A regression model for special proportions

A regression model for special proportions

Credit cards are a financial product with special characteristics. Dividing the amount paid by the customer in a given month by the total bill results in a variable that is partly discrete and partly continuous, which we call the relative payment amount (RPA). This variable is discrete at 0, c and 1...

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Bibliographic Details
Published in:Statistical modelling Vol. 13; no. 2; pp. 125 - 151
Main Authors: Pereira, Gustavo HA, Botter, Denise A, Sandoval, Mônica C
Format: Journal Article
Language:English
Published: New Delhi, India SAGE Publications 01-04-2013
Sage Publications Ltd
Subjects:
Credit cards
Customers
Delinquency
Mathematical models
Maximum likelihood method
Monte Carlo simulation
Population
Regression analysis
Statistical analysis
Studies
Variables
truncated inflated beta distribution
maximum likelihood estimator
credit card
proportions
beta distribution
inflated distributions
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Summary:Credit cards are a financial product with special characteristics. Dividing the amount paid by the customer in a given month by the total bill results in a variable that is partly discrete and partly continuous, which we call the relative payment amount (RPA). This variable is discrete at 0, c and 1, and it is continuous in the open interval (c, 1). The 0<c<1 value is known and is given by the ratio between the value of the minimum payment and the full amount, and this value is not fixed for all customers. Thus, in practice, the RPA is a variable whose support of its distribution is non-constant across population units. In this work, we propose a regression model for the RPA. The model allows all of the unknown parameters of the conditional distribution of the response variable to be modelled as a function of the explanatory variables, and it also accounts for the non-constant known parameter c. The estimation of the parameters of this model is discussed, diagnostic analysis is addressed and closed-form expressions for the score function and for the Fisher’s information matrix are provided. Moreover, some results related to the non-constant nature of c are obtained, simulation studies are performed and an application using real credit card data is presented.
ISSN:1471-082X
1477-0342
DOI:10.1177/1471082X13478274