A parametric quantile regression approach for modelling zero‐or‐one inflated double bounded data

Menezes, André Felipe Berdusco; Mazucheli, Josmar; Bourguignon, Marcelo

doi:10.1002/bimj.202000126

Cited by 9 publications

(6 citation statements)

References 28 publications

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“…Liu & Kong, 2015;P. Liu, Yuen, Wu, Tian, & Li, 2020;Menezes, Mazucheli, & Bourguignon, 2021;Ospina & Ferrari, 2012;Queiroz & Lemonte, 2021;Santos & Bolfarine, 2015;Swearingen, Castro, & Bursac, 2012). This poses a challenge to analysts who want to model free-list salience scores as a dependent variable and calls for general guidelines on how to go about modeling salience scores and similar zero-one inflated and bounded data.…”

Section: Introductionmentioning

confidence: 99%

Cognitive and cultural models in psychological science: A tutorial on modeling free-list data as a dependent variable in Bayesian regression.

Bendixen¹,

Purzycki²

2023

Psychological Methods

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Assessing relationships between culture and cognition is central to psychological science. To this end, freelisting is a useful methodological instrument. To facilitate its wider use, we here present the free-list method along with some of its many applications and offer a tutorial on how to prepare and statistically model freelist data as a dependent variable in Bayesian regression using openly available data and code. We further demonstrate the real-world utility of the outlined workflow by modeling within-subject agreement between a free-list task and a corollary item response scale on religious beliefs with a cross-culturally diverse sample. Overall, we fail to find a reliable statistical association between these two instruments, an original empirical finding that calls for further inquiry into identifying the cognitive processes that item response scales and free-list tasks tap into. Throughout, we argue that free-listing is an unambiguous measure of cognitive and cultural information and that the free-list method therefore has broad potential across the social sciences aiming to measure and model individual-level and cross-cultural variation in mental representations.

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Section: Introductionmentioning

confidence: 99%

Cognitive and cultural models in psychological science: A tutorial on modeling free-list data as a dependent variable in Bayesian regression.

Bendixen¹,

Purzycki²

2023

Psychological Methods

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“…Chai et al (2018) present in their work a detailed discussion comparing the regression models reparametrized on the marginal mean and the conditional mean (continuous component). For more details on regression structure involving mixed models see BOLFARINE, 2015BOLFARINE, , 2018CHAI et al, 2018;BOURGUIGNON, 2021;QUEIROZ;LEMONTE, 2021;SILVA et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

The Zero, One and Zero-and-One-Inflated New Unit-Lindley Distributions

FERREIRA¹,

Mazucheli

2022

Braz. J. Biom.

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In this paper, we propose the zero, one and zero-and-one-inflated New unit-Lindley distributions as natural extensions of the New unit-Lindley distribution to model continuous responses measured at the following intervals [0, 1), (0, 1] and [0, 1]. They were constructed based on convex combinations between the New unit-Lindley distribution and the distributions degenerate at zero, one, and Bernoulli distribution. They also have a number of interesting properties, such as being members of the exponential family. Besides, they have closed forms for the cumulative distribution functions, quantiles, and moments. Inferential aspects and regression structures arediscussed in this work as well as a Monte Carlo simulation study to evaluate theperformance of the regressors. Finally, we bring an application to real data on the suicide rate in the year 2016.

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“…Recently, researchers are interested in deriving distributions with bounded support. Some of these distributions are the unit Birnbaum-Saunders (UBS) [1], unit gamma [2], unit Gompertz [3], unit inverse-Gaussian [4], unit Lindley [5,6], unit Weibull (UWEI) [7][8][9], and trapezoidal beta [10] models, among others.…”

Section: Introductionmentioning

confidence: 99%

A New Quantile Regression for Modeling Bounded Data under a Unit Birnbaum–Saunders Distribution with Applications in Medicine and Politics

et al. 2021

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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.

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A parametric quantile regression approach for modelling zero‐or‐one inflated double bounded data

Cited by 9 publications

References 28 publications

Cognitive and cultural models in psychological science: A tutorial on modeling free-list data as a dependent variable in Bayesian regression.

Cognitive and cultural models in psychological science: A tutorial on modeling free-list data as a dependent variable in Bayesian regression.

The Zero, One and Zero-and-One-Inflated New Unit-Lindley Distributions

A New Quantile Regression for Modeling Bounded Data under a Unit Birnbaum–Saunders Distribution with Applications in Medicine and Politics

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