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Inflated Kumaraswamy regressions with application to water supply and sanitation in Brazil

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  • Fábio M. Bayer
  • Francisco Cribari‐Neto
  • Jéssica Santos

Abstract

Models based on the Kumaraswamy law are used with variables that assume values in (0, 1). In some cases, however, the data contain zeros and/or ones, that is, there is data inflation. We introduce a class of regression models that can be used with such inflated data, namely: the class of inflated Kumaraswamy regression models. We consider inflation at zero, at one, and at both zero and one. We introduce the model and provide closed‐form expressions for its score vector and Fisher's information matrix. The proposed model is used to evaluate the impacts of different conditioning variables on the proportion of people who live in households with inadequate water supply and sewage in Brazilian municipalities. Our results reveal that policies directed to increasing the population share with college education in places where it is low are particularly effective in reducing the prevalence of people who live under inadequate sanitation conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:4:p:453-481
    DOI: 10.1111/stan.12242
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    References listed on IDEAS

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    1. Guilherme Pumi & Cristine Rauber & Fábio M. Bayer, 2020. "Kumaraswamy regression model with Aranda-Ordaz link function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1051-1071, December.
    2. Anjali Adukia, 2017. "Sanitation and Education," American Economic Journal: Applied Economics, American Economic Association, vol. 9(2), pages 23-59, April.
    3. 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.
    4. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    5. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    6. Morgan, B.J.T. & Palmer, K.J. & Ridout, M.S., 2007. "Negative Score Test Statistic," The American Statistician, American Statistical Association, vol. 61, pages 285-288, November.
    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.
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    Cited by:

    1. Jorge Figueroa-Zúñiga & Juan G. Toledo & Bernardo Lagos-Alvarez & Víctor Leiva & Jean P. Navarrete, 2023. "Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

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