Inflated Kumaraswamy regressions with application to water supply and sanitation in Brazil. (18th April 2021)

• Record Type: Journal Article
• Authors: Bayer, Fábio M.; Cribari‐Neto, Francisco; Santos, Jéssica
• Is Part Of: Statistica Neerlandica. Volume 75:Number 4(2021)
• Page Start: 453
• Page End: 481
• Publication Date: 2021-04-18
• Subjects: double bounded data -- inflated distribution -- Kumaraswamy distribution -- likelihood inference -- regression model; Statistics -- Periodicals; 519.5; 314.92
• DOI: 10.1111/stan.12242
• Languages: English
• ISSNs: 0039-0402

Abstract

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.