Regression Model Fitting With Quadratic Term Leads to Different Conclusion in Economic Analysis of Washington State Smoking Ban - Preventing Chronic Disease: January 2011: 10_0213

LETTER (english only)
Regression Model Fitting With Quadratic Term Leads to Different Conclusion in Economic Analysis of Washington State Smoking Ban


Suggested citation for this article: Ma M, McClintock S. Regression model fitting with quadratic term leads to different conclusion in economic analysis of Washington state smoking ban [letter]. Prev Chronic Dis 2011;8(1).
http://www.cdc.gov/pcd/issues/2011/jan/10_0213.htm. Accessed [date].


To the Editor:

Authors of a recent article studied the economic effect of a 2006 smoking ban on bars and taverns in Washington State (1). Their findings of higher-than-expected taxable sales in bars and taverns could have a broad influence on future policy decisions in other states that still do not have these laws.

We found some issues with the authors’ methods. The authors used taxable retail sales (TRS) data from 2002 through 2007 to fit the following regression model:

ln(TRS_bar)i = b0 + b1SFLi + b2Q2i + b3Q3i + b4Q4i + b5ti + b6SFLi ti+ b7UNEMPi + b8lnPOPi + b9lnINCi + ei

Based on the raw TRS data provided to us by the authors (Table 1) the taxable retail sales from 2002 to 2005 or 2007 do not seem to follow a linear trend over time. Instead, the overall trend from 2002 to 2005 or 2007 seems to be parabolic. Thus, the quadratic model is a better fit for the data than the linear model (Figure).

full-text (large):
Preventing Chronic Disease: January 2011: 10_0213






LETTER
Regression Model Fitting With Quadratic Term Leads to Different Conclusion in Economic Analysis of Washington State Smoking Ban [Response to Letter]

Suggested citation for this article: Boles M, Dent C, Dilley J, Maher JE, Boysun MJ, Reid T. Regression model fitting with quadratic term leads to different conclusion in economic analysis of Washington State smoking ban [response to letter]. Prev Chronic Dis 2011;8(1). http://www.cdc.gov/pcd/issues/2011/jan/10_0222.htm. Accessed [date].

To the Editor:

We were interested to read Ma and McClintock’s letter (1) about our analysis of taxable retail sales (TRS) data (2). Although we agree in general that different models of data can lead to different conclusions, we disagree that our analysis misrepresents those data. Rather, we find the reanalysis and presentation in their letter to be misleading.

Ma and McClintock reiterate our observation that the TRS data during this time do not follow a linear trend — with an obvious upturn in 2006 through 2007 and a smaller downturn in 2002 through 2003 — and question our use of a linear model to describe these data. In our analyses, we examined a segmented regression approach (3) to address this nonlinearity, using a theoretical break point at 2006 to delineate periods before and after passage of a smoke-free law (SFL) in Washington. Ma and McClintock put forth a linear model with a quadratic term to address the nonlinearity in these data, with no theoretical justification for the mechanism that would drive such a function. The use of a quadratic term suggests an exponential growth in TRS post-SFL, whereas we suggest a theory-based, more moderate, and flexible linear growth function due to the SFL. Although the figure presented by Ma and McClintock correctly represents their model, it misrepresents our model as a single straight-line fit when it actually has 2 linear segments (Figure).

full-text:
Preventing Chronic Disease: January 2011: 10_0222