Alejandro Quiroz Flores is a Reader (Associate Professor) and Chief Scientific Adviser at the Institute for Analytics and Data Science (IADS), University of Essex. He obtained his PhD in Politics at New York University. He specializes in Econometrics, Machine Learning, and Political Economy. His work has appeared at Global Environmental ChangeBritish Journal of Political SciencePolitical Science Research and Methods, and International Studies Quarterly, among others. He is the author of Ministerial Survival During Political and Cabinet Change: Foreign Affairs, Diplomacy and War, by Routledge (2016). 

 

 

Course Content
This course will cover the statistical concepts and techniques that are used to model time. These models are also known as survival or event history models, and we use them to analyze the duration of time until some event happens—the termination of civil wars, the completion of a medical treatment, or the loss of political office, among other events.  

The course will be divided into two main sections: 

1. Continuous Time Duration Models: We will examine parametric duration models (exponential, Weibull, log-logistic, generalized gamma, etc.), semi-parametric duration models (Cox model) and Kaplan-Meier estimates.  In addition to exploring how these models are estimated and interpreted, we will also look at typical problems in estimation and various residual-based diagnostic tests.

2. Discrete Time Duration Models and Advanced Techniques: We will look at the connection between discrete time duration models and binary time-series-cross-section models.  We will examine various ways to deal with time dependence, ongoing events, multiple events, and time varying covariates, as well as Markov transition models. In the section for advanced techniques, we will examine models for competing risks, heterogeneity and frailty, and repeated events.

 

Course Objectives 
The central objective of this course is to learn how to identify, and correctly apply, the statistical techniques appropriate to answering questions relating to time and duration.  Students will be able to identify and classify data problems in survival analysis, define the appropriate survival function, distribution function, hazard function, relative hazard, and cumulative hazard, as well as summarize and interpret analyses of survival data using various estimators. By the end of the course, students should be quite adept at programming Stata to estimate and interpret a wide variety of different duration models. 

Course Prerequisites
Students should already have some experience with the theory behind Maximum Likelihood Estimation.  Some knowledge of basic calculus (differentiation and integration), exponents and logarithms, and Stata code will be helpful. 

Representative Background Reading
King, Gary, James Alt, Michael Laver & Nancy Burns. 1990. “A Unified Model of Cabinet Dissolution in Parliamentary Democracies.” American Journal of Political Science 34: 847-871.
Diermeier, Daniel and Randy T. Stevenson. 1999. “Cabinet Survival and Competing Risks.” American Journal of Political Science 43: 1051-1098.
Box-Steffensmeier, Janet M. & Christopher J. W. Zorn. 2001. “Duration Models and Proportional Hazards in Political Science.” American Journal of Political Science 45: 972-988. 

Required texts
Box-Steffensmeier, Janet & Bradford S. Jones. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press. 

Background knowledge required

Statistics
OLS = strong
MLE= moderate

Computer Background
STATA= moderate

Course Outline

 

Day 1: Introduction and preliminaries. Survival models and the analysis of time. Key probability concepts. Continuous time duration models.  Parametric models: exponential, Weibull, log-logistic, generalized gamma, etc.  Estimation and interpretation.

Exercise:

• Identifying duration data in Stata.
• Correctly setting survival time in Stata.
• Estimation and interpretation of parametric duration models.
• Model selection.

Reading:

• Box-Steffensmeier, Janet M. and Bradford S. Jones. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press. Ch. 2-3.
• King, Gary, James Alt, Michael Laver and Nancy Burns. 1990. “A Unified Model of Cabinet Dissolution in Parliamentary Democracies.” American Journal of Political Science 34: 847-871.

 

Day 2: Continuous time duration models. Kaplan-Meier estimates. The Cox semi-parametric model.  Dealing with tied data.  Obtaining baseline hazard and survivor functions.

Exercise:

• Producing Kaplan-Meier estimates.
• Estimation and interpretation of the Cox model.
• Quantities of interest and marginal effects.

Reading:

• Box-Steffensmeier, Janet M. and Bradford S. Jones. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press. Ch. 4.

 

Day 3: Continuous time duration models. Typical problems in estimation. Proportionality. Diagnostic tests and solutions.

Exercise:

• Diagnostic tests and solutions.

Reading:

• Box-Steffensmeier, Janet M. and Bradford S. Jones. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press. Ch. 8.
• Keele, Luke. 2010. “Proportionally Difficult: Testing for Nonproportional Hazards in Cox Models.” Political Analysis 18 (2): 189-205.
• Licht, Amanda. 2011. “Change Comes with Time: Substantive Interpretation of Nonproportional Hazards in Event History Analysis.” Political Analysis 19 (2): 227-243.
• Park, Sunhee, and David J. Hendry. 2015. “Reassessing Schoenfeld Residual Tests of Proportional Hazards in Political Science Event History Analyses.” American Journal of Political Science 59 (4): 1072-1087.

 

Day 4: Discrete time duration models. The structure of survival data. The modeling of duration dependence in discrete models. Time-varying covariates. Complex spells of time. Markov transition models.

Exercise:

• Working with discrete survival data.
• Estimation and interpretation.
• Types of spells of time.
• Estimation and interpretation of Markov transition models.

Reading:

• Box-Steffensmeier, Janet M. and Bradford S. Jones. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press. Ch. 5, 7.
• Beck, Nathaniel, Jonathan N. Katz, and Richard Tucker. 1998. “Taking Time Seriously: Time-Series Cross-Section with a Binary Dependent Variable.” American Journal of Political Science 42: 1260-1288.
• Box-Steffensmeier, Janet M. 1996. “A Dynamic Analysis of the Role of War Chests in Campaign Strategy.” American Journal of Political Science 40: 352-371.
• Oneal, John and Bruce Russett. 1999. “Assessing the Liberal Peace with Alternative Specifications: Trade Still Reduces Conflict.” Journal of Peace Research 36: 423-442.
• Przeworski, Adam, Michael E. Alvarez, José Antonio Cheibub and Fernando Limongi. 2000. Democracy and Development: Political Institutions and Well-Being in the World, 1950-1990. New York: Cambridge University Press. Ch. 2.

 

Day 5: Competing risks models. Continuous time models and multinomial logit models. Unobserved heterogeneity and frailty models. Multiple failures and repeated events models.

Exercise:

• Estimation and interpretation.

Reading:

• Box-Steffensmeier, Janet M. and Bradford S. Jones. 2004. Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press. pp. 166-182.
• Diermeier, Daniel and Randy T. Stevenson. 1999. “Cabinet Survival and Competing Risks.” American Journal of Political Science 43: 1051-1098.
• Box-Steffensmeier, Janet M. and Christopher J. W. Zorn. 2002. “Duration Models for Repeated Events.” Journal of Politics 64: 1069-1094.
• Box-Steffensmeier, Janet M. and Suzanna De Boef. 2007. “Event Dependence and Heterogeneity in Duration Models: The Conditional Frailty Model.” Political Analysis.