Instructors’ publication (IP) is one of a major activity in higher education institutes. Currently, IP faced problem both high prevalence and severity in Ethiopian public universities. Publication was affected approximately around 352 (73.9%) instructors have not done publication in Ethiopian public universities even if there is a problem in both developing and developed countries. Since, the outcomes from IP factors are mostly discrete variable; they are often modeled using advanced count regression models. It is therefore, the purpose of this study was to determine the appropriate count regression model that efficiently fit the IP data and further to identify the key risk factors contributing significantly to IP in public universities in Ethiopian. The data were collected between November 2015 through November 2016 from selected thirteen (13) public universities in Ethiopian through both questionnaires and interview. A cross sectional study design was employed using IP data. A simple random sampling technique was applied to the population of Ethiopian public universities to obtain a sample of 13 universities or 476 individual instructors were selected. The average age of the 476 participants were found to be 30 years with 31 (6.5%) being females and 445 (93.5%) being males. The count outcomes obtained were modeled using count regression models which included Poisson, Negative Binomial, Zero-Inflated Negative Binomial (ZINB), Zero-Inflated Poisson (ZIP) and Poisson Hurdle regression models. In order to compare the performance and the efficiency of the listed count regression models with respect to the IP data, the various model selection methods such as the Vuong Statistic (V) and Akaikes Information Criterion (AIC) were used. The ZINB count regression model with reference to the values of the Vuong Statistic and AIC were selected as the most appropriate and efficient count regression model for modeling IP data. Based on the ZINB model the variables age, experience, average work-load, association member and motivation to work were statistically significant risk factors contributing to IP in Ethiopian public universities.