Electronic Journal of Statistics

Estimating equations and diagnostic techniques applied to zero-inflated models for panel data

Maria Kelly Venezuela and Rinaldo Artes

Full-text: Open access


Many practical studies analyze semi-continuous longitudinal data using, for example, ZAIG (Zero-Adjusted Inverse Gaussian) or BEZI (Beta Zero-Inflated) models as marginal distributions. We develop herein estimating equations analogous to Liang and Zeger’s estimating equation of independence and related diagnostic techniques for regression models, with zero-inflated response variable and panel data structure. A simulation study to evaluate some properties of the estimators obtained from the estimating equations and two applications with real data are presented.

Article information

Electron. J. Statist., Volume 8, Number 1 (2014), 1641-1660.

First available in Project Euclid: 8 September 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J20: Diagnostics
Secondary: 62J12: Generalized linear models 62H12: Estimation

Estimating equations diagnostic techniques zero inflated data


Venezuela, Maria Kelly; Artes, Rinaldo. Estimating equations and diagnostic techniques applied to zero-inflated models for panel data. Electron. J. Statist. 8 (2014), no. 1, 1641--1660. doi:10.1214/14-EJS936. https://projecteuclid.org/euclid.ejs/1410181227

Export citation


  • [1] Couturier, D.-L. and Victoria-Feser, M.-P. (2010). Zero-inflated truncated generalized Pareto distribution for the analysis of radio audience data. Annals of Applied Statistics 4(4) 1824–1846.
  • [2] Dobbie, M. J. and Welsh, A. H. (2001). Modelling correlated zero-inflated count data. Australian and New Zealand Journal of Statistics 43 431–444.
  • [3] Gan, N. (2000). General zero-inflated models and their applications. Thesis (Ph.D.), North Carolina State University. 132 pp.
  • [4] Hall, D. B. and Zhang, Z. (2004). Marginal models for zero inflated clustered data. Statistical Modelling 4 161–180.
  • [5] Heller, G., Stasinopoulos, M. and Rigby, B. (2006). The zero-adjusted inverse gaussian distribution as a model for insurance claims. Proceedings of the 21th International Workshop on Statistical Modelling, Ireland-Galway. http://studweb.north.londonmet.ac.uk/~stasinom/papers/ZAIG.pdf.
  • [6] Hofert, M., Kojadinovic, I., Maechler, M. and Yan, J. (2014). Copula: Multivariate Dependence with Copulas. R package version 0.999-10. http://CRAN.R-project.org/package=copula.
  • [7] Jong, P. and Heller, G. Z. (2008). Generalized Linear Models for Insurance Data. Cambridge University Press.
  • [8] Jørgensen, B. (1997). The Theory of Dispersion Models. Chapman & Hall, London.
  • [9] Jørgensen, B. and Labouriau, R. S. (1994). Exponential Families and Theoretical Inference. Lecture Notes, Department of Statistical, University of British Columbia.
  • [10] Liang, K.-Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73 13–22.
  • [11] Martinez, R. O. (2008). Modelos de regressão beta inflacionados. Thesis (Ph.D.). IME-USP, São Paulo.
  • [12] Mills, E. D. (2013). Adjusting for covariates in zero-inflated gamma and zero-inflated log-normal models for semicontinuous data. Thesis (Ph.D.), Graduate College of The University of Iowa. 280 pp. http://ir.uiowa.edu/etd/2583/. Acessed in 2014/07/29.
  • [13] Min, Y. and Agresti, A. (2005). Random effect models for repeated measures of zero-inflated count data. Statistical Modelling 5 1–19.
  • [14] Ospina, R. and Ferrari, S. L. P. (2010). Inflated beta distribution. Stat Papers 51 111–126.
  • [15] Pregibon, D. (1981). Logistic regression diagnostics. Annals of Statistics 9 705–724.
  • [16] R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/.
  • [17] Ridout, M. S., Demétrio, C. G. B. and Hinde, J. P. (1998). Models for count data with many zeros. Proceedings of the XIXth International Biometrics Conference. Cape Town.
  • [18] Song, X.-K. (2007). Correlated Data Analysis: Modeling, Analytics, and Applications. Springer, New York.
  • [19] Stasinopoulos, M., Rigby, B. and Akantziliotou, C. (2008). Instructions on How to Use the Gamlss Package in R. 2nd edition. http://studweb.north.londonmet.ac.uk/~stasinom/papers/gamlss-manual.pdf.
  • [20] Venezuela, M. K., Botter, D. A. and Sandoval, M. C. (2007). Diagnostic techniques in generalized estimating equations. Journal of Statistical Computation and Simulation 77 879–888.
  • [21] Yan, J. (2007). Enjoy the Joy of Copulas: With a Package Copula. Journal of Statistical Software 21(4) 1–21. http://www.jstatsoft.org/v21/i04/