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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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Items 101–200 of 262
Jaya, I. G. N. M., Folmer, H., & Lundberg, J. (2022) · The Annals of Regional Science · doi:10.1007/s00168-022-01191-1 · Cited by 16
“when the data contain large numbers of zeros, negative binomial (NB) distributions (Berk and MacDonald 2008; Payne et al. 2017), or zero-inflated Poisson (ZIP) distributions (Lewsey and Thomson 2004), or zero-inflated negative binomial (ZINB) distributions (Agarwal et al.”
Endesfelder, D., Kulka, U., Einbeck, J., & Oestreicher, U. (2020) · International Journal of Radiation Biology · doi:10.1080/09553002.2020.1829152 · Cited by 16
“In such cases, it is therefore crucial to identify missing predictors and adjust the statistical models accordingly (Berk and MacDonald 2008; Hilbe 2011).”
BackgroundProtecting High-Risk Youth in High-Risk Contexts: Neighborhoods, Parenting, and Victimization
Tillyer, M. S., Ray, J. V., & Hinton, M. E. (2018) · Journal of Youth and Adolescence · doi:10.1007/s10964-018-0832-7 · Cited by 16
Govorov, M., Beconytė, G., & Анатольевич, Г. Г. (2025) · Transactions in GIS · doi:10.1111/tgis.70051 · Cited by 9
Simelane, M. S., Vermaak, K., Zwane, E., & Masango, S. (2021) · PLoS ONE · doi:10.1371/journal.pone.0246100 · Cited by 15
“To address the limitation of the Poisson model, the negative binomial regression was used as a preferred model [37, 39].”
MethodStatistical techniques for juror and jury research
Wright, D. F. B., Strubler, K., & Vallano, J. (2011) · Legal and Criminological Psychology · doi:10.1348/135532510x487655 · Cited by 15
Focused deterrence, strategic management, and effective gun violence prevention
Braga, A. A., MacDonald, J., Douglas, S. D., Wade, B. A., & Struhl, B. (2024) · Criminology & Public Policy · doi:10.1111/1745-9133.12682 · Cited by 14
“Robust standard errors clustered at the city level were used to account for unmeasured dependence within cities over time and overdispersion (Berk & MacDonald, 2008).”
Self-citationThe Minimum Legal Drinking Age and Crime Victimization
Chalfin, A. J., Hansen, B., & Ryley, R. (2019) · National Bureau of Economic Research · doi:10.3386/w26051 · Cited by 17
“First,testsforoverdispersiondonotdistinguishbetween overdispersionandmisspecification — see Berk and MacDonald (2008) and Blackburn (2015).”
Control‐based imputation for sensitivity analyses in informative censoring for recurrent event data
Gao, F., Liu, G., Zeng, D., Xu, L., Lin, B., Diao, G.-Q., Golm, G., Heyse, J., & Ibrahim, J. (2017) · Pharmaceutical statistics · doi:10.1002/pst.1821 · Cited by 14
Mills, C. E., Schmuhl, M., & Capellan, J. A. (2020) · doi:10.1080/0735648x.2020.1738261 · Cited by 13
Park, S.-M., & Fisher, B. S. (2017) · Crime & Delinquency · doi:10.1177/0011128715607534 · Cited by 13
“The remaining variance after fitting the Poisson distribution is presented as over-dispersion (Berk & MacDonald, 2008; Osgood, 2000; Paternoster & Brame, 1997).”
MethodHammami, I., Garcia, A., & Nuel, G. (2013) · Malaria Journal · doi:10.1186/1475-2875-12-398 · Cited by 13
“Using the negative binomial distribution instead of the Poisson, allow to fix important errors inmodel specification [85].”
MethodA contaminated regression model for count health data
Otto, A. F., Ferreira, J. T., Tomarchio, S. D., Bekker, A., & Punzo, A. (2025) · Statistical Methods in Medical Research · doi:10.1177/09622802241307613 · Cited by 7
“9–12 As discussed by Hilbe, 13 there are two types of overdispersion: apparent and real.”
