Over-dispersion
In statistics , when modeling counting data , there is overdispersion , also known as over- scattering ( Latin dispersio = "scattering" or dispergere = "distribute, spread out, scatter") if the data show a greater scatter ( variance ) than the model ( e.g. binomial model or Poisson model) would be expected.
In a Poisson regression , if overdispersion is present, the variance is greater than the expected value . The counterpart of the dispersion over the lower dispersion . Undersispersion occurs when the data has less variation than the model assumes.
causes
Essentially the main causes of overdispersion are the presence of
- unobservable heterogeneity
- a positive correlation between the individual observations of the binary responses
Theoretical examples
Using the example of a Poisson regression
A characteristic of the Poisson distribution is that the expectation and the variance are at the same time :
- .
For reasons similar to binomial data, a significantly higher empirical variance is often observed when using Poisson regression. For this reason it is often useful to introduce an over- dispersion parameter on the assumption that
- .
Estimated over-dispersion parameter κ in selected infectious diseases
The over-dispersion parameter κ (incorrectly also referred to as dispersion parameter or dispersion factor and with instead of ) indicates in epidemiology how the spread is increasingly concentrated on individual organisms that are already infected with a pathogen ; the basic reproduction number enables statements about the distribution of κ . A value of put all infected organisms, the same number of uninfected. With values of , the infection with an infectious disease occurs more and more through so-called super spreaders .
Infectious disease | Estimated over-dispersion parameter κ |
---|---|
Seasonal flu | 1 |
SARS pandemic 2002/2003 | 0.16 |
MERS | 0.25 |
Spanish flu | 1 |
Remarks
- ↑ In statistics, Greek letters are conventionally used for population sizes and Latin letters for sample sizes .
Individual evidence
- ^ Ludwig Fahrmeir , Thomas Kneib , Stefan Lang, Brian Marx: Regression: models, methods and applications. Springer Science & Business Media, 2013, ISBN 978-3-642-34332-2 , p. 294.
- ↑ How super spreaders are affecting the pandemic . Accessed May 31, 2020.