The analysis of count data: a gentle introduction to poisson regression and its alternatives.
Abstract
Count data reflect the number of occurrences of a behavior in a fixed period of time (e.g., number of aggressive acts by children during a playground period). In cases in which the outcome variable is a count with a low arithmetic mean (typically < 10), standard ordinary least squares regression may produce biased results. We provide an introduction to regression models that provide appropriate analyses for count data. We introduce standard Poisson regression with an example and discuss its interpretation. Two variants of Poisson regression, overdispersed Poisson regression and negative binomial regression, are introduced that may provide more optimal results when a key assumption of standard Poisson regression is violated. We also discuss the problems of excess zeros in which a subgroup of respondents who would never display the behavior are included in the sample and truncated zeros in which respondents who have a zero count are excluded by the sampling plan. We provide computer syntax for our illustrations in SAS and SPSS. The Poisson family of regression models provides improved and now easy to implement analyses of count data. [Supplementary materials are available for this article. Go to the publisher's online edition of Journal of Personality Assessment for the following free supplemental resources: the data set used to illustrate Poisson regression in this article, which is available in three formats-a text file, an SPSS database, or a SAS database.].
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A second, independent Family Connects randomized clinical trial found a 44% decrease in child maltreatment investigations through 24 months of age.
“Findings from a second, independent FC RCT identified multiple positive effects: increased community connections, reduced postpartum mental health symptoms, reduced emergency medical care use for infants with 1 or more medical risks at birth, and a 44% decrease in child maltreatment investigations through 24 months of age.12”
From Effect of a Universal Postpartum Nurse Home Visiting Program on Child Maltreatment and Emergency Medical Care at 5 Years of Age: A Randomized Clinical Trial (2021) · cites this paper as [12]
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“Because pseudo R-squared in Poisson regression models measures improvements in model fit relative to the null model rather than explained variance, it does not allow for a direct interpretation of the proportion of variance accounted for by the predictors [56].”
- Authors
- Coxe, S., West, S. G., & Aiken, L. S.
- Affiliations
- Arizona State University (US)
- ORCID
- Coxe, Stefany
- Venue
- Journal of Personality Assessment
- Publisher
- Informa UK Limited
- Published
- 2009-02-10
- Volume
- 91
- Issue
- 2
- Pages
- 121-136
- ISSN
- 0022-3891 (ISSN-L)
- 1532-7752
- OpenAlex
- W2133992176
- Cited by
- 1,172
- References
- 50
- Citations by year
- 2026: 65 · 2025: 100 · 2024: 114 · 2023: 79 · 2022: 92 · 2021: 111 · 2020: 80 · 2019: 87 · 2018: 74 · 2017: 64 · 2016: 62 · 2015: 63 · 2014: 53 · 2013: 43 · 2012: 42
- FWCI
- 22.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Personality Assessment (publishedVersion)
- PubMed (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 › Statistical Methods in Epidemiology
- Keywords
- count data, Poisson regression, negative binomial regression, excess zeros, zero-inflated count data, SPSS syntax
- MeSH terms
- Aggression, Child, Child Behavior, Data Interpretation, Statistical, Humans, Psychometrics, Regression Analysis, Models, Statistical, Poisson Distribution
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