Mills, C. E., Schmuhl, M., Capellan, J. A., & Silva, J. R. (2023) · Social problems · doi:10.1093/socpro/spad020 · Cited by 12
Functional flexibility in a spider's orb web
Mulder, T., Mortimer, B., & Vollrath, F. (2020) · Journal of Experimental Biology · doi:10.1242/jeb.234070 · Cited by 12
“tugging bouts were analysed with a generalised linear mixed model (GLMM) with Poisson error distribution (Berk and MacDonald, 2008; Thomas, 2017).”
MethodKroll, M. (2017) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2018.07.003 · Cited by 12
Social Diversity and Civic Engagement
Polson, E. C. (2015) · Nonprofit and Voluntary Sector Quarterly · doi:10.1177/0899764014548424 · Cited by 12
“A negative binomial model would be appropriate if there were evidence of overdispersion, a situation occurring when the variance of the dependent variable exceeds its mean (Berk & MacDonald, 2008).”
BackgroundStatistical properties of parasite density estimators in malaria and field applications
Hammami, I. (2013) · theses.fr (ABES) · doi:10.70675/50337d41z245ez48cdzb739z38054acd2ab1
Estimating infant mortality in Colombia: some overdispersion modelling approaches
Quintero-Sarmiento, A., Cepeda-Cuervo, E., & Núñez-Antón, V. (2012) · doi:10.1080/02664763.2011.634395 · Cited by 12
“If there are omitted variables, the problem needs to be reformulated by including these variables, as discussed in, for example, [3].”
BackgroundMarczuk, A., & Strauss, S. (2023) · Zeitschrift für Erziehungswissenschaft · doi:10.1007/s11618-023-01175-7 · Cited by 11
“These generalised linear regression models are designed for count-dependent variables and model the logarithm of the expected values (Berk and MacDonald 2008); since they do not assume a normal distribution, they provide a reliable estimation when considering variables with skewed distribution.”
BackgroundAltinisik, Y. (2022) · Journal of Applied Statistics · doi:10.1080/02664763.2022.2096875 · Cited by 11
“Therefore it must be emphasized that the true definition of the overdispersion is the excess variation when the systematic structure of the model is correctly specified [8].”
BackgroundKondo, M., Keene, D., Hohl, B. C., MacDonald, J., & Branas, C. (2015) · PLoS ONE · doi:10.1371/journal.pone.0136595 · Cited by 11
“We used Poisson random-effects regression models to estimate the impact of violation compliance and renovation permit on crime outcomes (Y), while controlling for demographic variables (negative binomial models were first attempted but would not converge) [28].”
MethodSelf-citationTables and Graphs for Monitoring Temporal Crime Patterns
Wheeler, A. P. (2015) · International Journal of Police Science & Management · doi:10.1177/1461355716642781 · Cited by 16
“Often the series have over-dispersion, which occurs when the variance of the series is greater than the mean (Berk and MacDonald, 2008; Osgood, 2000).”
BackgroundImpact of Brief Intervention Services on Drug-Using, Truant Youth Arrest Charges Over Time
Dembo, R., Briones-Robinson, R., Wareham, J., Schmeidler, J., Winters, K. C., Barrett, K. L. V., Ungaro, R. A., Karas, L. M., & Belenko, S. R. (2014) · Journal of Child & Adolescent Substance Abuse · doi:10.1080/1067828x.2012.741560 · Cited by 10
“For a Poisson model, ‘‘. . . the mean should be approximately the same as the variance’’ (Berk & MacDonald, 2008, p. 272).”
BackgroundPrediction of road accidents: comparison of two Bayesian methods
Deublein, M., Schubert, M., & Adey, B. T. (2013) · Structure and Infrastructure Engineering · doi:10.1080/15732479.2013.821139 · Cited by 11
Zhang, P., Wang, C.-Z., Chen, F., Cui, S., Cheng, J.-C., & Bo, W. (2022) · Sustainability · doi:10.3390/su14159061 · Cited by 10
Zhou, J.-C., Zhao, Q., Liu, S.-M., Shang, D.-D., Zhao, X., Huo, L., Dong, H., & Zhang, L.-S. (2021) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2021.730664 · Cited by 10
Jung, Y., Chun, Y., & Griffith, D. A. (2020) · Applied Geography · doi:10.1016/j.apgeog.2020.102340 · Cited by 11
Determining Associations and Estimating Effects with Regression Models in Clinical Anesthesia.
