üledispersioni

Üledispersioni, commonly called overdispersion in statistics, describes a situation in which the observed variability of a response variable exceeds what a chosen probabilistic model predicts. It is most often discussed with count data modeled by the Poisson distribution, where the variance is assumed to equal the mean, Var(Y)=E[Y]. When this equality fails, the data are said to be overdispersed.

Common causes include unobserved heterogeneity, clustering within groups, misspecified covariates, or excess zeros. Overdispersion means standard Poisson-based analyses underestimate the true variability, which can lead to biased standard errors and inflated type I error rates if not addressed.

Diagnostics use the dispersion parameter φ=Var(Y)/E[Y]. For Poisson data φ≈1; φ>1 indicates overdispersion, while φ<1 indicates underdispersion. Practical checks include the Pearson chi-square statistic divided by its degrees of freedom and residual plots, as well as model-specific likelihood-based tests.

Common remedies include negative binomial regression, which adds an extra parameter to allow Var(Y)=μ+αμ^2, and quasi-Poisson models that scale standard errors by φ. Other approaches handle clustering (mixed models, generalized estimating equations with robust SEs) or excess zeros (zero-inflated or hurdle models). Model diagnostics are essential to confirm reduced dispersion.

Recognizing üledispersioni is essential for valid inference, as ignoring it can distort standard errors and p-values. The goal is to choose a model that fits the data well and supports reliable conclusions.