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

ABSTRACT Generalized linear models (GLMs) are an extension of the linear model and include the normal, Poisson, and negative binomial distributions. Although GLMs were introduced in 1972, most seed technology studies, especially those involving count data, such as germination tests of seeds from the genus Eucalyptus, still using the analysis of variance, without analysis of the fit of other models. Thus, this study aimed to evaluate the most appropriate model in the GLM class for seed count data of Eucalyptus cloeziana. Data were obtained from a germination test using seeds from three lots of E. cloeziana. Each lot was separated by sieving into three material fractions based on size: small (<0.84 mm), medium (from 1.18 to 1.00 mm), and large (>1.18 mm). The data analysis was based on the use of GLMs adjusted to normal, Poisson, and negative binomial distributions, and the models were evaluated by the Akaike and Bayesian Schwartz criteria and Cook’s distance and half-normal diagnostic graphs. Compared to other adjustments, the normal distribution adjustment differed in the configuration of means submitted to the Tukey test, and although the data met all normality assumptions, the adjustment with the Poisson distribution was the most suitable for the count data from a germination test of E. cloeziana seeds.

摘要 广义线性模型（Generalized Linear Models, GLMs）是线性模型的扩展，涵盖正态分布、泊松分布与负二项分布。尽管广义线性模型于1972年被提出，但多数种子技术相关研究，尤其是涉及计数数据的研究——如桉属（Eucalyptus）种子发芽试验——仍采用方差分析，并未开展其他模型的拟合效果分析。为此，本研究旨在针对尾叶桉（Eucalyptus cloeziana）的种子计数数据，在广义线性模型类别中筛选最适配的模型。本研究数据取自3个批次尾叶桉种子的发芽试验。每个批次通过筛分按粒径划分为3个材料组分：小粒径（<0.84 mm）、中粒径（1.18~1.00 mm）与大粒径（>1.18 mm）。数据分析采用拟合了正态、泊松与负二项分布的广义线性模型，并通过赤池信息准则、贝叶斯施瓦茨准则、库克距离（Cook’s distance）以及半正态诊断图对各模型进行评估。相较于其他拟合方案，正态分布拟合在经Tukey检验的均值配置上存在差异；尽管数据满足全部正态性假设，但泊松分布拟合最适配尾叶桉种子发芽试验的计数数据。