Overdispersion

A common task in applied statistics is choosing a parametric model to fit a given set of empirical observations. This necessitates an assessment of the fit of the chosen model. It is usually possible to choose the model parameters in such a way that the theoretical population mean of the model is approximately equal to the sample mean. However, especially for simple models with few parameters, theoretical predictions may not match empirical observations for higher moments. When the observed variance is higher than the variance of a theoretical model, overdispersion has occurred. Conversely, underdispersion means that there was less variation in the data than predicted. Overdispersion is a very common feature in applied data analysis because in practice, populations are frequently heterogeneous.
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The term Overdispersion refers to the condition when the variance of an observed dependent (response) variable exceeds the nominal variance, given the respective assumed distribution . This condition occurs frequently when fitting generalized linear models to categorical response variables , and the assumed distribution is binomial , multinomial , ordinal multinomial , or Poisson . When overdispersion occurs, the standard errors of the parameter estimates and related statistics (e.g., standard errors of predicted and residual statistics) must be computed taking into account the overdispersion.
For details, see Agresti (1996); see also the description of Generalized Linear Models.