Aoyama, K., Pinto, R., Ray, J., Hill, A., Scales, D., & Fowler, R. (2020) · Anesthesiology · doi:10.1097/aln.0000000000003425 · Cited by 10
“21,22 A more detailed discussion of these and other considerations for assumptions to develop regression models is detailed well in recent reviews.(13,21,23,24)”
BackgroundStreet Light Outages, Public Safety and Crime Displacement: Evidence from ChicagoPreprint
Chalfin, A. J., Kaplan, J., & LaForest, M. (2020) · SSRN Electronic Journal · doi:10.2139/ssrn.3526467 · Cited by 10
“First, tests for overdispersion do not distinguish between overdispersion and misspecification (see Berk and MacDonald (2008); Blackburn (2015).”
Liang, Z., Li, J., Deane, G., Zhen, L., & Zhou, B. (2018) · Social Forces · doi:10.1093/sf/soy061 · Cited by 11
“…+xln i i T i Exponentiating both sides yields β βμ ε δ= ( ) ( ) = ( )x xexp expexp ,i i T i i T i where we define δ ε≡ ( )exp and then assume that δ is drawn from a gamma distribution and normalized so that the expected value δ( ) =E 1 (Long and Freese 2006, 372–73; Berk and MacDonald 2007, 12–14).”
BackgroundArmah, F. A., Ung, M., Boamah, S. A., Luginaah, I., & Campbell, G. (2015) · Journal of Environmental Studies and Sciences · doi:10.1007/s13412-015-0334-9 · Cited by 9
“the data than is specified by the Poisson model (Berk and MacDonald 2008; Hilbe 2011).”
Yao, D., Hill, N., Brown, B., Gule, D., Chabane, M., Mcingana, M., Willis, K., Shiba, V., Olawore, O., Nel, D., et al. (2024) · BMC Public Health · doi:10.1186/s12889-024-19679-0 · Cited by 9
“In cases where the variance was larger than the mean, we utilized the negative binomial model and incorporated an additional term to account for the excess variance [24].”
MethodThe community philanthropic foundation: A new form of independent public service provider for China?
Weng, S.-H., & Christensen, T. (2018) · Public Policy and Administration · doi:10.1177/0952076718784642 · Cited by 9
Camp, J., Joy, K., & Freestone, M. C. (2018) · International Journal of Offender Therapy and Comparative Criminology · doi:10.1177/0306624x17752254 · Cited by 10
“These statistical methods allow for more powerful statistical analysis of count data, and are helpful additions to the more typical nonparametric tests frequently used in this type of research (Berk & MacDonald, 2008).”
MethodRiithi, A. N., Irungu, P., & Munei, K. (2015) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.269714 · Cited by 9
“The NBRM takes care of any model misspecification (Berk and MacDonald, 2007).”
BackgroundInfluentialChun, Y., Kim, Y., & Campbell, H. (2012) · doi:10.1111/j.1467-9906.2011.00594.x · Cited by 9
“This random effect model specification is commonly used to accommodate overdispersion, which frequently occurs in Poisson models for empirical data sets (Berk & MacDonald, 2008).2 But these independent random effects do not resolve the spatial autocorrelation issue among observations.”
MethodLundman, R. J. (2012) · Race and Justice · doi:10.1177/2153368711431248 · Cited by 7
“…missing count (also see Table 1), the first dependent measure, Count Race and Ethnicity Missing, is fitted using negative binomial regression which is specifically intended for analyzing integer outcomes with a large number of zero counts (Berk & MacDonald, 2008; Hoffman, 2003; Long, 1997).”
MethodSunde, H. M., Weenink, D., & Lindegaard, M. (2023) · Policing and Society: An International Journal of Research and Policy · doi:10.1080/10439463.2023.2216839 · Cited by 8
“Therefore, we employed negative binomial regression models specifically fit for overdispersion (Berk and MacDonald 2008).”
MethodOh, M., Kim, S., & Choi, Y. (2020) · Tourism Economics · doi:10.1177/1354816619888337 · Cited by 8
“Therefore, this study adopted the negative binomial regression model by following the methods of previous studies (Berk and MacDonald, 2008; Chang, 2005; Dean, 1992; Liu et al., 2013; Weng et al., 2016).”
