&lt;b&gt;Applying regression models with skew-normal errors to the height of bedding plants of &lt;i&gt;Stevia rebaudiana&lt;/i&gt; (Bert) Bertoni

Guedes, Terezinha Aparecida; Rossi, Robson Marcelo; Martins, Ana Beatriz Tozzo; Janeiro, Vanderly; Carneiro, José Walter Pedroza

doi:10.4025/actascitechnol.v36i3.21191

Cited by 4 publications

(4 citation statements)

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“…When the residue does not follow the normal distribution, in general, researchers transform the data to lead to a normality, make inferences based on the distribution of errors (GUEDES et al, 2014) or use the theory of generalized linear models (KOKONENDJI; DEMÉTRIO;ZOCHI, 2007). Fernandes et al (2014) evaluated the coffee fruit growth, comparing the fit of Logistic and Gompertz models, both weighted, and found the best fit for the Gompertz model.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Models for Description of Cacao Fruit Growth With Assumption Violations

Muniz¹,

Nascimento²,

Fernandes³

2017

Rev. Caatinga

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-Cacao (Theobroma cacao L.) is an important fruit in the Brazilian economy, which is mainly cultivated in the southern State of Bahia. The optimal stage for harvesting is a major factor for fruit quality and the knowledge on its growth curves can help, especially in identifying the ideal maturation stage for harvesting. Nonlinear regression models have been widely used for description of growth curves. However, several studies in this subject do not consider the residual analysis, the existence of a possible dependence between longitudinal observations, or the sample variance heterogeneity, compromising the modeling quality. The objective of this work was to compare the fit of nonlinear regression models, considering residual analysis and assumption violations, in the description of the cacao (clone Sial-105) fruit growth. The data evaluated were extracted from Brito and Silva (1983), who conducted the experiment in the Cacao Research Center, Ilheus, State of Bahia. The variables fruit length, diameter and volume as a function of fruit age were studied. The use of weighting and incorporation of residual dependencies was efficient, since the modeling became more consistent, improving the model fit. Considering the first-order autoregressive structure, when needed, leads to significant reduction in the residual standard deviation, making the estimates more reliable. The Logistic model was the most efficient for the description of the cacao fruit growth.Keywords: Biological interpretation. Biometric measurement. Logistic model. Theobroma cacao L.. MODELOS NÃO LINEARES NA DESCRIÇÃO DO CRESCIMENTO DE FRUTOS DE CACAU COM VIOLAÇÕES DOS PRESSUPOSTOSRESUMO -O cacau é um importante produto para a economia brasileira, sendo cultivado principalmente no sul da Bahia. O ponto ótimo de colheita é um dos principais fatores de perda na qualidade do fruto e o conhecimento de suas curvas de crescimento pode auxiliar principalmente na identificação deste ponto. Os modelos de regressão não linear tem sido amplamente utilizados na descrição de curvas de crescimento. No entanto, em várias pesquisas nesse sentido não é realizada a análise de resíduos, não consideram a existência de uma possível dependência entre as observações longitudinais e nem a heterogeneidade de variâncias amostrais, comprometendo a qualidade da modelagem. Assim, este trabalho objetivou comparar o ajuste de modelos de regressão não lineares, considerando os possíveis desvios de pressuposição sobre os resíduos, na descrição do crescimento dos frutos de cacaueiro do clone Sial-105. Os dados analisados foram extraídos de Brito e Silva (1983) e correspondem a um experimento realizado no Centro de Pesquisa de Cacau, em Ilhéus-BA. As variáveis estudadas foram o comprimento, diâmetro e volume do fruto tomados em função da sua idade. O uso da ponderação e incorporação da dependência residual foi eficiente pois tornou a modelagem mais coerente melhorando a qualidade do ajuste. Considerar a estrutura auto-regressiva de primeira ordem, quando necessária, leva a redu...

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Section: Introductionmentioning

confidence: 99%

Nonlinear Models for Description of Cacao Fruit Growth With Assumption Violations

Muniz¹,

Nascimento²,

Fernandes³

2017

Rev. Caatinga

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“…Where u i = f 1 u i-1 +...+ f p u i-p + e i , with i = 1, 2, ..., n and n = 8, the number of times pequi fruits were measured; u i is the residual of adjustment at the i-th time; f 1 is the autoregressive parameter of order 1; u i-1 is the residual of time immediately before the i-th measure; f p is the autoregressive parameter of order p; u i-1 is the residual of adjustment in p times before the i-th measure; e i is the white residual with normal distribution N (0, a 2 ). When the residuals are independent, parameters f i will be null, and consequently u i = e i (MAZZINI et al, 2005;GUEDES et al, 2014).…”

Section: Methodsmentioning

confidence: 99%

“…In regression studies, it is usual to admit in the estimation process and inference under parameters that the errors are independent, which does not necessarily occur when working with time-ordered data that are potentially correlated (CASSIANO; SÁFADI, 2015). In this case, the model parameters estimates can be biased, with values below or above the actual value (GUEDES et al, 2014;MAZZINI et al, 2005;FERNANDES et al, 2014), and one should consider the autocorrelation structure present in data in the model adjustment (PRADO et al, 2013a;RIBEIRO et al, 2018), as it may affect the value of the standard error estimate.…”

