I have an upcoming project that involves the following:

  • A client will provide measurements of traffic counts on a daily basis over the period of a calendar year for about 60 out of 300 locations.
  • They would like to estimate the traffic counts for the remainder of their locations during the same period of time, based on the count data as as well as various covariates (urbanity, region, and other various characteristics). Covariate information is available throughout all of their locations.
  • Seasonality effect is expected, but I can include weather information for each day and location (temperature and whether it was sunny, cloudy, or rainy), and whether the day was a weekday vs. weekend or public holiday. I'm anticipating to also use this information as covariates. It is possible however that there is an increasing trend of traffic over the calendar year, which could be due to some investments they have made.

My first inclination was to use a Poisson multi-level Bayesian model using the brms package in R. However, the count data is over-dispersed and I suspect based on the above that I should use a time-series model, even if I use weather and type of day as covariates. The brms package doesn't appear to offer the ability to run a negative binomial time-series regression.

I'm looking for some guidance on the following:

  • Am I correct in assuming I'll need to run a time-series regression, even if I take into account seasonal effects such as type of day and weather?
  • If so, what materials could I read up on to determine how to run a time-series negative binomial multi-level regression, using Stan or JAGS in R?

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