Could anyone provide some suggestions on how to generate over-dispersed counts data with serial correlations? I am using R software to conduct a simulation study. Any references on this subject will be much appreciated.
Thanks for your help.
A standard way of generating overdispersed count data is to generate data from a Poisson distribution with a random mean: $Y_i\sim Poisson(\lambda_i)$, $\lambda_i \sim F$. For example, if $\lambda_i$ has a Gamma distribution, you will get the negative binomial distribution for $Y$.
You can easily impose serial correlation by imposing correlation on the $\lambda_i$'s. For example, you could have $\log\lambda_i \sim AR(1)$. Implemented in R:
Here $\lambda_i$'s come from a normal distribution, so the marginal distribution is not a classic distribution, but you could get more creative. Also note that the correlation of the $y$'s does not equal to
This is one way to do it: