Maximum likelihood function for fuzzy count data models (using heaped data as fuzzy)

Author:

Oketch Godrick1,Karaman Filiz1

Affiliation:

1. Department of Statistics, Yildiz Technical University, Davutpaşa Cad., Esenler-İstanbul, Turkey

Abstract

Count data models are based on definite counts of events as dependent variables. But there are practical situations in which these counts may fail to be specific and are seen as imprecise. In this paper, an assumption that heaped data points are fuzzy is used as a way of identifying counts that are not definite since heaping can result from imprecisely reported counts. Because it is practically unlikely to report all counts in an entire dataset as imprecise, this paper proposes a likelihood function that not only considers both precise and imprecisely reported counts but also incorporates α - cuts of fuzzy numbers with the aim of varying impreciseness of fuzzy reported counts. The proposed model is then illustrated through a smoking cessation study data that attempts to identify factors associated with the number of cigarettes smoked in a month. Through the real data illustration and a simulation study, it is shown that the proposed model performs better in predicting the outcome counts especially when the imprecision of the fuzzy points in a dataset are increased. The results also show that inclusion of α - cuts makes it possible to identify better models, a feature that was not previously possible.

Publisher

IOS Press

Subject

Artificial Intelligence,General Engineering,Statistics and Probability

Reference24 articles.

1. Bootstrap statistical inference about the regression coefficient based on fuzzy data;Akbari;International Journal of Fuzzy Systems,2012

2. Multidimensional least-squares fitting of fuzzy models;Celmins;Mathematical Modelling,1987

3. Measuring birth weight in developing countries: Does the method of reporting in retrospective surveys matter?;Channon;Maternal and Child Health Journal,2011

4. Zero-inflated models for regression analysis of count data: a study of growth and development;Cheung;Statistics in Medicine,2002

5. Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth-death processes;Crawford;Annals of Applied Statistics,2015

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