A beta regression analysis of COVID-19 mortality in Brazil.

Brazil was one of the countries most impacted by the COVID-19 pandemic, with a cumulative total of nearly 700,000 deaths by early 2023. The country's federative units were unevenly affected by the pandemic and adopted mitigation measures of different scopes and intensity. There was intense conflict between the federal government and state governments over the relevance and extent of such measures. We build a simple regression model with good predictive power on state COVID-19 mortality rates in Brazil. Our results reveal that the federative units' urbanization rate and per capita income are important for determining their mean mortality rate and that the number of physicians per 100,000 inhabitants is important for modeling the mortality rate precision. Based on the fitted model, we obtain approximations for the levels of administrative efficiency of local governments in dealing with the pandemic.

The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates.

The Beta distribution is the standard model for quantifying the influence of covariates on the mean of a response variable on the unit interval. However, this well-known distribution is no longer useful when we are interested in quantifying the influence of such covariates on the quantiles of the response variable. Unlike Beta, the Kumaraswamy distribution has a closed-form expression for its quantile and can be useful for the modeling of quantiles in the absence/presence of covariates. As an alternative to the Kumaraswamy distribution for the modeling of quantiles, in this paper the unit-Weibull distribution was considered. This distribution was obtained by the transformation of a random variable with Weibull distribution. The same transformation applied to a random variable with Exponentiated Exponential distribution generates the Kumaraswamy distribution. The suitability of our proposal was demonstrated to model quantiles, conditional on covariates, with two simulated examples and three real applications with datasets from health, accounting and social science. For such data sets, the obtained fits of the proposed regression model were compared with those provided by the Beta and Kumaraswamy regression models.

Modified likelihood ratio tests for unit gamma regressions.

Regression analyses are commonly performed with doubly limited continuous dependent variables; for instance, when modeling the behavior of rates, proportions and income concentration indices. Several models are available in the literature for use with such variables, one of them being the unit gamma regression model. In all such models, parameter estimation is typically performed using the maximum likelihood method and testing inferences on the model's parameters are usually based on the likelihood ratio test. Such a test can, however, deliver quite imprecise inferences when the sample size is small. In this paper, we propose two modified likelihood ratio test statistics for use with the unit gamma regressions that deliver much more accurate inferences when the number of data points in small. Numerical (i.e. simulation) evidence is presented for both fixed dispersion and varying dispersion models, and also for tests that involve nonnested models. We also present and discuss two empirical applications.

Burkholderia tropica as a Potential Microalgal Growth-Promoting Bacterium in the Biosorption of Mercury from Aqueous Solutions.

The use of microalgal biomass is an interesting technology for the removal of heavy metals from aqueous solutions owing to its high metal-binding capacity, but the interactions with bacteria as a strategy for the removal of toxic metals have been poorly studied. The goal of the current research was to investigate the potential of Burkholderia tropica co-immobilized with Chlorella sp. in polyurethane discs for the biosorption of Hg(II) from aqueous solutions and to evaluate the influence of different Hg(II) concentrations (0.041, 1.0, and 10 mg/l) and their exposure to different contact times corresponding to intervals of 1, 2, 4, 8, 16, and 32 h. As expected, microalgal bacterial biomass adhered and grew to form a biofilm on the support. The biosorption data followed pseudo-second-order kinetics, and the adsorption equilibrium was well described by either Langmuir or Freundlich adsorption isotherm, reaching equilibrium from 1 h. In both bacterial and microalgal immobilization systems in the coimmobilization of Chlorella sp. and B. tropica to different concentrations of Hg(II), the kinetics of biosorption of Hg(II) was significantly higher before 60 min of contact time. The highest percentage of biosorption of Hg(II) achieved in the co-immobilization system was 95% at pH 6.4, at 3.6 g of biosorbent, 30 ± 1°C, and a mercury concentration of 1 mg/l before 60 min of contact time. This study showed that co-immobilization with B. tropica has synergistic effects on biosorption of Hg(II) ions and merits consideration in the design of future strategies for the removal of toxic metals.

On nonlinear beta regression residuals.

We proposed a new residual to be used in linear and nonlinear beta regressions. Unlike the residuals that had already been proposed, the derivation of the new residual takes into account not only information relative to the estimation of the mean submodel but also takes into account information obtained from the precision submodel. This is an advantage of the residual we introduced. Additionally, the new residual is computationally less intensive than the weighted residual. Recall that the computation of the latter involves an n×n matrix, where n is the sample size. Obviously, that can be a problem when the sample size is very large. In contrast, our residual does not suffer from that. It can be easily computed even in large samples. Finally, our residual proved to be able to identify atypical observations as well as the weighted residual. We also propose new thresholds for residual plots and a scheme for the choice of starting values to be used in maximum likelihood point estimation in the class of nonlinear beta regression models. We report Monte Carlo simulation results on the behavior of different residuals. We also present and discuss two empirical applications; one uses the proportion of killed grasshoppers in an assay on the grasshopper Melanopus sanguinipes with the insecticide carbofuran and the synergist piperonyl butoxide, which enhances the toxicity of the insecticide, and the other uses simulated data. The results favor the new methodology we introduce.