Multivariate Zero-Inflated Poisson Models and Their Applications

Li, Chin‐Shang; Lu, Jye‐Chyi; Park, Jinho; Kim, Kyungmoo; Brinkley, Paul A.; Peterson, J.P.

doi:10.1080/00401706.1999.10485593

Cited by 113 publications

(89 citation statements)

References 10 publications

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“…In all the documents that reported the use of such models, including the ones pioneered by researchers in econometrics (Lambert, 1992;Zorn, 1996;Li et al, 1999), no discussion describing the boundary conditions delimiting the two states have been proposed. • If the site-specific traits that classify the two states are unobserved (i.e., not present in the observed data), what might they be?…”

Section: Logic Problems With the Zi Model In Highway Safety Modelingmentioning

confidence: 99%

Further notes on the application of zero-inflated models in highway safety

Lord¹,

Washington²,

Ivan³

2007

Accident Analysis & Prevention

191

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Section: Logic Problems With the Zi Model In Highway Safety Modelingmentioning

confidence: 99%

Further notes on the application of zero-inflated models in highway safety

Lord¹,

Washington²,

Ivan³

2007

Accident Analysis & Prevention

191

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“…As an extension of standard P and NB models, zeroinflated count models have gained considerable recognition as an alternative means of handling count data with a preponderance of zeros (Lambert, 1992;Gupta et al, 1996;Li et al, 1999;Lord et al, 2004;Lord, 2006). For this type of count data, more zeros are observed than would be predicted by a normal P or NB process (Park and Lord, 2009;Lord et al, 2007;Warton, 2005).…”

Section: Introductionmentioning

confidence: 96%

Statistical modelling for falls count data

Ullah

Finch

Day

2010

Accident Analysis & Prevention

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Falls and their injury outcomes have count distributions that are highly skewed toward the right with clumping at zero, posing analytical challenges. Different modelling approaches have been used in the published literature to describe falls count distributions, often without consideration of the underlying statistical and modelling assumptions. This paper compares the use of modified Poisson and negative binomial (NB) models as alternatives to Poisson (P) regression, for the analysis of fall outcome counts. Four different count-based regression models (P, NB, zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB)) were each individually fitted to four separate fall count datasets from Australia, New Zealand and United States. The finite mixtures of P and NB regression models were also compared to the standard NB model. Both analytical (F, Vuong and bootstrap tests) and graphical approaches were used to select and compare models. Simulation studies assessed the size and power of each model fit. This study confirms that falls count distributions are over-dispersed, but not dispersed due to excess zero counts or heterogeneous population. Accordingly, the P model generally provided the poorest fit to all datasets. The fit improved significantly with NB and both zero-inflated models. The fit was also improved with the NB model, compared to finite mixtures of both P and NB regression models. Although there was little difference in fit between NB and ZINB models, in the interests of parsimony it is recommended that future studies involving modelling of falls count data routinely use the NB models in preference to the P or ZINB or finite mixture distribution. The fact that these conclusions apply across four separate datasets from four different samples of older people participating in studies of different methodology, adds strength to this general guiding principle.

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“…However, most count models do not allow modeling two datasets simultaneously except that a data merging process is implemented beforehand (Lao et al, 2010). Recently, multivariate Poisson regression models (Miaou and Song, 2005;Ma and Kockelman, 2006;Park and Lord, 2007), multivariate zero-inflated Poisson regression models (Li et al, 1999), or multivariate Poissonlognormal regression models (Karim and Tarek, 2009) have been used for modeling different but correlated count data sets. As a special case of multivariate Poisson regression models, bivariate Poisson regression model can be used for paired count data sets.…”

Section: Introductionmentioning

confidence: 99%