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Overdispersion and Poisson Regression
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“Standard errors are clustered at the PSA level to account for unmeasured dependence within PSAs over time and overdispersion (Berk & MacDonald, 2008).”
From Police reform in public housing contexts: Body‐worn cameras, surveillance, and harm reduction in New York City Housing Authority Developments (2024) · cites this paper as Berk & MacDonald, 2008
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BackgroundCounterfactuals and Causal Inference: Methods and Principles for Social Research
Morgan, S. L., & Winship, C. (2007) · doi:10.1017/cbo9780511804564 · Cited by 1,146
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“and is particularly well-suited for data that are overdispersed (Berk and MacDonald 2008; Piza 2012).”
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“dispersion in urban areas in Poisson models (Paternoster and Brame 1997; Sampson and Laub 1997; Osgood 2000; Berk and MacDonald 2008; Famoye and Singh 2006; Maltz 1994), Negative Binomial models (Osgood 2000; Paternoster and Brame 1997; Sampson and Laub 1997), sometimes adjusted for the inflation of zeros (Famoye and…”
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“Although well-designed quasi-experimental research can provide results similar in quality to a randomized controlled trial (RCT; Berk & MacDonald, 2008), it is known to have a low degree of internal validity compared with RCTs.”
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“This common feature of count data (Herbison, Robertson, and McKensie 2015) implies the variability around the Poisson model’s fitted values is excessive potentially leading to misleading estimates (Berk and MacDonald 2008).”
Modeling the Number of Foreign Tourist Visits to Indonesia in 2020 Using GWPR Method
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“Poisson regression method is the right regression method used to analyze data containing a Poisson distribution [4].”
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“Frequently, violation of equidispersion is overdispersion, then one of the analysis methods to conquer ICMScE it is Negative Binomial Regression [2, 5–8].”
MethodNew zero-inflated regression models with a variant of censoring
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Systemic infinitesimal over-dispersion on graphical dynamic models
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“, [2]) uses the ratio-formed definition.”
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Uddin, M., & Safiullah (2021) · doi:10.11648/j.ajbls.20210901.11 · Cited by 1
“Poisson regression, which is also known as log-linear model, is a popular method used to predict a dependent variable which consists of ‘count data’ given one or more independent variables [23].”
MethodGaussianization Machines for Non-Gaussian Function Estimation Models
Cai, T. (2019) · Statistical Science · doi:10.1214/19-sts718 · Cited by 1
“Regression with count data arises in a range of applications, see, for example, Ver Hoef and Boveng (2007), Winkelmann (2003), Berk and MacDonald (2008), Kroll (2019). The Poisson regression model is one of the most natural approaches to count data regression. Besbeas, De Feis and Sapatinas (2004) provided a review of…”
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“The second part of the ZINB model includes both true zeros (i.e., the portion of the sample that has the ability to be victimized but is not) and positive integers (i.e., those who report instances of victimization) (Berk & MacDonald, 2008; Lambert, 1992; Simons, Neal, & Gaher, 2006).”
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“Results did not differ significantly; for ease of interpretation, we report results from Poisson regression models (see Berk and MacDonald 2008).”
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“We believe that our structural models are properly specified (Berk and MacDonald 2008); nonetheless we detected overdispersion.”
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“39 The analysis followed a hierarchical, three-stage modeling strategy: Model 1 addressed distal structural factors, Model 2 focused on proximal individual determinants, and Model 3 integrated both into a final combined model.”
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“…coefficients remain consistent, the standard errors of the estimated regression coefficients are usually biased downwards, resulting in inflated test statistics, underestimated confidence intervals, and a higher probability of committing a Type I error in hypothesis testing [10, 11, 12, 13, 14].”
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“3 However, our robustness checks using Poisson regression models, which do not assume a normal distribution (Berk and MacDonald 2008), closely resemble the findings from the linear regression models.”
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“Berk and MacDonald (2008) argued that the challenge of overdispersion can be alleviated using the negative Binomial and Generalized Poisson only if the problem of lack of fit of the Poisson distribution on overdispersed data does not stem from the stochastic part of the model.”
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“Berk and MacDonald (2008) contend that “the negative binomial variant of the Poisson-based regression model is now a conventional way to address apparent overdispersion” (p. 270).”
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“Based on the log-likelihood and handling of overdispersion, the negative binomial model is preferred as it provides a better fit and more reliable inferences in the presence of overdispersion (Berk & MacDonald, 2008).”
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“However, these models are not the most adequate for modelling this type of data since the may incur in overdispersion [1]; hence, it is necessary to search for a new methodology capable of overcoming the problems at hand and of improving model estimations and general adjustment.”
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“Although overdispersion is a crucial consideration in fitting the negative binomial distribution, Berk and MacDonald (2008) reported that, aside from the distribution of count variables, there are at least four explanations for heightened variability around conditional expectations within count…”
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“However, studies [14], [15] report sensitivity to small and large counts.”
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“When no distributive hypothesis is desired, “(2)” can be used alone.”
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“Overdispersion is the presence of greater variability than is expected in the dataset (Berk and MacDonald, 2008).”
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Metadata
- Authors
- Berk, R., & MacDonald, J. M.
- Affiliations
- University of Pennsylvania (US)
- Corresponding author
- Berk, Richard
- Venue
- Journal of Quantitative Criminology
- Published
- 2008-04-10
- Volume
- 24
- Issue
- 3
- Pages
- 269-284
- ISSN
- 0748-4518 (ISSN-L)
- 1573-7799
- OpenAlex
- W2060831261
- Cited by
- 299
- References
- 0
- Citations by year
- 2026: 17 · 2025: 13 · 2024: 17 · 2023: 21 · 2022: 19 · 2021: 24 · 2020: 18 · 2019: 15 · 2018: 16 · 2017: 19 · 2016: 11 · 2015: 17 · 2014: 20 · 2013: 18 · 2012: 28
- FWCI
- 7.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Quantitative Criminology (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- overdispersion, Poisson regression, negative binomial distribution, count data, count data models, Poisson distribution, criminology
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