Title: The zero-inflated negative binomial multilevel model: demonstrated by a Brazilian dataset

Authors: Luiz Paulo Lopes Fávero

Addresses: School of Economics, Business and Accounting, University of São Paulo, Av. Prof. Luciano Gualberto, 908 – FEA 3, Cidade Universitária, 05508-900 São Paulo, Brazil

Abstract: To account for the preponderance of zero counts, a class of zero-inflated count data models without and with random effects is presented. Within a Brazilian traffic dataset, three techniques are compared, being two 'traditional' approaches (a zero-inflated Poisson model and a zero-inflated negative binomial model) and being the third a zero-inflated negative binomial multilevel model with random effects. The objective of this paper is to present and discuss a relatively new type of a regression estimation that takes into account a multilevel model (negative binomial) in nested data structure for count outcome variable with an excess of zeros. A Vuong test with AIC and BIC correction for zero-inflation is also presented. Model fit indicators and residual terms obtained from differences between observed and estimated count of traffic accidents per month in 1,062 municipal districts located in 234 cities in all 27 states of Brazilian Federation were used for comparisons.

Keywords: count data; Poisson; negative binomial; zero-inflated model; multilevel model.

DOI: 10.1504/IJMOR.2017.085381

International Journal of Mathematics in Operational Research, 2017 Vol.11 No.1, pp.90 - 106

Received: 05 Oct 2015
Accepted: 07 Nov 2015
Published online: 25 Jul 2017 *

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