Análise de experimentos de germinação usando os modelos lineares generalizados

• Autor(a) principal: Carvalho, Fábio Janoni
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/12237; http://doi.org/10.14393/ufu.di.2016.13
• topic: Copaíba; Critério de informação de Akaike (AIC); Critério de informação Bayesiano (BIC); Espécie florestal; Pressuposições da ANOVA; MLG; Binomial; Q-q plots; Validação; Sementes - Germinação; Modelos lineares (Estatística); Akaike s information criterion (AIC); Bayesian s information criterion (BIC); Forest species; ANOVA assumptions; GLM; Validation; CNPQ::CIENCIAS AGRARIAS::AGRONOMIA

CHAPTER II: Analysis of variance (ANOVA) is one of the most important statistical models applied in agronomic experiments, especially in the seeds area. Based on strong assumptions, it lasted for many years with the support of techniques such as data transformation. As ANOVA being a special case of Generalized Linear Models (GLM), a classic experiment of seeds germination of tree species Copaifera langsdorffii Desf. can show the mirroring between both methods of analysis, and this is one of the goals of this research. It also aimed to compare the quality of the adjustment and the efficiency of the models for the germination, expressed in percentage with Normal distribution and number of germinated seeds with Binomial distribution. To meet these objectives, seeds of C. langsdorffii were arranged in a completely randomized design with four replications of 25 seeds in a 4 x 3 factorial scheme, in which the first factor refers to the methods to overcome dormancy (M1, M2, M3 and M4) and the second effect is related to samples (A1, A2 and A3). For the results expressed in percentage of germination, the assumptions of normality and independence of residuals and homoscedasticity were tested by Shapiro-Wilk, Durbin-Watson and Levene, respectively. Then, it was applied an ANOVA model, as well as GLM with Normal distribution and identity link function. About the data expressed as number of germinated seeds, GLM was performed with Binomial distribution and logistics link function. For both distributions, the quality of the adjustment was determined by Akaike information criterion (AIC) and Bayesian information criterion (BIC), Cook s distance and q-q plot analysis. As expected, ANOVA model was equal to GLM with Normal distribution for the percentage of copaiba seed germination, and they indicated a significant effect of sample and interaction, as a previous analysis confirmed that all assumptions of the model were held. The GLM with Binomial distribution had the same significance of the effects as the Normal GLM. However, AIC and BIC indicated that Binomial model was better adjusted to data, and the accommodation of values to the simulated envelope with 95% confidence was greater. Cook s distance did not discriminate the models, since they approached to the same amount of influential points. CHAPTER III: Seed germination experiments are constantly analyzed using ANOVA, but it is also faced the problem of not holding the assumptions; when these ones are violated, the reliability of all parametric tests is compromised. To solve this problem, some authors suggest angular transformation of the data, as in many other cases the use of this technique with no care. Another suggested alternative, with less impact to the data, is the application of statistics methodologies that do not need to answer these assumptions. Among the existing methodologies, Generalized Linear Models (GLM) stands out. Despite the common representation of the number of germinated seeds in percentage, the original nature of data is discrete and follows all the criteria of Binomial distribution. Thus, GLM emerge as an alternative to solve ANOVA restrictions and to bring different statistical techniques, allowing a better data processing. GLM are poorly known in agronomy, and there are not works to the seed analysis that investigate the applicability and the adjustment of this technique, comparing to ANOVA and data transformation. In this way, the objective of this study was to compare the GLM methodology with ANOVA by checking the impact caused by them within seed germination variable. It was also aimed to apply the data transformation and compares it to GLM, checking which the best one for the studied data is. Statistical analysis focused on the characteristic of normal seedlings obtained from the process of validation of methods for germination test of 50 forest species seeds. ANOVA is a part of GLM, and its incorporation was made assuming the Normal distribution of random component and the identity link function. The number of normal seedlings followed a Binomial distribution, corresponding to the event of success with a logistic link function for this GLM. Only 41% of species that hold the assumptions and 22% of those which did not had the same interpretation about the effects of the factors, which proves that the analysis change within GLM was radical even for species that attended the assumptions. Registrations of AIC can conclude that the Binomial model with logit function was more harmonious for the data set and have fewer parameters to explain the variation, which made it a more parsimonious model. Normal plots graphics allude to a better linearity of the residuals from Binomial distribution data. The angular transformation was able to correct the problems in a completely meeting the assumptions in only ten species, in relation to the 23 that were studied. It proves that the application of GLM with an immediately Binomial distribution was essential for 13 of them.