Over‐dispersed count data in crop and agronomy research

Abstract

While 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.

Extreme variability modelling of overdispersed germination count experiments

“…Germination counts of Z. mays were determined not to have overdispersion (Pearson chi-square/df = 1.06). Overdispersion is accepted as 1.0 < Pearson chi-square/df < 1.0 dispersion status in most studies (Kosma et al, 2019;Michelon et al, 2019;Prazaru et al, 2021) as a general approach to determine over, dispersion or perfect fit to Poisson distribution. However, there is no official criterion for this.…”

“…In generalized linear mixed model, both diffusion measures and AIC and BIC measures act parallel to each other. However, Gbur et al (2012), Michelon et al (2019) and Kosma et al (2019) showed that although AIC and BIC criteria are effective in model selection, a decision should be made by examining Pearson chi-square/df since they cannot distinguish over or under dispersion in Poisson distribution. The results obtained from the culture plant B. vulgaris support this situation because the dispersion statistics for NB-GLIMMIX and GP-GLIMMIX were obtained as 0.97 and 1.05.…”

“…This assumption is difficult to achieve in practice. The variance of the count-based dependent variable increases depending on the widening of the count range (excess variability or heterogeneity), and the variance is found to be greater than the mean (Kosma et al, 2019;Gianinetti, 2020). By ignoring overdispersion and using any statistical analysis method, standard errors will result in smaller than expected, inflated test statistics (e.g., F value) and rather large Type I error.…”

Eucalyptus cloeziana seed count data: a comparative analysis of statistical models

“…Count data can be conceptualized as representing how often a specific event occurs, resulting in nonnegative integer values (Kosma et al, 2019). In the biological sciences, count data are produced in a variety of experiments, such as the analysis of fungal colonies (Pereira et al, 2016), counting of weed species in a given area (Heap;Duke, 2017), and counting of the number of leaves per seedling (Silva et al, 2019).…”

“…ANOVA requires that the following assumptions be met: homogeneity of variances, normally distributed residuals and independent distributions. However, the data produced by experiments involving count data in the biological sciences often do not meet such assumptions (St-Pierre;Shikon;Schneider, 2018;Kosma et al, 2019), as seen in studies of seeds of genetically impoverished species, which present a high variability rate, such as forest seeds Araújo, 2018). Sileshi (2012) showed that in 429 studies with seed viability data published from 2002 to 2012, 70% of researchers used ANOVA to analyse the data, and among those who did, only 20% performed tests to verify the homogeneity of variances and normality of residuals.…”