Bell Marginal Models for Longitudinal Count Outcomes

Akdur H. T. K.

6th INTERNATIONAL E – CONFERENCE ON ADVANCES IN STATISTICS , Ankara, Turkey, 16 - 18 October 2020, pp.31

  • Publication Type: Conference Paper / Summary Text
  • City: Ankara
  • Country: Turkey
  • Page Numbers: pp.31
  • Gazi University Affiliated: Yes


Correlated count responses are usually observed in clinical, economical and biological researches. The main assumption is to assume that a dependency structure exists between observations in the same experimental unit or cluster while no dependency exists between observation from different experimental units. Longitudinal count models are generally modelled through the use of generalized estimating equations firstly introduced by Liang and Zeger (1986) [1] (GEEs). Popular count marginal models are usually based on poisson and negative binomial distribution. In this study, a new marginal model is introduced and develop for longitudinal count responses based on bell distribution [2]. Bell distribution and its related regression model have been recently proposed by Castellares et al. [2] for count dataset. Although the bell distribution does not contain a dispersion parameter, it can model overdispersion. It indicates that this is more practical and useful than the negative binomial distribution. Real data application is presented to illustrate the new marginal model. The working covariance model selection method the “quasi-likelihood under the independence model criterion” (QIC) is utilized for the application [3]. The parameter estimations of the bell marginal model based on GEEs are obtained by geeM R package [4]. Some diagnostic measures are also provided for the bell marginal model.

Key Words: Bell distribution; Generalized Estimating Equations; count outcomes; quasi-likelihood; correlation.


[1] Liang KY, Zeger, SL (1986). Longitudinal data analysis using generalized linear models.

Biometrika, 73:13–22.

[2] Castellares F, Ferrari SL, Lemonte AJ. (2018). On the Bell distribution and its associated regression model for count data. Applied Mathematical Modelling, 56, 172-185.

[3] Pan W (2001). Akaike’s information criterion in generalized estimating equations. Biometrics, 57:120–125.

[4] McDaniel LS, Henderson NC, Rathouz PJ (2013). Fast pure R implementation of GEE: application of the matrix package. The R journal, 5(1), 181.