= Solution
Under fit.2, observations in each period are independent <Poisson random variables> with a common mean, so each <sample variance> should fluctuate around its <sample mean>. The plot instead has <variances> roughly 130–300 for means roughly 80–120, well above the line <variance> equals mean. This is <overdispersion>.
Day-to-day traffic variation can produce a <Poisson mixture>: a random daily intensity increases the marginal <variance> and can correlate observations from the same day. A useful replacement is a <negative binomial regression>, with <variance> $\mu+\mu^2/\kappa$, or a <Poisson generalized linear mixed model> with a day <random intercept>. A day-factor effect can also be included if inference is restricted to the observed days. A <Quasi-Poisson regression> estimates a dispersion multiplier for uncertainty, but does not itself explain the shared-day dependence and has no ordinary likelihood-based AIC. The means can retain the period-factor or selected jump structure.
Back to article page