MethodMobile Phones and Crime: The Protective Effect of Mobile Network Infrastructures
Felka, P., Mihale-Wilson, C., & Hinz, O. F. (2019) · Journal of Quantitative Criminology · doi:10.1007/s10940-019-09437-6 · Cited by 9
Registered Sex Offenders and Reported Sex Offenses
Stucky, T. D., & Ottensmann, J. (2016) · doi:10.1177/0011128714556738 · Cited by 8
Modeling the delivery of security advisories and CVEs
Ruohonen, J., Hyrynsalmi, S., & Leppänen, V. (2017) · Computer Science and Information Systems · doi:10.2298/csis161010010r · Cited by 8
Predicting road traffic accidents using artificial neural network models
de Soto, B. G., Bumbacher, A., Deublein, M., & Adey, B. (2018) · Infrastructure Asset Management · doi:10.1680/jinam.17.00028 · Cited by 7
Knorre, A. V., & Macdonald, J. (2023) · Journal of criminal justice · doi:10.1016/j.jcrimjus.2023.102068 · Cited by 7
Self-citationExploring the relationship between super bowls and potential online sex trafficking
Huang, X., Yoder, B. R., Tsoukalas, A. P., Entress, R. M., & Sadiq, A.-A. (2022) · Trends in Organized Crime · doi:10.1007/s12117-022-09472-z · Cited by 7
Adoption of Patient-Reported Outcomes by Health Systems and Physician Practices in the USA
Rodriguez, H. P., Kyalwazi, M. J., Lewis, V. A., Rubio, K., & Shortell, S. (2022) · Journal of general internal medicine · doi:10.1007/s11606-022-07631-0 · Cited by 7
Dynamic environments do not appear to constrain spider web building behaviour
Mulder, T., Wilkins, L., Mortimer, B., & Vollrath, F. (2021) · SCIENCE NATURE · doi:10.1007/s00114-021-01725-1 · Cited by 7
“Multiple LMMs and the radial count GLMM were overfitted (i.e. not optimally parsimonious (Hawkins 2004)) due to the inclusion of the random effect.”
MethodInfluentialDetermination of overlapping crime and collision hotzones for focused law enforcement
Oluwajana, S., Takyi, E., & Park, P. Y. (2020) · Journal of Transportation Safety & Security · doi:10.1080/19439962.2019.1580327 · Cited by 7
Jung, Y., Chun, Y., & Kim, K. (2020) · doi:10.1177/0011128720948037 · Cited by 7
Letter from the Editors--Fourth international symposium on naturalistic driving research.
Planek, T., Sinelnikov, S., Thomas, J. N., Kolosh, K. P., & Porretta, K. (2015) · Journal of Safety Research · doi:10.1016/j.jsr.2015.06.003 · Cited by 7
PTSD course and predictors in a 15 year longitudinal cohort following suspected serious injury
Karchoud, J. F., Hoeboer, C. M., Karaban, I., Mouthaan, J., Sijbrandij, M., Olff, M., van de Schoot, R., & van Zuiden, M. (2025) · npj Mental Health Research · doi:10.1038/s44184-025-00153-7 · Cited by 5
“…responsecategoriesbetweenthevalue0andtheotherlowvaluesofthe dependentvariable(whichisthecaseinthecommonlyusednegative binominalregressionandzero-in fl ated Poisson) 43,44 ; and well-suited for our relatively modest sample size 45 – 47 .”
