3,223 patients), the Alzheimer's disease neruroimaging initiative study database (186 patients), and summary data from 73 literature references (representing 17,235 patients) were fit to a BR drug-disease-trial model. Treatment effects for currently available acetyl cholinesterase inhibitors, longitudinal changes in disease severity, dropout rate, placebo effect, and factors influencing these parameters were estimated in the model. Based on predictive checks and external validation, an adequate BR meta-analysis model for ADAS-cog using both summary-level and patient-level data was developed. Baseline ADAS-cog was estimated from baseline MMSE score. Disease progression was dependent on time, ApoE4 status, age, and gender. Study drop out was a function of time, baseline age, and baseline MMSE. The use of the BR constrained simulations to the 0-70 range of the ADAS-cog, even when residuals were incorporated. The model allows for simultaneous fitting of summary and patient level data, allowing for integration of all information available. A further advantage of the BR model is that it constrains values to the range of the original instrument for simulation purposes, in contrast to methodologies that provide appropriate constraints only for conditional expectations.

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

This paper considers and studies a distinct special case of omega distribution defined on the unit interval (0, 1), called unit-omega distribution. Thanks to its simple form, some of its basic properties are derived. The maximum likelihood method, Bayes method, and the method of moments are used to estimate the parameters of unit-omega distribution. These estimation methods are examined by conducting a simulation study. More importantly, the quantile function of unit-omega distribution has a closed-form expression that allows modeling the conditional quantiles of a unit response variable as a function of covariates. Residual analysis is performed using randomized quantile residuals and Cox–Snell residuals. The proposed approach is used to model the quantiles of child mortality rates, conditional on covariates. These covariates represent the proportions of people left behind across three key indicators: nutrition, availability of safe drinking sources and adequate education. Another application that relates to recovery rates of viable CD34+ cell is presented. From both applications, the fitting results of the proposed regression model outperform those of beta, Kumaraswamy and unit-Weibull regression models.

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.

Mapping the Lequesne Functional Index Into the EQ-5D-5L Utility Index in Patients With Knee Osteoarthritis

Mixed beta regression: A Bayesian perspective

Beta regression model is used for modeling proportions measured on a continuous scale; its parameters are estimated with the maximum likelihood method. Classical regression models, such as linear regression model and nonlinear regression models like logistic regression are not suitable for such situations. As in linear regression model, the independent variables are assumed to be uncorrelated if this assumption is not met, then the multicollinearity appears. Multicollinearity problem means that there is a near dependency between the independent variables. Biased estimators are commonly used for correcting the multicollinearity problem. In this study, we propose a generalized biased estimator for correcting multicollinearity in beta regression that is generalize beta ridge regression estimator (GBRRE). The performance of the proposed generalized biased estimator is evaluated theoretically via the matrix mean squared errors and the scalar mean squared errors; and practically using a Monte Carlo simulation study. The simulation results show that the optimal shrinkage estimator is K1 and the worst one is K2. Also, the proposed generalized estimator is applied to a real data set of pre-university education students in Egypt during the academic year (2018/2019) and we found the application results agree with the simulation results. Finally based on the results of the simulation study and the application the performance of the suggested generalized biased estimator is better than maximum likelihood estimators.

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.