Bayesian approach for the zero-modified Poisson–Lindley regression model

Bertoli, Wesley; Conceição, Katiane S.; Andrade, Marinho G.; Louzada, Francisco

doi:10.1214/19-bjps447

Cited by 4 publications

(5 citation statements)

References 43 publications

(45 reference statements)

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“…[ 43 ] have proposed a new class of zero-modified models, whose baseline distributions are Poisson mixtures, including the

. The present paper also extends the works of [ 40 , 41 ] since the

model differentiates from the zero-modified Poisson–Lindley and Poisson–Shanker by the ability, for example, to describe better (by adjusting its shape parameter) those discrete phenomena in which the probabilities of observing 0 s and 1 s are low (see [ 43 ], Figure 2).…”

Section: Introductionsupporting

confidence: 54%

See 1 more Smart Citation

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Bertoli

Conceição

Andrade

et al. 2021

Entropy

Self Cite

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Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper’s primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson–Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators’ empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.

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“…[ 43 ] have proposed a new class of zero-modified models, whose baseline distributions are Poisson mixtures, including the

. The present paper also extends the works of [ 40 , 41 ] since the

Section: Introductionsupporting

confidence: 54%

“…[ 40 ] have proposed the zero-modified Poisson–Shanker regression model, whose usefulness was illustrated through its application to fetal death notification data, and ref. [ 41 ] have introduced the zero-modified Poisson–Lindley regression model with fixed-effects under a fully Bayesian approach.…”

Section: Introductionmentioning

confidence: 99%

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Bertoli

Conceição

Andrade

et al. 2021

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let us now describe two forms of ZMD which were introduced to study the count regression models. The first one initially studied by Dietz and Bohning (2000) for a zero modified Poisson model and then generalized by Bertoli et al (2019) is defined by…”

Section: Zmscd Models Generated By Markovian Intensitiesmentioning

confidence: 99%

Zero-modified Count Time Series with Markovian Intensities

Balakrishna¹,

Anvar²,

Abraham³

2021

Preprint

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This paper proposes a method for analyzing count time series with inflation or deflation of zeros. In particular, zero-modified Poisson and zero-modified negative binomial series with intensities generated by non-negative Markov sequences are studied in detail. Parameters of the model are estimated by the method of estimating equations which is facilitated by expressing the model in a generalized state space form. The latent intensities required for estimation are extracted using generalized Kalman filter. The applications of proposed model and its estimation methods are illustrated using simulated and real data sets.

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“…Accordingly, this paper aims to extend the work of Bertoli et al. (2019) in the sense of developing a new mixed‐effects regression model for zero‐modified count data based on a reparameterization of the zero‐modified Poisson–Lindley

(ZMPL)

distribution introduced by Bertoli, Conceição, Andrade, and Louzada (2020). A discrete random variable

Y

defined on

{scriptY}_{0} = false{0, 1, \dots false}

is said to follow a hurdle Poisson–Lindley

(HPL)

distribution if its probability mass function (pmf) can be written as

{normalP}_{*} (Y = y; μ, ω) = (1 - ω) δ_{y} + ω {normalP}^{*} (Y = y; μ), y \in {scriptY}_{0}

for

ω \in [0, 1]

and where

δ_{y}

is an indicator function, so that

δ_{y} = 1

y = 0

and

δ_{y} = 0

otherwise.…”

Section: Introductionmentioning

confidence: 99%

“…Bertoli, Conceição, Andrade, and Louzada (2018) have proposed the zero‐modified Poisson–Shanker regression model, whose usefulness was illustrated through its application to fetal death notification data. Bertoli, Conceição, Andrade, and Louzada (2019) have introduced the zero‐modified Poisson–Lindley regression model with fixed‐effects under a fully Bayesian approach. While zero deflation has not been addressed in this context until now, a comprehensive approach for the zero‐modified Poisson and zero‐modified Negative Binomial models in a regression framework with mixed‐effects is provided by Neelon et al.…”

Section: Introductionmentioning

confidence: 99%

A new mixed‐effects regression model for the analysis of zero‐modified hierarchical count data

et al. 2020

Self Cite

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Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero‐modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)–(b) and (b)–(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed‐effects regression model based on the hurdle version of the Poisson–Lindley distribution. In this framework, the zero‐modification is incorporated by assuming that a binary probability model determines which outcomes are zero‐valued, and a zero‐truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well‐established mixed‐effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian ‐value and the randomized quantile residuals were considered for model diagnostics.

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Bayesian approach for the zero-modified Poisson–Lindley regression model

Cited by 4 publications

References 43 publications

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Zero-modified Count Time Series with Markovian Intensities

A new mixed‐effects regression model for the analysis of zero‐modified hierarchical count data

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