InfluentialTrivariate Kernel Density Estimation of Spatiotemporal Crime Events with Case Study for Lithuania
Govorov, M., Beconytė, G., & Gienko, G. (2023) · Sustainability · doi:10.3390/su15118524 · Cited by 6
Mataba, G. R., Munishi, L., Brendonck, L., & Vanschoenwinkel, B. (2022) · Journal of Vector Ecology · doi:10.52707/1081-1710-47.1.69 · Cited by 6
The importance of regional models in assessing canine cancer incidences in Switzerland
Boo, G., Leyk, S., Brunsdon, C., Graf, R., Pospischil, A., & Fabrikant, S. (2018) · PLoS ONE · doi:10.1371/journal.pone.0195970 · Cited by 6
Poisson Regression Analysis of Highway Fatality Accident Data in Oklahoma
Comer, J., Rose, N. J., & Bombom, L. (2014) · International Journal of Applied Geospatial Research · doi:10.4018/ijagr.2014100105 · Cited by 6
BONDING AND BRIDGING ACTIVITIES OF U.S. PENTECOSTALS
Dougherty, K. D., de Jong, F., Garofano, R., Jamir, J. I., Park, N. J., & Timmermans, R. (2011) · doi:10.1080/02732173.2011.557039 · Cited by 6
“Negative binomial regression is an extension of Poisson models used to estimate parameters for a variable with overdispersion (Berk and MacDonald 2008 ).”
MethodRoadway accident risk prediction based on Bayesian probabilistic networks
Deublein, M. (2013) · doi:10.3929/ethz-a-009795915 · Cited by 6
Braga, A. A., MacDonald, J. M., & McCabe, J. E. (2024) · Criminology & Public Policy · doi:10.1111/1745-9133.12679 · Cited by 6
Self-citationCollaborative problem-solving at youth crime hot spots: a pilot study
Gill, C., Weisburd, D., Vitter, Z., Gross Shader, C., Nelson-Zagar, T., & Spain, L. (2018) · Policing: An International Journal · doi:10.1108/pijpsm-12-2017-0152 · Cited by 5
Poisson-based framework for predicting count data: Application to traffic counts in Prague areas
Uglickich, E., & Nagy, I. (2025) · Journal of Computer Science · doi:10.1016/j.jocs.2025.102534 · Cited by 5
Yoon, J., & Oh, S. J. (2024) · Cross Cultural & Strategic Management · doi:10.1108/ccsm-08-2023-0166 · Cited by 5
Measurement error–tolerant Poisson regression for Valley Fever incidence prediction
Yang, H., Pan, F.-L., Tong, D.-Q., Brown, H. E., & Liu, J. (2024) · IISE Transactions on Healthcare Systems Engineering · doi:10.1080/24725579.2024.2370243 · Cited by 5
“Overdispersion may violate this assumption and lead to higher bias and variance of the estimates (Berk & MacDonald, 2008).”
Dardir, M., Berardi, U., & Wilson, J. (2023) · Sustainable Cities and Society · doi:10.1016/j.scs.2023.104853 · Cited by 7
Latent Growth Models for Count Outcomes: Specification, Evaluation, and Interpretation
Seddig, D. (2023) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2023.2175684 · Cited by 7
“Apparent reasons for violations of equidispersion may be outliers, omitted predictor variables, or functional misspecifications (Berk & MacDonald, 2008; Hilbe, 2011).”
BackgroundWork‐from‐home and the risk of securities misconduct
Cumming, D. J., Firth, C. P., Gathergood, J., & Stewart, N. (2023) · European Financial Management · doi:10.1111/eufm.12426 · Cited by 5
Does Criminal Thinking Predict Prison Misconduct? An Evaluation of TCU’s Criminal Thinking Scales
Duwe, G., Clark, V. A., & McNeeley, S. (2023) · Criminal Justice and Behavior · doi:10.1177/00938548231163111 · Cited by 6
“, & Bonta, J. (2010). Rehabilitating criminal justice policy and practice. Psychology, Public Policy, and Law, 16(1), 39–55. https://doi.org/10.1037/a0018362 Andrews, D. A., Bonta, J., & wormith, S. J. (2000). Level of service/case management inventory: LS/CMI. Multi-Health Systems. Andrews, D. A., Bonta, J., & wormit…”
BackgroundMethodInfluentialSong, G.-W., Zhang, C., Xiao, L.-Z., Wang, Z., Chen, J.-G., & Zhang, X. (2022) · ISPRS Int. J. Geo Inf. · doi:10.3390/ijgi11120615 · Cited by 5
