Illustration of Gravity Model K Factor Effects

While the use of K factors can be very questionable when applied inappropriately, they have been a practice in gravity models for a very long time.  For some regions where psychological boundaries (e.g. state lines, river crossings, etc.) cause an effect on travel, K factors have been used to correct problems.

I decided to take a closer look on the effects of K factors on a small model in R.  I fixed the friction factors to 1 to eliminate the effects of the friction factors an just show the effects of K factors.

Using a single constraint gravity model, the effects are quite pronounced:

This is the base - all K factors are set to 1

This is the base - all K factors are set to 1

Scenario 2 - K factors for 1-5 and 5-1 are set to 2.

Scenario 2 - K factors for 1-5 and 5-1 are set to 2.

Scenario 3 - the K factors for 1-5 and 5-1 are set to 0.5.

Scenario 3 - the K factors for 1-5 and 5-1 are set to 0.5.

Looking at the three, the two things that stand out is that a K of 2 or 0.5 does not mean that twice or half as many trips will be forecasted to those zones.  Also, since this is a single-constrained model, the production totals are all the same, but the attraction totals vary.  The code to run this is on a Github Gist.

This is just a quick example.  It would change with a doubly-constrained model (which I haven't attempted yet).  The details of that may be posted soon.

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