The generalized estimating equation (GEE) approach of Zeger and Liang facilitates analysis of data collected in longitudinal, nested, or repeated measures designs. GEEs use the generalized linear model to estimate more efficient and unbiased regression parameters relative to ordinary least squares regression in part because they permit specification of a working correlation matrix that accounts for the form of within-subject correlation of responses on dependent variables of many different distributions, including normal, binomial, and Poisson. The author briefly explains the theory behind GEEs and their beneficial statistical properties and limitations and compares GEEs to suboptimal approaches for analyzing longitudinal data through use of two examples. The first demonstration applies GEEs to the analysis of data from a longitudinal lab study with a counted response variable; the second demonstration applies GEEs to analysis of data with a normally distributed response variable from subjects nested within branch offices ofan organization.
Get full access to this article
View all access options for this article.
References
1.
Ahuja, G., & Katila, R. (2001). Technological acquisitions and the innovation performance of acquiring firms: A longitudinal study. Strategic Management Journal, 22, 197-220.
2.
Ahuja, G., & Lampert, C. M. (2001). Entrepreneurship in the large corporation: A longitudinal study of how established firms create breakthrough inventions. Strategic Management Journal, 22, 521-543.
3.
Barnhart, H. X., & Williamson, J. M. (1998). Goodness-of-fit tests for GEE modeling with binary responses. Biometrics, 54, 720-729.
4.
Bryk, A. S., Raudenbush, S. W., & Congdon, R. T. (2003). HLM: Hierarchical linear and non-linear modeling with the HLM/2L and HLM/3L programs. St. Paul, MN: Assessment Systems Corporation.
5.
Cook, D., & Weisberg, J. (1982). Residuals and influence in regression. London: Chapman and Hall.
6.
Conaway, M. R., & Lohr, S. L. (1994). A longitudinal analysis of factors associated with reporting violent crimes to the police. Journal of Quantitative Criminology, 10, 23-39.
7.
Diggle, P. J., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data (2nd ed). Oxford, UK: Oxford University Press.
8.
Fitzmaurice, G. M. (1995). A caveat concerning independence estimating equations with multivariate binary data. Biometrics, 51, 309-317.
9.
Fitzmaurice, G. M., Laird, N. M., & Rotnitzky, A. (1993). Regression models for discrete longitudinal responses. Statistical Science, 8, 284-309.
10.
Gardner, W., Mulvey, E. P., & Shaw, E. C. (1995). Regression analyses of counts and rates: Poisson, overdispersed Poisson and negative binomial models. Psychological Bulletin, 118, 392-404.
11.
Goodman, J. S., & Blum, T. C. (1996). Assessing the non-random sampling effects of subject attrition in longitudinal research. Journal of Management, 22, 627-652.
12.
Hardin, J. W., & Hilbe, J. M. (2003). Generalized estimating equations. Boca Raton, FL: Chapman and Hall/CRC Press.
13.
Harrison, D. A. (2002) Structure and timing in limited range dependent variables: Regression models for predicting if and when. In F. Drasgow & N. Schmitt (Eds.), Measuring and analyzing behavior in organizations: Advances in measurement and data analysis (pp. 446-497). San Francisco: Jossey-Bass.
14.
Harrison, D. A., & Hulin, C. L. (1989). Investigations of absenteeism: Using event-history models to study the absence-taking process. Journal of Applied Psychology, 74, 300-316.
15.
Haveman, H. A., & Nonnemaker, L. (2000). Competition in multiple markets: The impact on growth and market entry. Administrative Science Quarterly, 45, 232-267.
16.
Horton, N. J., Bebchuk, J. D., Jones, C. L., Lipsitz, S. R., Catalano, P. J., Zahner, G. E. P., & Fitzmaurice, G. M. (1999). Goodness-of-fit for GEE: An example with mental health service utilization. Statistics in Medicine, 18, 213-222.
17.
Horton, N. J., & Lipsitz, S. R. (1999). Review of software to fit generalized estimating equation regression models. American Statistician, 53, 160-169.
18.
Lepine, J. A., Colquitt, J. A., & Erez, A. (2000). Adaptability to changing task contexts: Effects of general cognitive ability, conscientiousness, and openness to experience. Personnel Psychology, 53, 563-593.
19.
Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
20.
Martocchio, J. J., & Harrison, D. A. (1993). To be there or not to be there? Questions, theories and methods in absenteeism research. In G. R. Ferris (Ed.), Research in personnel and human resources management (Vol. 11, pp. 259-328). Greenwich, CT: JAI.
21.
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). London: Chapman and Hall.
22.
Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A, 135, 370-384.
23.
Pan, W. (2001). Akaike’s information criterion in generalized estimating equations. Biometrics, 57, 120-125.
24.
Pindyck, R. S., & Rubinfeld, D. L. (1998). Econometric models and economic forecasts (4th ed.). Boston: Irwin, McGraw-Hill.
25.
Preisser, J. S., & Qaqish, B. F. (1996). Deletion diagnostics for generalized estimating equations. Biometrika, 83, 551-562.
26.
Prentice, R. L.(1988). Correlated binary regression with covariates specific to each binary observation. Biometrics, 44, 1033-1048.
27.
Rotnitzky, A., & Jewell, N. P. (1990). Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data. Biometrika, 77, 485-497.
28.
Sheu, C.-F. (2000). Regression analysis of correlated binary outcomes. Behavior Research Methods, Instruments, & Computers, 32, 269-273.
29.
Stokes, M. E. (1999). Recent advances in categorical data analysis. 24th Annual Meeting of the SAS Users Group International. Cary, NC: SAS Institute.
30.
Stokes, M. E., Davis, C. S., & Koch, G. G. (2000). Categorical data analysis using the SAS system (2nd ed.). Cary, NC: SAS Institute.
31.
Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439-447.
32.
Welbourne, T. M., & Trevor, C. O. (2000). The roles of departmental and position power in job evaluation. Academy of Management Journal, 43, 761-771.
33.
Zeger, S. L., & Liang, K.-Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42, 121-130.
34.
Zeger, S. L., Liang, K.-Y., & Albert, P. S. (1988). Models for longitudinal data: Ageneralized estimating equation approach. Biometrics, 44, 1049-1060.
35.
Zheng, B. (2000). Summarizing the goodness of fit on generalized linear models for longitudinal data. Statistics in Medicine, 19, 1265-1275.
36.
Zorn, C. J. W. (2001). Generalized estimating equation models for correlated data: A review with applications. American Journal of Political Science, 45, 470-4900.