The Role of Greenness of School Grounds in Student Violence in the Chicago Public Schools
Lee, J., & Movassaghi, K. S. (2022) · Children, Youth and Environments · doi:10.7721/chilyoutenvi.31.2.0054 · Cited by 5
“…of the selected four indicators for student violence can be over-dispersed with greater variances from a Poisson formulation than their means (Berk & MacDonald, 2008; Cameron & Trivedi, 1990; Dean, 1992), On the basis of this result, we tested the effect of greenness at school sites on…”
Xu, L.-J., Chen, J., Zhan, Z.-Y., Chen, T.-T., Liu, W., Qian, J., & Ou, C. (2020) · Vaccine · doi:10.1016/j.vaccine.2020.04.053 · Cited by 5
The Effect of Reentry Court Participation on Post-Release Supervision Outcomes and Re-Arrest
Crow, M. S., & Smykla, J. O. (2019) · Corrections · doi:10.1080/23774657.2019.1647805 · Cited by 6
“We used negative binomial regression models for this analysis due to the overdispersion of these count variables (Berk & MacDonald, 2008) and include an additional variable to account for the varying duration of timeframe being analyzed.6”
MethodBoo, G., Leyk, S., Fabrikant, S., Pospischil, A., & Graf, R. (2017) · Geospatial Health · doi:10.4081/gh.2017.539 · Cited by 5
“As previously mentioned, such improvement might be linked to the change of the statistical distribution of the incidence data used to fit the two modelling scenarios (Cameron and Trivedi, 1990; Berk and MacDonald, 2008).”
BackgroundMethodInfluentialMalek‐Ahmadi, M. H., Mufson, E. J., Perez, S. E., & Chen, K. (2017) · Biostatistics & Epidemiology · doi:10.1080/24709360.2017.1342186 · Cited by 9
“For Poisson models, it is assumed that the mean and variance of the outcome (dependent) variable are equal or approximately equal, while the NB model is used when the variance is substantially greater than the mean [28].”
MethodPodvalna, H., Bochko, O., Kuziak, V., & Stasyuk, N. (2021) · E3S Web of Conferences · doi:10.1051/e3sconf/202123400056 · Cited by 5
From mobility to crime: Collective patterns of human mobility and gun violence in Baltimore City
Situ, X.-Y. (2024) · Journal of criminal justice · doi:10.1016/j.jcrimjus.2024.102256 · Cited by 4
Explaining Theft Using Offenders' Activity Space Inferred from Residents' Mobile Phone Data
Liu, L., Li, C.-C., Xiao, L.-Z., & Song, G.-W. (2023) · ISPRS Int. J. Geo Inf. · doi:10.3390/ijgi13010008 · Cited by 4
Weisburd, D., Wilson, D. B., Wooditch, A. C., & Britt, C. (2021) · Advanced Statistics in Criminology and Criminal Justice · doi:10.1007/978-3-030-67738-1_6 · Cited by 4
Saunders, J., Midgette, G., Taylor, J., & Faraji, S.-L. (2020) · Criminology & Public Policy · doi:10.1111/1745-9133.12534 · Cited by 4
Hosseini, A., & Hosseini, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.08389 · Cited by 4
“Thall and Veil (1990), Berk and MacDonald (2008) and Zheng et al (2006)).”
Marshall, H. (2013) · doi:10.1177/1043986213485619 · Cited by 4
Analysis of Zero-Inflated Count Data From Clinical Trials With Potential Dropouts
Yang, J., Li, X.-M., & Liu, G. (2012) · doi:10.1080/19466315.2012.698937 · Cited by 4
“The NB model has separate parameters for the mean and variance to capture the extra variability due to overdispersion, which can be derived from a Poisson model with a random intensity parameter (Berk and MacDonald 2008).”
MethodDiverging Realities: Differential George Floyd Effects on Violence Against the Police
Sheppard, K. G., Billmeier, A., & Swagar, N. (2026) · Journal of research in crime and delinquency · doi:10.1177/00224278261420326 · Cited by 3
“Although counts of assaults exhibited overdispersion, Poisson regression with robust standard errors was utilized as it is robust to overdispersion and does not risk estimation bias associated with negative binomial models when errors are not randomly distributed (Berk and MacDonald, 2008).”
