This article presents an autoregressive random coefficient model with overdispersed negative multinomial marginal distributions for the analysis of heterogeneity and serial dependencies in multivariate longitudinal count data. The model structure consists of four components that take into account (a) individual difference effects, (b) random time effects, (c) multiple event categories, and (d) autodependencies. The last component is based on a stochastic integer-valued autoregressive process proposed by McKenzie. The model is applied to analyze count data from a panel diary study about the relationship between personality factors and emotion experiences. It is shown that there are large and stable individual personality differences in the incidence and duration of self-reported emotional experiences. Theoretical and clinical implications of this result are discussed.