Analysis of Over-Dispersed Count Data: Application to Obligate Parasite Pasteuria penetrans IOANNIS VAGELAS Department of Agriculture Crop Production and Rural Environment, University of Thessaly, Volos, GREECE Abstract: - In this article we present with STATA regression models suitable for analyzing over-dispersed count outcomes. Specifically, the Negative Binomial regression can be an appropriate choice for modeling count variables, usually for over-dispersed count outcome variables. The common problem with count data with zeroes is that the empirical data often show more zeroes than would be expected under either Poisson or the Negative Binomial model. We concluded, this publications showcases that Zero-inflated models can be used to model count data that has excessive zero counts. Keywords: - Biological control; P. penetrans; over-dispersion; Excess zero-count data; Zero Inflation. Received: April 25, 2021. Revised: January 5, 2022. Accepted: January 23, 2022. Published: March 1, 2022. 1 Introduction Plant-parasitic nematodes such as the Meloidogyne species are recognized as major agricultural pathogens worldwide. Meloidogyne javanica is one of the most damaging crop parasites often causing heavy losses. Nowadays, the most reliable practices to control the pathogen are preventive e.g. crop rotation including the choice of plant varieties or the use of biological control agents such as the obligate hyperparasitic bacterium Pasteuria penetrans [1]. The literature review shows that the most widely studied bacterial pathogen of Meloidogyne species (root-knot nematodes) is in the genus Pasteuria. Pasteuria penetrans is a mycelial, endospore- forming, bacterial parasite that has shown remarkable potential as a biological control agent of second-stage juvenile (J2) of root-knot nematodes. The biological control potential of Pasteuria spp. has been demonstrated on many crops and has been reported to develop endospores only in females of Meloidogyne spp. [1]. Based on previous research [2], attachment count data were observed to be over- dispersed concerning high numbers of spores attaching on each J2 at 6 and 9 h after spore application. It was concluded that the negative binomial distribution was found to be the most acceptable model to fit the observed data sets considering that P. penetrans spores are clumped. This issue of over-dispersion with zeros exists in a dataset [2] we recently analyzed. Based on this class of distributions, we tested two approaches to adjust the over-dispersed count data with zeros [3-5]. The first approach was to scale the variance of the Poisson distribution by submitting a dispersion parameter and multiplying it by the variance. The second approach was to test another probability distribution to handle the count data dispersion, such as the Negative binomial the Zero-inflated Poisson (ZIP) or the Zero-inflated negative binomial (Zinb) model. Overall, in this paper, we employed and compare these different models with a particular focus, on the over-dispersed count data with zeros. Moreover, this paper attempts to encourage researchers dealing with biological data not to ignore the over-dispersion which statistically influence the conclusions by underestimating the variability of the data. 2 Materials and Methods 2.1 Meloidogyne spp. Culture A culture of M. javanica was maintained on tomato plants (cherry tomato variety Tiny Tim) in the glasshouse. Eggs were collected by dissolving the gelatinous matrix into a solution of 0.5% sodium hypochlorite (NaOCl) (10% commercial bleach), passing the solution through a 200-mesh (75 µm) sieve, nested over a 500-mesh (26 µm) sieve and rinsing the eggs under slow running tap water to remove residual NaOCl [6]. Second stage juveniles (J2) were then hatched using standard laboratory practices [7]. WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT DOI: 10.37394/232015.2022.18.33 Ioannis Vagelas E-ISSN: 2224-3496 333 Volume 18, 2022