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

Abstract

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

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

Dates
First available in Project Euclid: 8 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1410181227

Digital Object Identifier
doi:10.1214/14-EJS936

Mathematical Reviews number (MathSciNet)
MR3263133

Zentralblatt MATH identifier
1297.62171

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

Keywords
Estimating equations diagnostic techniques zero inflated data

Citation

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

References

  • [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/