Dispersion insensitive truncated models for inflated count data with upper bound

Abstract

Zero-inflated regression models are generally accepted for modeling data with inflated amounts of zeros. The principle used in constructing the distribution for these models has been extended to modeling certain types of data with inflation at the upper bound of the support. An excellent example of this is the zero and κ-inflated truncated Poisson regression model which utilizes the Poisson distribution. However, the equi-dispersion nature of the Poisson distribution makes the model less suitable for data that are under-dispersed and over-dispersed. Models based on exponentiated exponential geometric distribution (EEGD) are presented as alternatives for modeling any count data with an upper bound, irrespective of the nature of dispersion. The models are obtained by truncating the EEGD at the top and inflating at either or both zero and κ. A simulation study is conducted to examine the performances of the models under certain conditions. The result shows that the closer the dispersion parameter c is from the equi-dispersion line, the better the estimates for over-dispersed data, while the farther the dispersion parameter from the equi-dispersed line, the better the estimates for an under-dispersed model. The application of the models is illustrated using data from the Behavioral Risk Factor Surveillance System 2011.