could anyone help me with a correlational analysis between compositional variables and non-compositional ones. To make it clear I am interested in the correlations between the shares of employees in agriculture, services and manufacturing in total employment and GDP. The shares, obviously, add up to 100% (closed data). In other words, my goal is to correlate first the share of agriculture with GDP, then the share of manufacturing with GDP and so on. I would be more than grateful for any hints.
$\begingroup$
$\endgroup$
3
-
2$\begingroup$ A straightforward way would consider re-expressing the proportions, say by the ILR, and proceeding with whatever methods you are familiar with. $\endgroup$– whuber ♦Commented Jul 15, 2020 at 13:56
-
$\begingroup$ Dear Whuber, many thankls for your suggestion. That is what I was thinking about, i.e. using the cantered logratio transformation and then the Pearson coefficient. Am I correct in thinking that using the Pearson coeff for raw (untransformed shares) will always result in spurious correlations? $\endgroup$– ZbigniewCommented Jul 16, 2020 at 9:34
-
$\begingroup$ It depends on what you mean by "spurious correlation." The correlation matrix will be singular, but that's not necessarily a problem. $\endgroup$– whuber ♦Commented Jul 16, 2020 at 13:24
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
One can look at this as a constraint modelling exercise, but my personal observation of poor performance with this path suggests a different approach.
I would start by identifying the employment segment that is apparently in decline, and just leave it out of the analysis. Then, attempt to forecast the missing segment by a difference from the Total Employment forecast.
If this missing segment value is negative or realistically too low,I would base a forecast for this segment based on a model of people (not percent change) which includes an intercept (which may represent a base of insulated workers). Employ this forecast for this segment and slightly prune the larger segment respective forecasts.
Alternatively, look for other higher figures for the Total Employment projection, which then allows a difference from total forecast that is seemingly more reasonable.
So, to directly answer the question how to correlate closed data, try to avoid doing so, and only address the constraint issue (by segment model choice, for example) upon review of a unconstrainted approach with an apparent issue.
-
$\begingroup$ Dear AJKoer Many thanks for your swift reply and the thought-provoking solution. I do really appreciate it. $\endgroup$– ZbigniewCommented Jul 16, 2020 at 9:25