I have 3 years of yearly historic data on the results of a harvest (of truffles) from multiple different areas involving multiple individuals harvesting in each area. The dataset contains:
- name of the person collecting
- time spent collecting in days
- amount collected in gram
The goal is to figure out how to allocate a fixed pool of individuals for the next year's collection across different areas, for which I need to first estimate what will be the area with the best average output per collector per day next year (I presume it is independent of the number of collectors - see comment at the bottom).
For that purpose I have calculated the average historic amount collected per individual and per day for each of the sites across multiple years. Which leaves me with a mean value and confidence interval across time for each area.
Does anyone have a proposition for a suitable model for forecasting the next years mean collected amount, including a prediction interval? Should I be looking into running a longitudinal analysis, or perhaps just combine the observations across multiple years? Is there a good Bayesian approach for this?
I'm making the assumption that the average amount collected doesn't depend on the number of individuals for the site because the number of collectors in each location remained stable over time, and I know it will not change dramatically this year. Also, while the efficiency of collectors shows some variance, I cannot know if they will participate at the next harvest so the individual efficiency is irrelevant for the problem.