Statistics on the Henley Street Bridge Data

Recently, the James White Parkway extension EIS study was released.  There has been much controversy and media attention brought to the subject.

I came across a list of traffic counts from 1985-2011 for Henley Street Bridge, Chapman-City, Chapman-County, Chapman-Seymour, and the JWP Bridge.  I would qualify myself to perform this analysis based on my research in building mathematical models and using statistics to match models to existing experimental data.   I will perform a simple analysis on the traffic data to determine whether the overall trend supports an increasing trend or a positive trend. 

Given this data, it is possible to consider two different models for each scenario: either constant (c) or linear increasing (a x + b).   If the data points appear to be increasing, the linear model will be distinguishable from the constant model, even if the increase is some trend other than linear increasing (for example, exponential increasing).

The next step is to assume the observational error of each measurement is normally distributed about the observed traffic count.  It is assumed that TDOT has more data for each measurement, although this will not significantly alter the results of this statistical test unless the variance of the samples for each year is very high.  Carrying forward, it is safe to assume TDOT has faith in these estimates or they would not have published them.

Both models are fitted to the time-series data using sum of squares (which is proportional to likelihood if the variances are the same for each measurement).  Once the model parameters are found, the AIC can be calculated to select the model that best describes the data (relative to the other model).  For example, if the AIC values are similar, we must conclude that no model can describe the model any better than other.  However, if one of the models has an AIC that is much lower than the other, then we can conclude that model explains the data better than the other.

If the linear model is better than constant model, then we conclude there is a measurable upward trend in the data.  If the constant model and linear model fits are the same, then we conclude that there is very little (or no) observable increasing trend in the time-series data.

I will present my findings for each data set below:

  Henley Street Bridge Counts

Henley Street Bridge Projections.  The black line is an approximation of how
TDOT would project 63,000 cars by 2035.  The lack of support of the line for years
before 2008 is evidence that the line is not a good fit.

This data appears to be taken over the Tennessee River. Both best-fit models are shown in the figure, along with the measurements.  The linear model is in red and the constant model is in blue.  The AIC for the linear model was 550.2, while the AIC for the constant model was 548.5.  Based on the statistical test, there is no way to distinguish whether this data is constant or increasing.

Chapman-City Limits Counts

Chapman Highway near Sonic within the city limits.  There is no way to distinguish
constant or increasing traffic counts.

This data appears to be taken near Gwinfield Dr, south of Woodlawn Pike. Both best-fit models are shown in the figure, along with the measurements.  The linear model is in red and the constant model is in blue.  The AIC for the linear model was 512.6, while the AIC for the constant model was 512.8.  Based on the statistical test, there is no way to distinguish whether this data is constant or increasing.

Chapman-County Counts

This data was taken south of E Hendron Chapel Road, near Bower Field. Both best-fit models are shown in the figure, along with the measurements.  The linear model is in red and the constant model is in blue.  The AIC for the linear model was 482.2, while the AIC for the constant model was 524.4.  Based on the statistical test, the traffic counts are increasing on Chapman at the county line.

Seymour Counts

Seymour traffic counts for Chapman Highway.  Traffic has been increasing
over the past 25 years.

This data was taken near the Dollar General in Seymour. Both best-fit models are shown in the figure, along with the measurements.  The linear model is in red and the constant model is in blue.  The AIC for the linear model was 499.9, while the AIC for the constant model was 536.7.  Based on the statistical test, the traffic counts are increasing along Chapman in Seymour.

James White Parkway Counts

James White Parkway traffic counts.  The increase in 2001 is from the
closing of the Gay St Bridge.  Interestingly, it appears that when
Gay St reopened, many more cars continued using JWP as they had grown
accustomed to it being faster than Gay St.  Will this trend continue when
Henley reopens?

This data was taken over the Tennessee River on James White Parkway. Both best-fit models are shown in the figure, along with the measurements.  The linear model is in red and the constant model is in blue.  The AIC for the linear model was 508.2, while the AIC for the constant model was 538.4.  Based on the statistical test, the traffic counts are increasing on the James White Parkway Bridge.

Furthermore, we can do some multivariate analysis on how the other traffic counts affect the Henley Street Bridge AADT's.  Consider we want to make a multivariate model of Y_Henley=a₁ X_Ch.City+a₂ X_Ch.County +a₃ X_Ch.Sey, where X are the data counts, Y is the predicted value, and the a's are the coefficients associated with each data point.  This asks the question: Does the traffic on Henley reflect as functions of all city data, county data, and Seymour data?  The p-values for the City coefficient were 0.014, for the County it was 0.658 and for Seymour the p-value was 0.683.  At a significance level of 0.05, the only dataset that has a direct impact on the Henley Street Bridge is the city counts, and there is no evidence to support the County data or the Seymour data impacting the Henley traffic counts.

This suggests that despite South Knox County and Seymour growing in population, the increase in traffic statistically has no effect on the Henley Street Bridge counts.

In conclusion, we chose to model the traffic counts as either constant or linear increasing.  If the AIC model selection statistic is similar to that of the other model for the same data set, then the model selection criteria fails to identify an increasing trend in the data.  The traffic counts for the Henley Street Bridge and Chapman Highway in the City Limits do not demonstrate an increasing trend.  However, the traffic counts for Seymour, Chapman Highway past the proposed extension terminus, and the James White Parkway Bridge do show a positive increasing trend.

Based on this statistical analysis, I question TDOT’s analysis that traffic counts will increase at Henley Street and on Chapman at the city limits when I have proven that a statistician cannot distinguish between a constant model and linear increasing model for the traffic counts for those two areas.