How to normalize and compare growth rates between variables at different stages of some kind of growth model "curve"?

Question

I have a data frame that has various capital and metropolitan cities with various economic, market and performance data. One set of variables is each total annual non-domestic visitor volume and the recent annual growth rates in that volume.

As you might expect cities with smaller annual total volumes tend to see larger annual growth percentages; and as cities grow to see larger total visitor volumes their annual growth rate tends to get smaller and flatten.

A sample of the dozens of cities might be: - City 2014-intl-arr-000s Travel-%incr-13-14 - Abu Dhabi 2200.3 5.9 - Bangalore 856.6 31.1 - Hanoi 3000 29.9 - Istanbul 11871.2 13.2 - London 17383.9 3.6 - NYC 12230 3.2

Running correlations and regressions on various other data variables I have in the dataset have worked fine for drawing some insight, but my stats experience isn't deep enough for how best to make a fair comparison in visitor growth (%) performance between these cities.

Is there a stats process(es) I can/should follow to 'normalize" these particular data so I make a fairer judgement of comparative significance of performance between the different growth rates, since they are obviously at different stages of any potential growth curve by which I might compare or model them?

I was thinking I could geographically subgroup them and compare a city's performance vs the median (and/or mean) of the region. Or possibly subgroup by tiers of visitor totals, and do the same. And then maybe attribute a score based on an ANOVA result. But I wonder how I might consider comparing all cities against the performance of each of the others -- unless this is a fool's errand.

Answer 1

There is no standard protocol for addressing your question that I'm aware of.

A key point of clarification is that absolute and relative metrics are getting somewhat confounded -- city size is absolute whereas growth rate is relative. Equilibrating them to create a "fair comparison" is a daunting task for which there are any number of approaches to doing so:

• An applied practitioner might suggest partitioning each factor into, e.g., low, medium and high "intl arr" and "%incr," and then examine the crosstab of the two partitions.

• A statistician might suggest including city population size in the regression as a control variable to "normalize" the resulting growth rates for that factor. That same statistician might also suggest using natural logs for "intl arr" since this transformation puts absolute metrics on a relative scale.

• An econometrician would note that, for the most part, cities are synonymous with countries and might suggest including national GDP or even % change in GDP as instrumental variables and proxies for levels of development. They might also suggest breaking out "developed" separately from "developing" markets for the analysis. Another useful metric could be the magnitude of import-export trade or FDI -- foreign direct investment -- as a control.

Among the factors that should be included but are not mentioned are things like international marketing budgets and efforts. In other words, here in the US, advertising intended to stimulate travel to specific countries airs on TV all the time.

The point is that this is the kind of question with multiple answers, none of which can be described as the single, true, "correct" way to do it -- at least in my experience and opinion. However, unless you are doing a dissertation you can't report results based on all. So, for the purposes of your analysis, you will want to settle on one approach. Just be prepared to motivate it in the unlikely event that it is challenged.

Answer 2

Run a regression using the growth rates by annual number of visitors (predictor); and then analyze the residuals. If the residual is positive it suggests the growth rate is greater than otherwise expects based on annual number of visitors.