EM Estimation for Zero- and k-Inflated Poisson Regression Model

Arora, Monika; Chaganty, N. Rao

doi:10.3390/computation9090094

Cited by 7 publications

(3 citation statements)

References 35 publications

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“…The inflation could be due to various reasons such as the design of the study or types of responses. For example, the number of pap smear tests performed on women had zero and six inflated [24,25]. Similarly, the data on the number cigarettes smoked have zero (non-smokers) and 20 (a pack of cigarettes) inflated [25], while in a survey on the number of divorces, counts zero and 1 are likely to be inflated.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, the data on the number cigarettes smoked have zero (non-smokers) and 20 (a pack of cigarettes) inflated [25], while in a survey on the number of divorces, counts zero and 1 are likely to be inflated. Arora and Chaganty [24] described such situations where, besides zero, another count k > 0 is also inflated, and applied zero-and k-inflated Poisson (ZkIP) models. The ZkIP model for count data is defined by a mixture of three distributions, which assumes that each count observation is a draw from a degenerate distribution at zero with probability π 1 , from a degenerate distribution at value k > 0 with probability π 2 , or from a Poisson distribution with probability (1 − π 1 − π 2 ).…”

Section: Introductionmentioning

confidence: 99%

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Application of Mixture Models for Doubly Inflated Count Data

Arora

Chaganty

2023

Analytics

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In health and social science and other fields where count data analysis is important, zero-inflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero- and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation–maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero- and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Mixture Models for Doubly Inflated Count Data

Arora

Chaganty

2023

Analytics

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“…By properly selecting the values of the weights in (2.2) for the MZKIPS distribution, the zero and

k

inflated distribution is also obtained (see Arora et al, 2021). Also, Arora and Chaganty (2021) worked on the zero and

k

inflated Poisson model using the EM algorithm. They also included the ZOIP model in the article.…”

Section: Three Subfamilies Of the Mzkips Distributionmentioning

confidence: 99%

Flexible multivariate zero to k inflated power series regression model with applications

Saboori

Doostparast

2022

Stat

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Inflated distributions are applied in various fields, including insurance, traffic networks and survival analyses. First, they are defined by a baseline discrete distribution, and then, extra masses are added to some points of interest, called inflated points, to achieve more flexible models for data analyses. The baseline distribution is arbitrary and application dependent. Here, the rich family of power series distributions is considered as the baseline, which includes various common discrete distributions such as Poisson, negative binomial, multinomial and logarithmic series distributions. This paper deals with an extension of previous works in two directions. The former is an extension of the univariate inflated distributions to multivariate ones, and the latter is the generalization of the inflated points from the zero single point to the set k=0,1,…. Under this setting, various inflated distributions in the literature fall into the proposed family of distributions. These extensions make the proposed model flexible and practically useful in data analyses. To do this, the problem of estimating parameters with various approaches as well as hypotheses testing is studied in detail. Multivariate‐generalized linear models with inflated multivariate discrete responses are also discussed. To assess the performance of the proposed family of inflated distributions, simulation studies are conducted, and a real data set on an Australian health survey study is also analysed.

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Multiple arbitrarily inflated negative binomial regression model and its application

Abusaif,

Kuş

2024

Soft Comput

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This paper introduces a novel modification of the negative binomial distribution, which serves as a generalization encompassing both negative binomial and zero-inflated negative binomial distributions. This innovative distribution offers flexibility by accommodating an arbitrary number of inflation points at various locations. The paper explores key distributional properties associated with this modified distribution. Additionally, this study proposes several estimators designed to obtain estimates for the unknown parameters. Furthermore, the paper introduces a new count regression model that utilizes the modified distribution. To assess the performance of the proposed distribution and the count regression model, a comprehensive Monte Carlo simulation study is conducted. In the final stage of the paper, a real-world dataset is scrutinized to ascertain the superiority of the proposed model. This empirical analysis contributes to validating the practical applicability and effectiveness of the newly introduced distribution in comparison to existing models.

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EM Estimation for Zero- and k-Inflated Poisson Regression Model

Cited by 7 publications

References 35 publications

Application of Mixture Models for Doubly Inflated Count Data

Application of Mixture Models for Doubly Inflated Count Data

Flexible multivariate zero to k inflated power series regression model with applications

Multiple arbitrarily inflated negative binomial regression model and its application

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