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 (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）是线性模型的扩展形式，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，如桉树属（Eucalyptus）种子发芽试验——仍普遍采用方差分析，未开展其他模型的拟合效果评估。为此，本研究旨在针对大花序桉（Eucalyptus cloeziana）的种子计数数据，筛选广义线性模型框架下的最优适配模型。本研究数据来源于一项发芽试验，试验所用种子来自三批次大花序桉种子。每批次种子经筛分按粒径划分为三个组分：小粒径组（1.18 mm）。数据分析采用适配正态分布、泊松分布与负二项分布的广义线性模型开展，并通过赤池信息准则（Akaike Information Criterion）、施瓦茨贝叶斯信息准则（Bayesian Schwarz Criterion）、库克距离（Cook’s distance）以及半正态诊断图对各模型进行评估。与其他拟合方式相比，正态分布拟合在经图基检验（Tukey test）的均值配置上存在差异；尽管本研究数据满足所有正态性假设，但泊松分布拟合仍是适配大花序桉种子发芽试验计数数据的最优方案。