Skip to main content Accessibility help

Aggregation Among Binary, Count, and Duration Models: Estimating the Same Quantities from Different Levels of Data

  • James E. Alt (a1), Gary King (a2) and Curtis S. Signorino (a3)


Binary, count, and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all of these three data types, the statistical literature is not very helpful in providing methods to estimate parameters of the same process from each. In fact, only a single theoretical process exists for which known statistical methods can estimate the same parameters—and it is generally used only for count and duration data. The result is that seemingly trivial decisions about which level of data to use can have important consequences for substantive interpretations. We describe the theoretical event process for which results exist, based on time independence. We also derive a set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.



Hide All
Aalen, Odd O. 1992. “Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution.” Annals of Applied Probability 2(4): 951972.
Allison, Paul. D. 1982. “Discrete-Time Methods for the Analysis of Event Histories.” In Sociological Methodology 1982, ed. Leinhardt, S. San Francisco: Jossey-Bass, pp. 6198.
Allison, Paul D. 1984. Event History Analysis: Regression for Longitudinal Event Data. Beverly Hills, CA: Sage.
Alt, James E., and King, Gary. 1994. “Transfers of Governmental Power: The Meaning of Time Dependence.” Comparative Political Studies 27(2): 190211.
Beck, Nathaniel. 1998. “Modeling Space and Time: The Event History Approach.” In Research Strategies in the Social Sciences, eds. Scarbrough, Elinor and Tanenbaum, Eric. Oxford: Oxford University Press. pp. 192212.
Beck, Nathaniel, Katz, Jonathan N., and Tucker, Richard. 1998. “Taking Time Seriously: Time-Series-Cross-Section Analysis with a Binary Dependent Variable.” American Journal of Political Science 42(4): 12601288.
Bennett, D. Scott. 1997. “Testing Alternative Models of Alliance Duration, 1816–1984.” American Journal of Political Science 41(3): 846878.
Bennett, D. Scott, and Stam, Allan C. III. 1996. “The Duration of Interstate Wars, 1816–1985.” American Political Science Review 90(2): 239257.
Bienen, Henry, and van de Walle, Nicolas. 1991. “Time and Power in Africa.” American Political Science Review 83: 1934.
Box-Steffensmeier, Janet M., and Jones, Bradford S. 1997. “Time Is of the Essence: Event History Models in Political Science.” American Journal of Political Science 41(4): 14141461.
Cameron, A. Colin, and Trivedi, Pravin K. 1998. Regression Analysis of Count Data. Cambridge: Cambridge University Press.
D’Agostino, Ralph B., Lee, Mei-ling, and Belanger, Albert J. 1990. “Relation of Pooled Logistic Regression to Time Dependent Cox Regression Analysis: The Framingham Heart Study.” Statistics in Medicine 9: 15011515.
Dean, C. B., and Balshaw, R.Efficiency Lost by Analyzing Counts Rather than Event Times in Poisson and Overdispersed Poisson Regression Models.” Journal of the American Statistical Association 92(440): 13871398.
Diermeier, Daniel, and Stevenson, Randolph. 1999. “Cabinet Terminations and Critical Events,” American Journal of Political Science (in press).
Feller, William. 1968. An Introduction to Probability Theory and Its Application, Vol. I, 3rd ed., New York: Wiley.
Feng, Yi, and Zak, Paul. 1999. “The Determinants of Democratic Transitions.” Journal of Conflict Resolution 43(2): 162177.
Freeman, John. 1989. “Systematic Sampling, Temporal Aggregation, and the Study of Political Relationships.” Political Analysis 1: 6198.
Gasiorowski, Mark J. 1995. “Economic Crisis and Political Regime Change: An Event History Analysis.” American Political Science Review 89(4): 882897.
Gertsbakh, I. B. 1989. Statistical Reliability Theory. New York: Marcel Dekker.
Hannan, Michael. 1991. “Theoretical and Methodological Issues in Analysis of Density-Dependent Legitimation in Organizational Evolution.” Sociological Methodology 21: 142.
Kalbfleisch, J. D., and Prentice, R. L. 1980. The Statistical Analysis of Failure Time Data. New York: Wiley.
King, Gary. 1988. “Statistical Models for Political Science Event Counts: Bias in Conventional Procedures and Evidence for The Exponential Poisson Regression Model.” American Journal of Political Science 32(3): 838863.
King, Gary. 1989. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. New York: Cambridge University Press.
King, Gary. 1997. A Solution to the Ecological Inference Problem. Princeton, NJ: Princeton University Press.
King, Gary, Alt, James E., Burns, Nancy, and Laver, Michael. 1990. “A Unified Model of Cabinet Dissolution in Parliamentary Democracies.” American Journal of Political Science 34(3): 846871.
Lancaster, Tony. 1990. The Econometric Analysis of Transition Data. New York: Cambridge University Press.
Londregan, John B., and Poole, Keith T. 1990. “Poverty, the Coup Trap, and the Seizure of Executive Power.” World Politics 42: 151183.
Lupia, Arthur, and Strom, Kaare. 1995. “Coalition Termination and the Strategic Timing of Parliamentary Elections.” American Political Science Review 89(3): 648669.
Parzen, Emanuel. 1962. Stochastic Processes. Oakland, CA: Holden-Day.
Petersen, Trond. 1991. “Time-Aggregation Bias in Continuous-Time Hazard-Rate Models.” Sociological Methodology 21: 263290.
Ross, Sheldon M. 1993. Introduction to Probability Models, 5th ed. San Diego: Academic Press.
Signorino, Curtis S. 1999. “Strategic Interaction and the Statistical Analysis of International Conflict.” American Political Science Review 93(2): 279298.
Signorino, Curtis S., and Yilmaz, Kuzey. 2000. “Strategic Misspecification in Discrete Choice Models.” Paper presented at the 2000 annual meeting of the Midwest Political Science Association and at the 2000 Summer Political Methodology Conference.
Stoker, Thomas M. 1993. “Empirical Approaches to the Problem of Aggregation Over Individuals.” Journal of Economic Literature XXXI (Dec.): 18271874.
Swaminathan, Siddharth. 1999. “Time, Power, and Democratic Transitions.” Journal of Conflict Resolution 43(2): 178191.
Tuma, Nancy Brandon, and Hannan, Michael T. 1984. Social Dynamics. New York: Academic Press.
Warwick, Paul. 1994. Government Survival in Parliamentary Democracies. Cambridge: Cambridge University Press.
Winkelmann, R. 1995. “Duration Dependence and Dispersion in Count-Data Models.” Journal of Business and Economic Statistics 13: 467474.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed