I was wondering if anyone here has much experience in building econometric models - specifically in calculating diminishing returns as there are tonnes of different ways to go about this. For simplicity, I have previously used an exponential decay (e to the power of -(a.x) where a is the rate of diminishing returns and x is the rate of media spend - but there are many other ways to model this (e.g. Linear log models, Multiplicative Competitive Interaction) and I'd be interested to hear of people's experiences as to which of these have worked well.
I have worked on a project just like this one. Our statement was, holding other factors constant, increasing the amount of media spend in your budget will increase x up to a certain point. It will get to a point where increasing the amount of media spend will not result in any meaningful increase in x, where x is your KPI. We decided to use R in this analysis and liked the package nlstools. Something like, KPI ~ alpha * exp(beta * media cost) + theta. We also used grid search to find the best values for alpha, beta, and theta.
Hope this helps, if you have any questions you can inbox me!
Thanks Timothy - and for the R tip too - which is my language of choice! I will have a look at this next week and let you know if I have any more questions.
Hi Timothy --
When you use the grid search, what criteria do you usually use to specify the best values for the parameters?
The grid search will take each set of parameters and fit the model. Then you can print out a few measures or just one. There are a few different measures you could use. You can use the accuracy, R-squared, AIC, BIC, etc.