Back to the Future: Modeling Time Dependence in Binary Data

Abstract

Since Beck, Katz, and Tucker (1998), the standard method for modeling time dependence in binary data has been to incorporate time dummies or splined time in logistic regressions. Although we agree with the need for modeling time dependence, we demonstrate that time dummies can induce estimation problems due to separation. Splines do not suffer from these problems. However, the complexity of splines has led substantive researchers (1) to use knot values that may be inappropriate for their data and (2) to ignore any substantive discussion concerning temporal dependence. We propose a relatively simple alternative: including t, t2, and t3 in the regression. This cubic polynomial approximation is trivial to implement—and, therefore, interpret—and it avoids problems such as quasi-complete separation. Monte Carlo analysis demonstrates that, for the types of hazards one often sees in substantive research, the polynomial approximation always outperforms time dummies and generally performs as well as splines or even more flexible autosmoothing procedures. Due to its simplicity, this method also accommodates nonproportional hazards in a straightforward way. We reanalyze Crowley and Skocpol (2001) using nonproportional hazards and find new empirical support for the historical-institutionalist perspective.

Political opportunity structures, democracy, and civil war

“…Although conflicts are recorded as starting on a particular date in the Uppsala data, this normally refers to the first casualties in a conflict that eventually reaches the 25 deaths threshold, and the activities of the organization may in some cases precede the dates (Harbom, Strand & Nygård, 2009: 8-9). 7 We have also considered two alternative approaches for dealing with time dependence, namely cubic spline functions of time as suggested by Beck, Katz & Tucker (1998) or cubic polynomial of time as suggested by Carter & Signorino (2007). We find that the latter actually fits the data less well than our exponential function, while the former has a marginally better fit.…”

“The silent revolution:” How the staff exercise informal governance over IMF lending

“…While tests indicate that serial correlation is not present in the loan commitment specification, I account for a country's past history with the IMF by including a dummy variable that takes the value of one when a county is already under an IMF program. 16 In the binary program participation specifications, where the dependent variable takes on a value of one if a country received an IMF loan in a given year, I control for temporal dependence using the country-specific number of years since the last IMF program, its square, and its cube (Carter and Signorino 2010). 17…”

It Is All about Political Incentives: Democracy and the Renewable Feed-in Tariff

“…where X i,t−1 is a vector of controls, θ j denotes region fixed effects for five UN regions j (Africa, Americas, Asia, Europe, and Oceania), and t, t 2 , t 3 denote linear, quadratic, and cubic time trends (Carter and Signorino, 2010). The error term is ε i,t .…”