Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications

Everything, altogether, all at once: Addressing data challenges when measuring speech intelligibility through entropy scores

When investigating unobservable, complex traits, data collection and aggregation processes can introduce distinctive features to the data such as boundedness, measurement error, clustering, outliers, and heteroscedasticity. Failure to collectively address these features can result in statistical challenges that prevent the investigation of hypotheses regarding these traits. This study aimed to demonstrate the efficacy of the Bayesian beta-proportion generalized linear latent and mixed model (beta-proportion GLLAMM) (Rabe-Hesketh et al., Psychometrika, 69(2), 167-90, 2004a, Journal of Econometrics, 128(2), 301-23, 2004c, 2004b; Skrondal and Rabe-Hesketh 2004) in handling data features when exploring research hypotheses concerning speech intelligibility. To achieve this objective, the study reexamined data from transcriptions of spontaneous speech samples initially collected by Boonen et al. (Journal of Child Language, 50(1), 78-103, 2023). The data were aggregated into entropy scores. The research compared the prediction accuracy of the beta-proportion GLLAMM with the normal linear mixed model (LMM) (Holmes et al., 2019) and investigated its capacity to estimate a latent intelligibility from entropy scores. The study also illustrated how hypotheses concerning the impact of speaker-related factors on intelligibility can be explored with the proposed model. The beta-proportion GLLAMM was not free of challenges; its implementation required formulating assumptions about the data-generating process and knowledge of probabilistic programming languages, both central to Bayesian methods. Nevertheless, results indicated the superiority of the model in predicting empirical phenomena over the normal LMM, and its ability to quantify a latent potential intelligibility. Additionally, the proposed model facilitated the exploration of hypotheses concerning speaker-related factors and intelligibility. Ultimately, this research has implications for researchers and data analysts interested in quantitatively measuring intricate, unobservable constructs while accurately predicting the empirical phenomena.

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications

In this paper, we propose and derive a new regression model for response variables defined on the open unit interval. By reparameterizing the unit generalized half-normal distribution, we get the interpretation of its location parameter as being a quantile of the distribution. In addition, we can evaluate effects of the explanatory variables in the conditional quantiles of the response variable as an alternative to the Kumaraswamy quantile regression model. The suitability of our proposal is demonstrated with two simulated examples and two real applications. For such data sets, the obtained fits of the proposed regression model are compared with that provided by a Kumaraswamy regression model.

A Type I Generalized Logistic Distribution: Solving Its Estimation Problems with a Bayesian Approach and Numerical Applications Based on Simulated and Engineering Data

The family of logistic type distributions has been widely studied and applied in the literature. However, certain estimation problems exist in some members of this family. Particularly, the three-parameter type I generalized logistic distribution presents these problems, where the parameter space must be restricted for the existence of their maximum likelihood estimators. In this paper, motivated by the complexities that arise in the inference under the likelihood approach utilizing this distribution, we propose a Bayesian approach to solve these problems. A simulation study is carried out to assess the performance of some posterior distributional characteristics, such as the mean, using Monte Carlo Markov chain methods. To illustrate the potentiality of the Bayesian estimation in the three-parameter type I generalized logistic distribution, we apply the proposed method to real-world data related to the copper metallurgical engineering area.

A Study on Computational Algorithms in the Estimation of Parameters for a Class of Beta Regression Models

Beta regressions describe the relationship between a response that assumes values in the zero-one range and covariates. These regressions are used for modeling rates, ratios, and proportions. We study computational aspects related to parameter estimation of a class of beta regressions for the mean with fixed precision by maximizing the log-likelihood function with heuristics and other optimization methods. Through Monte Carlo simulations, we analyze the behavior of ten algorithms, where four of them present satisfactory results. These are the differential evolutionary, simulated annealing, stochastic ranking evolutionary, and controlled random search algorithms, with the latter one having the best performance. Using the four algorithms and the optim function of R, we study sets of parameters that are hard to be estimated. We detect that this function fails in most cases, but when it is successful, it is more accurate and faster than the others. The annealing algorithm obtains satisfactory estimates in viable time with few failures so that we recommend its use when the optim function fails.

A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.