Logsum Issues

February 11th, 2014

I've been working through distribution in the model, and I was having a little bit of trouble.  As I looked into things, I found one place where QC is necessary to verify that things are working right.

The Logsums.

I didn't like the shape of the curve from the friction factors I was getting, so I started looking into a variety of inputs to the mode choice model.  Like time and distance by car:

This is a comparison of distance.  The red line is the new model, the blue and green are two different years of the old model.

This is a comparison of distance. The red line is the new model, the blue and green are two different years of the old model.

This is a comparison of zone-to-zone times.  The red line is the new model, the blue and green are different years of the old model.

This is a comparison of zone-to-zone times. The red line is the new model, the blue and green are different years of the old model.

In both cases, these are as expected.  Since there are more (smaller) zones in the new model, there are more shorter times and distances.

The problem that crept up was the logsums coming from mode choice model for use in distribution:

These are the logsums from the old model.  Notice that the curve allows for some variation.

These are the logsums from the old model. Notice that the curve allows for some variation.

These are the logsums in the new model.  This is a problem because of that 'spike'.

These are the logsums in the new model. This is a problem because of that 'spike'.

I put all the logsums on this, notice how the curve for the old model is dwarfed by the spike in the new model.  This is bad.

I put all the logsums on this, notice how the curve for the old model is dwarfed by the spike in the new model. This is bad.

So the question remains, what went wrong?

I believe the ultimate problem was that there was no limit on Bike and Pedestrian trips in the model, so it was generating some extreme values and somewhere and an infinity was happening in those modes causing the curve shown above.  I tested this by limiting the pedestrian trips to 5 miles (a fairly extreme value) and bike trips to 15 miles and re-running.  The logsums looked very different (again, the new model is the red line):

This is a comparison between the two model versions with fixed bicycle and pedestrian utility equations.

This is a comparison between the two model versions with fixed bicycle and pedestrian utility equations.

Note that the X axis range went from 650 (in the above plots) to 1000.  I'm not too concerned that the logsums in the new model have a larger range.  In fact, as long as those ranges are in the right place distribution may be better.  This is not final data, as I am still looking at a few other things to debug.

Illustration of Gravity Model K Factor Effects

December 10th, 2013

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.

Gravity Model Calibration in R (Example)

December 3rd, 2013

Calibrating a gravity model for the first time is difficult.  I stumbled upon a webpage from a professor at Ohio State that really helps.  One thing I like to do is actually do the examples because I can ensure that my code works and it gives me some ideas.

The code to replicate Dr. Viton's work is below.

Obviously this runs really quick, since it is only three zones.  It is nice that R has some matrix tricks that help make it easy.  One thing to note is that running this for a large matrix in R takes forever (at least the way this is written).  It is possible to run it parallel across all processors, but it still takes forever.