I ran through one paper having similar kind of data I have but couldn't understand the statistical approaches they used. Can somebody provide useful information about over-dispersion (any examples)?
In many distribution models, the variance is not a "free" parameter. In such distributions, the variance depends (somehow) on the mean. A very famous example is the Poisson distribution which is used to model count of "event" observed in a given "interval", where the process is known to "produce" these events with a given constant rate λ. The mean (expected value) of this distribution ist just λ (events per interval). The variance of this distribution is also λ. Thus, the higher the rate, the more events per interval will be expected, and the higher the variance will be.
Now if one observes events from a real-world process and assumes that this is a process producing events with a constant rate, then one should get data where mean and variance are (quite) similar. However, in real data we often find that the variance of such count data is considerably larger than the mean. This indicates that our assumption that the rate is constant is not adequate. The fact that the variance is larger than the mean is called "over-dispersion".
The presence of overdispersion tells us that there is additional uncertainty in the rate as well. This can be considered in a probability model. If this is pluged into the Poisson distribution, the result is the negative binomal distribution that can handle over-dispersed data much better than the Poisson distribution.
Starting from here, you can find more information in Wikipedia and numerous examples all over the web, if you google for "over-dispersion", "poisson", "negative binomial", "analysis of count data" etc.
Dear Sujan, the following links may well help:
https://statistics.laerd.com/spss-tutorials/poisson-regression-using-spss-statistics.php
https://statistics.laerd.com/spss-tutorials/binomial-logistic-regression-using-spss-statistics.php
Best,
This is an old paper, but ... Article Overdispersion: Models and Estimation
You can use the link below. There are several examples.
https://www.google.com/search?num=100&client=firefox-b&ei=TXo5XJzVEYrwrgSjxaPIBg&q=overdispersion+test+spss&oq=overdispersion+test+in+spss&gs_l=psy-ab.1.0.0i22i30.55875.60089..62339...0.0..0.379.2667.0j1j0j7......0....1..gws-wiz.......0i13i10i30.il0zY4YCqIU
It is important to realize that apparent over dispersion can occur because the the fixed part of the model - the means - has been mis- specified. So if the responses is a count of number of sexual partners there may be apparent over dispersion around a single mean but that this much reduced when separate means are estimated for men and women.
One the other hand oversdispersion of count data is so common in reality that Hilbe changed the title of his book from Poisson regression to Negative Binomial Distribution to reflect this Hilbe, J.M. (2007) Negative Binomial Regression. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511811852. The NBD having at least one extra parameter as compared to the standard Poisson.
My experience of analysed data with an overdispersed model is that the parameter estimates usually change little but the standard errors can change quiet a bit.
And some shameless publicity:
Article Variance Partitioning in Multilevel Logistic Models That Exh...
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