How To Be Smooth: Automated Smoothing in Political Science

Smoothing is an important statistical tool in applied analysis of political data. Smoothers can be use to incorporate nonlinearity, deal with duration dependence, and diagnose residual plots. But smoothers invariably require the analyst to make choices about the amount of smoothing to apply and the criteria for this choice amounts to visual examination. Such visual methods can lead to seemingly arbitrary selection of smoothing parameters. I argue that instead of using a visual method for the selection of smoothing parameters, analysts should use automated methods where the level of smoothing is estimated from the data. I outline why such methods are preferable and then demonstrate with both simulated data and in empirical settings how automatic smoothing is superior to visual selection of smoothing parameters. Methods of smoothing the statistical relationship between two variables have gained increased currency in political science. Smoothers, often referred to as scatterplot smoothers or nonparametric regression, have a variety of uses. They can be used to incorporate nonlinearity into parametric models (Beck and Jackman 1998; Keele 2006). They can be used to smooth plots of hazard functions (Box-Steffensmeier and Jones 2004). They are also a key technique for the estimation of binary time-series cross sectional datasets (Beck, Katz and Tucker 1998). They can also be an important diagnostic tool for linear model residual plots (Fox 1997). While smoothers are readily available in a variety of statistical software packages, their use isn’t without complications. First, there are a bewildering array of different smoothers. For example, there are at least four different types of spline smoothers alone. Moreover, while smoothers replace strong linearity assumptions, analysts who use smoothers have to