Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-23T21:49:52.147Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  04 January 2017

James E. Alt ,
Gary King  and
Curtis S. Signorino
James E. Alt
Affiliation:
Department of Government, Harvard University. e-mail: JAlt@latte.harvard.edu
Gary King
Affiliation:
Department of Government, Harvard University and World Health Organization, Cambridge, MA 02138. e-mail: King@Harvard.EduWWW:http://GKing.Harvard.Edu
Curtis S. Signorino
Affiliation:
Department of Political Science, University of Rochester, Rochester, NY 14627. e-mail: sign@troi.cc.rochester.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Political Analysis , Volume 9 , Issue 1 , 2001 , pp. 21 - 44
Copyright
Copyright © 2001 by the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aalen, Odd O. 1992. “Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution.” Annals of Applied Probability 2(4): 951–972.Google Scholar
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. 61–98.Google Scholar
Allison, Paul D. 1984. Event History Analysis: Regression for Longitudinal Event Data. Beverly Hills, CA: Sage.CrossRefGoogle Scholar
Alt, James E., and King, Gary. 1994. “Transfers of Governmental Power: The Meaning of Time Dependence.” Comparative Political Studies 27(2): 190–211.Google Scholar
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. 192–212.Google Scholar
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): 1260–1288.Google Scholar
Bennett, D. Scott. 1997. “Testing Alternative Models of Alliance Duration, 1816–1984.” American Journal of Political Science 41(3): 846–878.CrossRefGoogle Scholar
Bennett, D. Scott, and Stam, Allan C. III. 1996. “The Duration of Interstate Wars, 1816–1985.” American Political Science Review 90(2): 239–257.Google Scholar
Bienen, Henry, and van de Walle, Nicolas. 1991. “Time and Power in Africa.” American Political Science Review 83: 19–34.CrossRefGoogle Scholar
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): 1414–1461.Google Scholar
Cameron, A. Colin, and Trivedi, Pravin K. 1998. Regression Analysis of Count Data. Cambridge: Cambridge University Press.Google Scholar
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: 1501–1515.Google Scholar
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): 1387–1398.Google Scholar
Diermeier, Daniel, and Stevenson, Randolph. 1999. “Cabinet Terminations and Critical Events,” American Journal of Political Science (in press).Google Scholar
Feller, William. 1968. An Introduction to Probability Theory and Its Application, Vol. I, 3rd ed., New York: Wiley.Google Scholar
Feng, Yi, and Zak, Paul. 1999. “The Determinants of Democratic Transitions.” Journal of Conflict Resolution 43(2): 162–177.Google Scholar
Freeman, John. 1989. “Systematic Sampling, Temporal Aggregation, and the Study of Political Relationships.” Political Analysis 1: 61–98.Google Scholar
Gasiorowski, Mark J. 1995. “Economic Crisis and Political Regime Change: An Event History Analysis.” American Political Science Review 89(4): 882–897.Google Scholar
Gertsbakh, I. B. 1989. Statistical Reliability Theory. New York: Marcel Dekker.Google Scholar
Hannan, Michael. 1991. “Theoretical and Methodological Issues in Analysis of Density-Dependent Legitimation in Organizational Evolution.” Sociological Methodology 21: 1–42.Google Scholar
Kalbfleisch, J. D., and Prentice, R. L. 1980. The Statistical Analysis of Failure Time Data. New York: Wiley.Google Scholar
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): 838–863.CrossRefGoogle Scholar
King, Gary. 1989. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. New York: Cambridge University Press.Google Scholar
King, Gary. 1997. A Solution to the Ecological Inference Problem. Princeton, NJ: Princeton University Press.Google Scholar
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): 846–871.Google Scholar
Lancaster, Tony. 1990. The Econometric Analysis of Transition Data. New York: Cambridge University Press.Google Scholar
Londregan, John B., and Poole, Keith T. 1990. “Poverty, the Coup Trap, and the Seizure of Executive Power.” World Politics 42: 151–183.CrossRefGoogle Scholar
Lupia, Arthur, and Strom, Kaare. 1995. “Coalition Termination and the Strategic Timing of Parliamentary Elections.” American Political Science Review 89(3): 648–669.Google Scholar
Parzen, Emanuel. 1962. Stochastic Processes. Oakland, CA: Holden-Day.Google Scholar
Petersen, Trond. 1991. “Time-Aggregation Bias in Continuous-Time Hazard-Rate Models.” Sociological Methodology 21: 263–290.Google Scholar
Ross, Sheldon M. 1993. Introduction to Probability Models, 5th ed. San Diego: Academic Press.Google Scholar
Signorino, Curtis S. 1999. “Strategic Interaction and the Statistical Analysis of International Conflict.” American Political Science Review 93(2): 279–298.Google Scholar
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.Google Scholar
Stoker, Thomas M. 1993. “Empirical Approaches to the Problem of Aggregation Over Individuals.” Journal of Economic Literature XXXI (Dec.): 1827–1874.Google Scholar
Swaminathan, Siddharth. 1999. “Time, Power, and Democratic Transitions.” Journal of Conflict Resolution 43(2): 178–191.Google Scholar
Tuma, Nancy Brandon, and Hannan, Michael T. 1984. Social Dynamics. New York: Academic Press.Google Scholar
Warwick, Paul. 1994. Government Survival in Parliamentary Democracies. Cambridge: Cambridge University Press.Google Scholar
Winkelmann, R. 1995. “Duration Dependence and Dispersion in Count-Data Models.” Journal of Business and Economic Statistics 13: 467–474.Google Scholar