IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1989-d618181.html
   My bibliography  Save this article

Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model

Author

Listed:
  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Hector W. Gomez

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

Abstract

Rate or proportion data are modeled by using a regression model. The considered regression model can be used for studying phenomena with a response on the (0, 1), [0, 1), (0, 1], or [0, 1] intervals. To connect the response variable with the linear predictor in the regression model, we use a logit link function, which guarantees that the obtained prediction ranges between zero and one in the cases inflated at zero or one (or both). The model is complemented with the assumption that the errors follow a power-skew-normal distribution, resulting in a very flexible model, and with a non-singular information matrix, constituting an advantage over other existing models in the literature. To explain the probability of point mass at the values zero and/or one (inflated part), we used a polytomic logistic model with covariates. The results of two illustrations showed that the proposed model is a better alternative compared to widely known models in the literature.

Suggested Citation

  • Guillermo Martínez-Flórez & Hector W. Gomez & Roger Tovar-Falón, 2021. "Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1989-:d:618181
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1989/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1989/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    3. Ramesh Gupta & Rameshwar Gupta, 2004. "Generalized skew normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 501-524, December.
    4. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    5. Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    6. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    7. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    8. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    9. Josmar Mazucheli & André Felipe Berdusco Menezes & Sanku Dey, 2018. "Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(15), pages 3767-3778, August.
    10. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    11. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.
    2. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    3. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    4. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    5. Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, vol. 2(3), pages 1-22, September.
    6. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    7. Guillermo Martínez-Flórez & Rafael B. Azevedo-Farias & Roger Tovar-Falón, 2022. "New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    8. Silvia Noirjean & Mario Biggeri & Laura Forastiere & Fabrizia Mealli & Maria Nannini, 2023. "Estimating causal effects of community health financing via principal stratification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1317-1350, October.
    9. Ehsan Bahrami Samani & Elham Tabrizi, 2023. "Joint Linear Modeling of Mixed Data and Its Application to Email Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 175-209, May.
    10. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    11. Murilo Wohlgemuth & Carlos Ernani Fries & Ângelo Márcio Oliveira Sant’Anna & Ricardo Giglio & Diego Castro Fettermann, 2020. "Assessment of the technical efficiency of Brazilian logistic operators using data envelopment analysis and one inflated beta regression," Annals of Operations Research, Springer, vol. 286(1), pages 703-717, March.
    12. Roger Tovar-Falón & Guillermo Martínez-Flórez & Heleno Bolfarine, 2022. "Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    13. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    14. Yury R. Benites & Vicente G. Cancho & Edwin M. M. Ortega & Roberto Vila & Gauss M. Cordeiro, 2022. "A New Regression Model on the Unit Interval: Properties, Estimation, and Application," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    15. Xiong, Qizhou, 2015. "Censored Fractional Response Model: Estimating Heterogeneous Relative Risk Aversion of European Households," IWH Discussion Papers 11/2015, Halle Institute for Economic Research (IWH).
    16. Hildete P. Pinheiro & Rafael P. Maia & Eufrásio A. Lima Neto & Mariana Rodrigues-Motta, 2019. "Zero-one augmented beta and zero-inflated discrete models with heterogeneous dispersion for the analysis of student academic performance," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 749-767, December.
    17. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    18. Raffaele Brancati & Emanuela Marrocu & Manuel Romagnoli & Stefano Usai, 2018. "Innovation activities and learning processes in the crisis: evidence from Italian export in manufacturing and services," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 27(1), pages 107-130.
    19. Guillermo Martínez-Flórez & Roger Tovar-Falón & Víctor Leiva & Cecilia Castro, 2024. "Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    20. Fábio M. Bayer & Francisco Cribari‐Neto & Jéssica Santos, 2021. "Inflated Kumaraswamy regressions with application to water supply and sanitation in Brazil," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 453-481, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1989-:d:618181. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.