# Log-Ratio \ Compositional analysis

I am not a trained statistician but I am trying to improve on my own MBA thesis which was essentially regression analysis of the factors affecting opening cinema box-office in the UK.

I am now trying to look at the mix of marketing channels used by distributors, specifically TV, Press, Outdoor, Radio and Web. My thesis looked at the absolute levels of marketing spend in each channel, but I am now more interested in the combinational proportions of spend across the channels; (e.g., 35% TV, 25% Press, 25% Outdoor, 10% Radio and 5% Web) which of course sum to 100%. The idea is to try to determine an optimal mix under a range of scenarios of budgets opening dates and screen-counts.

I have read that Log-Ratio compositional regression analysis can get around the obvious cross-correlations of inputs that sum to a constant, but I do not know where to start. Can anyone please point me to a novice's guide to log-ratio analysis, especially one that doesn't baffle me with too many strange symbols without definitions, (although I have printed the symbols list from Wikipedia!).

I am very competent with MS.Excel, (although I would prefer not to have to write macros unless I have to), so basing the analysis in it would please me, (and I don't really have any money for expensive 3rd party software).

Would anyone be able to kick-start me please?

• I could certainly be wrong about this, but my impression is that logratio analysis or related techniques like Dirichlet distribution fitting are multivariate approaches used when the outcomes variables are proportions, e.g., fractions of the budget of municipalities spent on categories school, police, and etc. In your case, the explanatory variables sum to one and the outcome is revenue. Maybe you can point us to an example that's similar to the media mix model you have in mind? – Dimitriy V. Masterov Aug 29 '12 at 3:37
• Take a look at the resources pointed on this question: stats.stackexchange.com/questions/35487/… – Zen Sep 1 '12 at 5:33