Quantile regression provides a framework for modeling the relationship between a response variable and covariates using the quantile function. This work proposes a regression model for continuous variables bounded to the unit interval based on the unit Birnbaum–Saunders distribution as an alternative to the existing quantile regression models. By parameterizing the unit Birnbaum–Saunders distribution in terms of its quantile function allows us to model the effect of covariates across the entire response distribution, rather than only at the mean. Our proposal, especially useful for modeling quantiles using covariates, in general outperforms the other competing models available in the literature. These findings are supported by Monte Carlo simulations and applications using two real data sets. An R package, including parameter estimation, model checking as well as density, cumulative distribution, quantile and random number generating functions of the unit Birnbaum–Saunders distribution was developed and can be readily used to assess the suitability of our proposal.
<p>Objetivo: Conhecer as experiências da maternidade e paternidade vivenciadas por adolescentes e a participação dos mesmos nos cuidados aos filhos. Método: Estudo descritivo, de natureza qualitativa realizado com 10 pais que vivenciaram a maternidade/paternidade na adolescência. Os dados foram coletados nos meses de novembro e dezembro de 2015, por meio de entrevistas semiestruturadas que foram submetidas à análise de conteúdo. Resultados: A gestação desencadeou conflitos, sentimento de felicidade, mudanças positivas e negativas na rotina diária dos adolescentes e de suas famílias. Os participantes destacaram não terem enfrentado dificuldades na realização dos cuidados com o recém-nascido, em razão do apoio fornecido pelos familiares e profissionais da saúde. Conclusão: A vivência da gestação não foi percebida como condição desfavorável ao casal adolescente; entretanto, o acompanhamento profissional e apoio dos pais é importante para a saúde da criança e desenvolvimento da nova família como um todo. </p><p><strong>Descritores:</strong> Adolescente. Gravidez na adolescência. Cuidado da criança.</p>
Covariate-related response variables that are measured on the unit interval frequently arise in diverse studies when index and proportion data are of interest. A regression on the mean is commonly used to model this relationship. Instead of relying on the mean, which is sensitive to atypical data and less general, we can estimate such a relation using fractile regression. A fractile is a point on a probability density curve such that the area under the curve between that point and the origin is equal to a specified fraction. Fractile or quantile regression modeling has been considered for some statistical distributions. Our objective in the present article is to formulate a novel quantile regression model which is based on a parametric distribution. Our fractile regression is developed reparameterizing the initial distribution. Then, we introduce a functional form based on regression through a link function. The main features of the new distribution, as well as the density, distribution, and quantile functions, are obtained. We consider a brand-new distribution to model the fractiles of a continuous dependent variable (response) bounded to the interval (0, 1). We discuss an R package with random number generators and functions for probability density, cumulative distribution, and quantile, in addition to estimation and model checking. Instead of the original distribution-free quantile regression, parametric fractile regression has lately been employed in several investigations. We use the R package to fit the model and apply it to two case studies using COVID-19 and medical data from Brazil and the United States for illustration.
The Vasicek distribution is a two-parameter probability model with bounded support on the open unit interval. This distribution allows for different and flexible shapes and plays an important role in many statistical applications, especially for modeling default rates in the field of finance. Although its probability density function resembles some well-known distributions, such as the beta and Kumaraswamy models, the Vasicek distribution has not been considered to analyze data on the unit interval, especially when we have, in addition to a response variable, one or more covariates. In this paper, we propose to estimate quantiles or means, conditional on covariates, assuming that the response variable is Vasicek distributed. Through appropriate link functions, two Vasicek regression models for data on the unit interval are formulated: one considers a quantile parameterization and another one its original parameterization. Monte Carlo simulations are provided to assess the statistical properties of the maximum likelihood estimators, as well as the coverage probability. An R package developed by the authors, named vasicekreg, makes available the results of the present investigation. Applications with two real data sets are conducted for illustrative purposes: in one of them, the unit Vasicek quantile regression outperforms the models based on the Johnson-SB, Kumaraswamy, unit-logistic, and unit-Weibull distributions, whereas in the second one, the unit Vasicek mean regression outperforms the fits obtained by the beta and simplex distributions. Our investigation suggests that unit Vasicek quantile and mean regressions can be of practical usage as alternatives to some well-known models for analyzing data on the unit interval.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.