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

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).