We Need to Improve Our System Modeling
This article is published in the River Hill “The Villager”, November 2017 Issue.
In this column, I will briefly present information about two system modeling problems that negatively impact the River Hill community from Columbia Association (CA) and Howard County Public School System (HCPSS).
Case I: Columbia Association Assessment Share Formula.
A CA work team has been analyzing the formula that determines the amount of money that is distributed to each village association from the assessments paid by Columbia property owners. This Assessment Share forms the foundation for each village’s income stream, with additional revenue generated by rental of the village-managed buildings, newsletter advertising, and various programs and services. As the River Hill Board of Directors was preparing a response to the CA work team on the revised formula, there was a debate on how to simplify the formula. CA board members hear complaints that the current formula is too complicated and a simpler model is needed.
The fallacy is that simplicity results in a better or more accurate model. During the River Hill Board’s discussion, one example of over simplicity identified was with the computation of the newsletter printing costs that was factored into the formula component . The proposed formula uses a flat rate:
where x is the printing rate and N is the number of copies. So, if we print 2000 copies, the cost is 2000 * x dollars. If we print 10000 copies, the cost is 10000 * x dollars. Based on this, the more copies a village needs (a.k., the larger population the village has), the more beneficial the assessment share formula will be. However, in reality, we know printing rates vary depending on the volume of the copies. A slightly better model will account for varying rates, for example:
where we have two different printing rates, , for different printing volumes. Usually, x1 is larger than x2.
As a result, the over-simplified model in Equation (1) gives unfair advantage to villages printing more newsletters. Villages with smaller populations, such as River Hill, are negatively impacted. Similarly, other over-simplified models were used to compute other cost components of the assessment share formula. As a result, the final recommended formula does not accurately reflect the true expenses of each village.
Case II: School Population Prediction.
When Renee Kamen, Manager of Office of School Planning of HCPSS, attended a recent redistricting forum sponsored by the River Hill Community Association, she stated the HCPSS student population prediction model is accurate within 1% error, which implied the predictions model is very accurate. However, based on research by River Hill residents, Pointers Run Elementary School (PRES) consistently receives around 10% more students than predicted by the HCPSS model in recent years. So, the overall accuracy of the model masks the populations in some schools. After examining the actual enrollment numbers at PRES during 2002-2012, analysis shows a continuous decline in student population. However, the student population bounces back very quickly after that. In the HCPSS student projection model, student population at PRES decreases continuously into 2018. Obviously, the HCPSS prediction model does not take into account the current enrollment trend at PRES.
In this case, for each individual school, no matter how accurate the overall prediction is, it does not matter. It only matters when the model predicts the right student number at the school. If not, the model fails. The school system needs to find a way to modify, improve and validate the current student population prediction model as it is being used to support school redistricting.
I hope this article gives you some idea of how an over-simplified or inaccurate model can impact our community and the importance of getting the mathematical modeling correct.
Chao Wu, Ph.D.
River Hill Representative to Columbia Council and Columbia Association Board of Directors
Disclaimer: This letter only represents Dr. Chao Wu’s personal opinion. It does not represent River Hill Board of Directors nor Columbia Association’s Board.