Over‐dispersed count data in crop and agronomy research

Abstract

AbstractWhile evaluating plant response to biotic or abiotic stress and genotype–environment interactions and searching causes of yield gap, very often are observed data with non‐normal distributions. One of the commonly encountered types of variables with a non‐normal distribution is count data. Count data are defined as the type of observations which have a positive, non‐zero, integer value. The selection of appropriate probability distributions and model types is very important due to the risk of estimating the variance incorrectly—the phenomenon of over‐dispersion. Increasingly, biologists and agronomists have been using methods based on generalized linear models. However, sometimes, when including count data, they are not aware of or disregard their over‐dispersion. One of the solutions for over‐dispersed count data is to use probability distributions and model types which assume a more flexible mean and variance relationship. Thus, the aim of this study is to present various ways of assessing over‐dispersion. Additionally, we present alternative distributions and discuss other approaches to solve the problem of over‐dispersion in count data sets. As examples in this study are used real data sets from different agricultural experiments. In our study, in one out of the two data sets used, this phenomenon occurred. Thus, in the analysis of count data, instead of using default distribution (usually Poisson distribution), other distributions should be considered because of the possible occurrence of over‐dispersion. We also observed that there is not one universal distribution to use and each data set might need a separate assessment to choose its distribution. For an efficient and proper count data analysis, with potential over‐dispersion, it is important to explore several options, i.e. evaluate models with an alternative to Poisson probability distributions and then make an informed choice.