Thi, H. D., Nguyen, D. K., Thanh, T. N., Ngoc, N. N., Pham, H. T. D., Van, T. T., Van, T. Q., Minh, P. N., Thanh, T. V., Sy, H. H., et al. (2025) · Clinical and Experimental Obstetrics & Gynecology · doi:10.31083/ceog43781 · Cited by 3
Liu, L., Liu, H., Long, D.-P., & Huang, X.-H. (2025) · Humanities and Social Sciences Communications · doi:10.1057/s41599-025-04507-6 · Cited by 3
“The Poisson regression model assumes that the mean of the dependent variable is equal to its variance (Berk and MacDonald 2008).”
Digdowiseiso, K. (2024) · Cogent Social Sciences · doi:10.1080/23311886.2024.2432070 · Cited by 3
“…binomial model as a substitute for the poisson model in cases where there is evidence of over-dispersion is just one potential choice. according to Berk and MacDonald (2007), if there are mistakes in the way the poisson regression model is specified, using the negative binomial distribution may…”
Mataba, G. R., Munishi, L. K., Brendonck, L., & Vanschoenwinkel, B. J. (2023) · Hydrobiologia · doi:10.1007/s10750-023-05414-0 · Cited by 4
Quantifying the risk of mass shootings at specific locations
Lei, X., & MacKenzie, C. (2023) · Risk Analysis · doi:10.1111/risa.14197 · Cited by 3
“The Poisson regression model is a special case of the negative binomial regression model, the latter of which does not assume that the mean and variance are equal (Berk & MacDonald, 2008; Gardner et al., 1995; Hilbe, 2011).”
MethodArmir, N. A. Z., Zakaria, S., Begum, R., Ariff, N. M., Chamhuri, N., Harun, J., Talib, N. M., & Kadir, M. A. (2021) · Environment, Development and Sustainability · doi:10.1007/s10668-021-01760-y · Cited by 3
Yotenka, R., & Banapon, A. (2020) · doi:10.2991/assehr.k.201010.007 · Cited by 3
“(2) With μ is the average of the Poisson distributed response variable where the average value and variance of Y have a value of more than 0.”
BackgroundBarua, P., & Narattharaksa, K. C. (2019) · The International Journal of Health Planning and Management · doi:10.1002/hpm.2913 · Cited by 5
A longitudinal examination of the influence of a smoke-free law on the bar–crime relationship
Briggs, S. J., & Myer, A. J. (2017) · doi:10.1080/0735648x.2016.1189844 · Cited by 3
Lyons, B. P., & Levine, H. (2013) · Journal of Health and Human Services Administration · doi:10.1177/107937391303600303 · Cited by 3
“According to Berk and MacDonald (2007), the Poisson formulation has obvious appeal due to its relative ease of interpretation given the right hand side is the familiar linear combination of predictors and because when exponentiated, the regression coefficients can be interpreted as multipliers.”
BackgroundMorris, N. A., & Slocum, L. A. (2012) · Journal of Quantitative Criminology · doi:10.1007/s10940-011-9158-2 · Cited by 29
Cultural differences and moral intensity: an empirical analysis of South American values
Westerman, J. W., Moore, E. M., & Robertson, C. J. (2025) · Review of International Business and Strategy · doi:10.1108/ribs-07-2024-0084 · Cited by 1
Richter, E., Raudszus, J., & Lißner, S. (2025) · Journal of Cycling and Micromobility Research · doi:10.1016/j.jcmr.2025.100073 · Cited by 2
Barton, M. S., Anderson, B., Charles, C. E., & Valasik, M. A. (2025) · Journal of criminal justice · doi:10.1016/j.jcrimjus.2024.102343 · Cited by 2
Abel, G. A., Agniel, D., & Elliott, M. N. (2024) · BMJ Quality & Safety · doi:10.1136/bmjqs-2023-017039 · Cited by 2
Wang, X., Tang, L., Zhang, L., & Zheng, J. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph191911961 · Cited by 2
“First, the dependent variable satisfied the fundamental assumption of Poisson regression that the respondent variable should be a discrete count variable rather than a continuous attribute [68].”
MethodA Study of Count Regression Models for Mortality Rate
Fitrianto, A. (2021) · CAUCHY · doi:10.18860/ca.v7i1.13642 · Cited by 2
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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