overdispersioni

Overdispersion refers to a phenomenon in statistical modeling where the observed variance in the data is greater than what would be expected under a given model. This is particularly common in count data modeled using a Poisson distribution. The Poisson distribution assumes that the mean and variance of the count are equal. If the observed variance is significantly larger than the mean, the data is said to be overdispersed.

The presence of overdispersion can lead to incorrect inferences if not properly addressed. Standard errors of estimated coefficients in models like Poisson regression will be underestimated, leading to inflated test statistics and potentially false positive conclusions. This means that factors might appear statistically significant when they are not, or the effect sizes might be overstated.

Several factors can cause overdispersion, including unobserved heterogeneity among individuals or units, clustering of observations, or a misspecification of the underlying distribution. For instance, if a study examines the number of doctor visits per patient, and some patients have chronic conditions leading to many more visits than others (unobserved heterogeneity), the variance will likely exceed the mean.

To handle overdispersion, alternative statistical models can be employed. For count data, common approaches include using a negative binomial regression model, which allows the variance to be a function of the mean and accommodates a larger variance. Alternatively, quasi-likelihood methods can be used, which relax the distributional assumptions and provide consistent estimates and valid standard errors even in the presence of overdispersion. Another approach is to incorporate random effects into a mixed-effects model to account for unobserved variability.