Skip to main content
Log in

On zero-inflated permutation testing and some related problems

  • Regular Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

The inferences on zero-inflated data are difficult to deal and the problem motivated a relevant part of the research since the earlier times of the statistical science. The case of multivariate zero-inflated data is still subject of active debates. In this contribution we primarily deal with a permutation-based test for comparisons of two groups with multivariate zero-inflated data. By the use of a leading example, we formulate different questions and translate them on different inferential hypotheses. A permutation-based solution is proposed for each of them and their interpretation is discussed. Finally, we extend the method to the general case of—possibly many—continuous predictors and the presence of covariates (nuisance). The data and the R code are implemented in the library flip on CRAN repository and on the web-appendinx of this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Aitchison J (1955) On the distribution of a positive random variable having a discrete probability mass at the origin. J Am Stat Assoc 50(271):901–908

    MathSciNet  MATH  Google Scholar 

  • Basso D, Pesarin F, Salmaso L, Solari A (2009) Permutation tests for stochastic ordering and ANOVA: theory and applications in R. Lecture notes no. 194. Springer, New York

  • Diallo AO, Diop A, Dupuy J-F (2016) Asymptotic properties of the maximum likelihood estimator in zero-inflated binomial regression. Commun Stat Theory Methods 46(20):9930–9948

    Article  MathSciNet  Google Scholar 

  • Dupuy J-F (2017) Inference in a generalized endpoint-inflated binomial regression model. Statistics 51(4):888–903

    Article  MathSciNet  Google Scholar 

  • Edgington E, Onghena P (2007) Randomization tests, 4th edn. Chapman & Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Faroughi P, Ismail N (2017) Bivariate zero-inflated negative binomial regression model with applications. J Stat Comput Simul 87:457–477

    Article  MathSciNet  Google Scholar 

  • Finos L (2014) flip: multivariate permutation tests. R package version 2.4.3

  • Gómez-Déniz E, Vázquez-Polo FJ, García-García V (2014) A discrete version of the half-normal distribution and its generalization with applications. Stat Pap 55:497–511

    Article  MathSciNet  Google Scholar 

  • Good P (2005) Permutation, parametric, and bootstrap tests of hypotheses, 3rd edn. Springer, New York

    MATH  Google Scholar 

  • Gschlößl S, Czado C (2006) Modelling count data with overdispersion and spatial effects. Stat Pap 49:531

    Article  MathSciNet  Google Scholar 

  • Hall DB (2000) Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics 56(4):1030–1039

    Article  MathSciNet  Google Scholar 

  • Hall DB, Berenhaut KS (2002) Score tests for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models. Can J Stat 30:415–430

    Article  MathSciNet  Google Scholar 

  • Karlis D, Ntzoufras I (2003) Analysis of sports data by using bivariate Poisson models. J R Stat Soc Ser D (Stat) 52:381–393

    Article  MathSciNet  Google Scholar 

  • Lambert D (1992) Zero-inflated Poisson regression, with an application to defeats in manufacturing. Technometrics 34:1–14

    Article  Google Scholar 

  • Li C-S, Lu J-C, Park J, Kim K, Brinkley PA, Peterson JP (1999) Multivariate zero-inflated Poisson models and their applications. Technometrics 41:29–38

    Article  Google Scholar 

  • Marcus R, Peritz E, Gabriel K (1976) On closed testing procedures with special reference to ordered analysis of variance. Biometrika 63:655–660

    Article  MathSciNet  Google Scholar 

  • Min Y, Agresti A (2002) Modeling nonnegative data with clumping at zero: a survey. J Iran Stat Soc 1(1–2):7–33

    MATH  Google Scholar 

  • Mullahy J (1986) Specification and testing of some modified count data models. J Econom 33(3):341–365

    Article  MathSciNet  Google Scholar 

  • Partha D, Trivedi PK (1997) Demand for medical care by the elderly: a finite mixture approach. J Appl Econom 12:313–336

    Article  Google Scholar 

  • Pesarin F (2001) Multivariate permutation test with application to biostatistics. Wiley, Chichester

    MATH  Google Scholar 

  • Pesarin F, Salmaso L (2010) Permutation tests for complex data: theory, applications and software. Wiley, Chichester

    Book  Google Scholar 

  • Ridout M, Hinde J, DemAtrio CGB (2001) A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. Biometrics 57:219–223

    Article  MathSciNet  Google Scholar 

  • Rodríguez-Avi J, Olmo-Jiménez MJ (2015) A regression model for overdispersed data without too many zeros. Stat Pap 58(3):749–773

    Article  MathSciNet  Google Scholar 

  • Roy S (1953) On a heuristic method of test construction and its use in multivariate analysis. Ann Math Stat 24:220–238

    Article  MathSciNet  Google Scholar 

  • Saei A, McGilchrist C (1997) Random threshold models applied to inflated zero class data. Aust J Stat 39:5–16

    Article  Google Scholar 

  • Sáez-Castillo AJ, Conde-Sánchez A (2017) Detecting over- and under-dispersion in zero inflated data with the hyper-Poisson regression model. Stat Pap 58:19–33

    Article  MathSciNet  Google Scholar 

  • Sen PK (2007) Union-intersection principle and constrained statistical inference. J Stat Plan Inference 137:3741–3752

    Article  MathSciNet  Google Scholar 

  • Shankar V, Milton J, Mannering F (1997) Modeling accident frequencies as zero-altered probability processes: an empirical inquiry. Accid Anal Prev 29(6):829–837

    Article  Google Scholar 

  • Tian G-L, Ma H, Zhou Y, Deng D (2015) Generalized endpoint-inflated binomial model. Comput Stat Data Anal 89:97–114

    Article  MathSciNet  Google Scholar 

  • Wang SC (1998) Analysis of zero-heavy data using a mixture model approach. PhD Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA

  • Westfall PH, Young SS (1993) Resampling-based multiple testing: examples and methods for P-value adjustment. Wiley, New York

    MATH  Google Scholar 

  • Young DS, Raim AM, Johnson NR (2017) Zero-inflated modelling for characterizing coverage errors of extracts from the us census bureau’s master address file. J R Stat Soc Ser A (Stat Soc) 180:73–97

    Article  MathSciNet  Google Scholar 

  • Zeileis A, Kleiber C, Jackman S (2008) Regression models for count data in R. J Stat Softw 27:1–25

    Google Scholar 

Download references

Acknowledgements

LF was supported by grant from the University of Padua (Project CPDA158444/15).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Livio Finos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Finos, L., Pesarin, F. On zero-inflated permutation testing and some related problems. Stat Papers 61, 2157–2174 (2020). https://doi.org/10.1007/s00362-018-1025-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-018-1025-x

Keywords

Navigation