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Modelling length of traffic jam using a neural network

frankderuyck

I have a 760 record daabase with length of traffic jam data; so fatr there is one very significant input variable as expected the hour of the day: there is a sharp maximum at 8:00 hour in the morning and a broad maximum around 16:00 hour in the afternoon. It is possible the model quite accurately the traffic jam lenghth as a function of day hour with a 10th order polynomal function (no overfitting, the coëfficiënt of the 10th power is significant) using least squares regression. However trying to model with a one layer neural network and several nodes the broad maxiumum at 4 - 5 in the afernoon is OK but in the morning a sharp maximum always occurs one hour too early i.e. at 7 am; increasing the number of nodes from 2 even to10 does not help. Should I use more layres? Possible in jmp? How many nodes/layer are recomended?

Thanks for help, I will get more data and inputs soon and I would like to train and build a model using a neural network.

Accepted answers

Mark_Bailey

Thank you for sharing your example. I did not find any effect of Day, alone or as part of an interaction with any power of Hour, so it is eliminated. You can now use the Bivariate platform and the Flexible > Spline fit. Adjust the parameter as needed. I started with a value of 1 and got good results:

(You can also include terms as spline effects with Fit Model, but it easier to explore the needed flexibility here.)

You can save the fit and the residuals by clicking the red triangle next to Smoothing Spline Fit under the scatter plot and selecting Save Predicteds and Save Residuals.Here is the actual L by predicted L scatter plot with the identity line added for reference:

Looks very good to me! Here are the L residuals by predicted L:

Likewise, these results look very good. You can use the column formula for predictions, too:

This way seems more straight-forward and satisfying than polynomial models (fixed shapes) or neural network models. I explored NN models, too, because they are generally excellent approximators. The NN with 8 hidden nodes using the hyperbolic tangent activation function in a single layer seemed to minimize bias and variance nicely, and predictions agree well with spline model:

What is the advantage of log L? People have easier interpretation when distance is linear.

frankderuyck

Marc, this works fine, thanks a lot for your expert avidvice. I had never realized that so many nodes are required with only hour as input. I have more potential input variables so I can imagine that > 8 nodes will be required? Is there anay guideline about #nodes? I read an article that this is square root of #data, in this case 2 - 3, obviously wrong. Kind regards, Frank

All comments

Mark_Bailey

I am not discouraging you from modeling the data with a neural network but since your response is 'life' or 'time to event' data, have you considered using a reliability/survival model?

frankderuyck

Marc, my is response a length in km, input is the hour of the day where for length I get two maxima: one at 8:00 am and one at 16:00 h

Mark_Bailey

see, then forget survival analysis. I am surprised that you require such a high order polynomial to fit the data. even if the highest order term is significant, what does the residual analysis, leverage, and influence show?

I am also surprised that a neural network with that many nodes did not fit as well. They are very flexible interpolaters.

You might consider splines and Gaussian process models for purely predictive applications.

frankderuyck

I don't understand why neural net can't model my case; it is used intensively in machine learning. Why does neural net always predict the maximum traffic jam length one hour to early in the morning? Maybe I should use more layers in my neural net to ge an accurate prediction, I don't know..