# Average correlation as a criterion for choosing among indices

I am modelling industrial diversity in American MSAs (Metropolitan Statistical Areas) as an inverse Hirschman-Herfindahl index (IHH). I have a choice between 4 levels of NAICS industrial classification levels (equivalent to 3- to 6- digits NAICS codes) to aggregate the data before computing this IHH. I don't know how to choose among the 4 levels of aggregation. To help me decide, I computed the IHH at each level of aggregation (based on 2015 employment in 381 MSAs). Then I computed (in R) the correlation matrix between each level, which is :

          2         3         4         5
2 1.0000000 0.8534376 0.8464508 0.7728744
3 0.8534376 1.0000000 0.9935018 0.9541631
4 0.8464508 0.9935018 1.0000000 0.9587253
5 0.7728744 0.9541631 0.9587253 1.0000000


Would it be meaningful/acceptable to pick the level (i.e. level 3) with the highest average coefficients respective to other levels as a "good" level of aggregation, i.e. the level which least diverges from all other levels, i.e. the most "representative" among all 4 levels? I understand there may be many other criteria for research design and modelling. What I am asking if this particular line of reasoning holds any water, statistically speaking.

• I say no, if I understand this correctly. Aggregation typically reduces variability and thus increases correlations. High correlation is typically a measure of how much information you have thrown away. In any case what does representative mean? Being representative of data implies no aggregation at all. – Nick Cox Sep 30 '17 at 9:03
• @NickCox Thanks. I guess this answers my question! – syre Sep 30 '17 at 11:41