Quasi-negative binomial distribution: Properties and applications

Li, Shubiao; Yang, F.; Famoye, Felix; Lee, Carl; Black, Dennis

doi:10.1016/j.csda.2011.02.003

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…This is a pity, as the distribution has the type of properties we would be interested in. Specifically, where there are not an oversupply of zeros it can often produce a good fit for more highly skewed data as it has a ‘fat tail’ – more extreme high values 3 (Hassan & Bilal, 2008 ; Li, Yang, Famoye, Lee, & Black, 2011 ).…”

Section: Count Distributionsmentioning

confidence: 99%

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Green

2021

Health Psychology and Behavioral Medicine

103

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Background: Dependent variables in health psychology are often counts, for example, of a behaviour or number of engagements with an intervention. These counts can be very strongly skewed, and/or contain large numbers of zeros as well as extreme outliers. For example, ‘How many cigarettes do you smoke on an average day?’ The modal answer may be zero but may range from 0 to 40+. The same can be true for minutes of moderate-to-vigorous physical activity. For some people, this may be near zero, but take on extreme values for someone training for a marathon. Typical analytical strategies for this data involve explicit (or implied) transformations (smoker v. non-smoker, log transformations). However, these data types are ‘counts’ (i.e. non-negative whole numbers) or quasi-counts (time is ratio but discrete minutes of activity could be analysed as a count), and can be modelled using count distributions – including the Poisson and negative binomial distribution (and their zero-inflated and hurdle extensions, which alloweven more zeros). Methods: In this tutorial paper I demonstrate (in R, Jamovi, and SPSS) the easy application of these models to health psychology data, and their advantages over alternative ways of analysing this type of data using two datasets – one highly dispersed dependent variable (number of views on YouTube, and another with a large number of zeros (number of days on which symptoms were reported over a month). Results: The negative binomial distribution had the best fit for the overdispersed number of views on YouTube. Negative binomial, and zero-inflated negative binomial were both good fits for the symptom data with over-abundant zeros. Conclusions: In both cases, count distributions provided not just a better fit but would lead to different conclusions compared to the poorly fitting traditional regression/linear models.

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Section: Count Distributionsmentioning

confidence: 99%

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Green

2021

Health Psychology and Behavioral Medicine

103

View full text Add to dashboard Cite

show abstract

“…This is a pity, as the distribution has the type of properties we would be interested in. Specifically, where there are not an oversupply of zeros it can often produce a good fit for more highly skewed data as it has a 'fat tail'more extreme high values 3 (Hassan & Bilal, 2008;Li, Yang, Famoye, Lee, & Black, 2011).…”

Section: Count Distributionsmentioning

confidence: 99%

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Green¹

2020

Preprint

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Dependent variables in health psychology can be very strongly skewed, and/or contain large numbers of zeros as well as extreme outliers. For example, “How many cigarettes do you smoke on an average day?” The modal answer may be zero, but may range from 0 to 40+. The same can be true for minutes of moderate to vigorous physical activity. For some people this may be near zero, but take on extreme values for someone training for a marathon. The measures could be counts of behaviour or number of engagements with an intervention. Typical analytical strategies for this data involve explicit (or implied) transformations (smoker v. non-smoker, log transformations). However, this data can be more accurately thought of as ‘counts’ (ie positive whole numbers) or quasi-counts (time is ratio, but discrete minutes of activity could be analysed as a count), and modelled using count distributions — including the Poisson and negative binomial distribution, and their zero-inflated and hurdle extensions, which model even more zeros. This paper demonstrates the easy application of these models to health psychology data, and their advantages over alternative ways of analysing this type of data.

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“…This is equivalent to QNBD proposed in Li et al (2011) which has the alternative probability mass function:…”

Section: The Quasi-negative Binomial-qnbdmentioning

confidence: 99%

“…The quasi-negative binomial distribution Janardan (1975); Sen & Jain (1996) and very recently by Li et al (2011) has the probability mass function Hassan & Bilal (2008) of the form:…”

Section: The Quasi-negative Binomial-qnbdmentioning

confidence: 99%

Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

Lawal¹

2017

IJSP

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In this paper, we examine some often ignored or assumed problems relating with fitting probability models to count data either exhibiting over, equi, or under dispersion. Of particular concern are last category truncated data, where most often, expected values in this last category are collapsed together so that the sum of the expected values sum to the sample size in the data. That is, so that k ∑ i=0m i = n, the sample size. We shall for illustrative purposes in this paper, consider the following distributions: the negative binomial (NB), the Inverse trinomial (IT), the hyper-Poisson (HP), the Quasinegative binomial (QNBD), the extended com-Poisson distribution (ECOMP) as well as the negative binomial-exponential distribution (NBGE).Though, we have restricted our discussion to these six distributions, other distributions may also be employed but the patterns are always the same, that is, the sum of the estimated probabilities does not equal 1.00 and consequently, the sum of the expected values is always less or equal (Poisson case only) the sample size in the observed data. We propose a common procedure to rectify this problem for both right truncated or non-truncated frequency count data exhibiting either excess zeros or regular frequency data.

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Quasi-negative binomial distribution: Properties and applications

Cited by 9 publications

References 14 publications

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression

Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

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