Section: Introductionmentioning

confidence: 99%

Description of the growth of pequi fruits by nonlinear models

et al. 2018

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Descrição do crescimento de frutos de pequizeiro por modelos não linearesResumo -O pequizeiro é uma espécie nativa do cerrado brasileiro, com ampla distribuição geográfica, cujo fruto é bastante apreciado na culinária, compondo pratos tradicionais. Em geral, o fruto do pequi é consumido quando maduro, na forma in natura ou nos diversos, produtos derivados tais como óleos, licores, doces, sorvetes, entre outros, envolvendo importante atividade socioeconômica geradora de emprego e renda na agricultura familiar. Este trabalho teve por objetivo avaliar o ajuste dos modelos Brody, Gompertz, Logístico e Von Bertalanffy no crescimento e no desenvolvimento de frutos de pequi, com base em suas características físicas, como diâmetro longitudinal e transversal, e massa fresca obtidos ao longo do tempo. Os parâmetros foram estimados por meio de rotinas do software R, utilizando-se do método de mínimos quad rados e o processo iterativo de Gauss-Newton. O ajuste dos modelos foi comparado, utilizando os critérios: desvio-padrão residual, coeficiente de determinação ajustado e critério de informação de Akaike corrigido. Em geral, os dados não apresentaram estrutura de erros correlacionados, e o modelo Von Bertalanffy não se ajustou aos dados de massa fresca. Os modelos apresentaram boa qualidade no ajuste aos dados de crescimento de pequi, exceto o modelo Brody para a variável massa fresca. Os modelos Gompertz e Logístico foram os que melhor descreveram as variáveis, sendo o Gompertz o mais indicado para descrever os dados de diâmetro e de massa. Com base no ajuste, observou-se um crescimento inicial lento até cerca de 20 dias após a antese; após este período, o fruto desenvolveu-se de modo mais acelerado até 90 dias e, então, apresentou tendência à estabilidade até o final da avaliação, aos 117 dias após a antese, com caráter sigmoide da curva. O fruto de pequizeiro obteve valores finais, em média, de 7,1 cm de diâmetro transversal, 6,8 cm de diâmetro longitudinal e 113g de massa fresca. Termos de indexação: Modelos de crescimento, medidas biométricas, curvas sigmoides, ajuste de modelos, pequi.Abstract-Pequi tree is a species native to the Brazilian cerrado, with wide geographic distribution, whose fruit is very appreciated in cooking, composing traditional dishes. In general, pequi fruit is consumed when ripe in the fresh form or in the various derived products such as oils, liqueurs, sweets, ice creams among others, involving important socioeconomic activity generating employment and income in family agriculture. The aim of this study was to evaluate the adjustment of Brody, Gompertz, Logistic and Von Bertalanffy models in the growth and development of pequi fruits based on their physical characteristics such as longitudinal and cross-sectional diameter and fresh mass obtained over time. Parameters were estimated using R software routines, using the least squares method and the Gauss-Newton iterative process. The adjustment of models was compared using the following criteria: residual standard deviation, adjusted determinati...

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“…The statistical properties and the application of skew-normal (SN) distribution are described in Azzalini and Dalla Valle (1996) and Azzalini and Capitanio (1999), respectively. Aparecida Guedes et al (2014) presents an example of applying a regression model with SN errors. Here, we present a brief introduction.…”

Section: Appendix A: Skew-normal Distributionmentioning

confidence: 99%

SMARTp: A SMART design for nonsurgical treatments of chronic periodontitis with spatially referenced and nonrandomly missing skewed outcomes

et al. 2019

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This paper proposes dynamic treatment regimes (DTRs) as effective individualized treatment strategies for managing chronic periodontitis. The proposed DTRs are studied via SMARTp—a two‐stage sequential multiple assignment randomized trial (SMART) design. For this design, we propose a statistical analysis plan and a novel cluster‐level sample size calculation method that factors in typical features of periodontal responses such as non‐Gaussianity, spatial clustering, and nonrandom missingness. Here, each patient is viewed as a cluster, and a tooth within a patient's mouth is viewed as an individual unit inside the cluster, with the tooth‐level covariance structure described by a conditionally autoregressive structure. To accommodate possible skewness and tail behavior, the tooth‐level clinical attachment level (CAL) response is assumed to be skew‐t, with the nonrandomly missing structure captured via a shared parameter model corresponding to the missingness indicator. The proposed method considers mean comparison for the regimes with or without sharing an initial treatment, where the expected values and corresponding variances or covariance for the sample means of a pair of DTRs are derived by the inverse probability weighting and method of moments. Simulation studies are conducted to investigate the finite‐sample performance of the proposed sample size formulas under a variety of outcome‐generating scenarios. An R package SMARTp implementing our sample size formula is available at the Comprehensive R Archive Network for free download.

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<b>Applying regression models with skew-normal errors to the height of bedding plants of <i>Stevia rebaudiana</i> (Bert) Bertoni

Cited by 4 publications

References 12 publications

Nonlinear Models for Description of Cacao Fruit Growth With Assumption Violations

Nonlinear Models for Description of Cacao Fruit Growth With Assumption Violations

Description of the growth of pequi fruits by nonlinear models

SMARTp: A SMART design for nonsurgical treatments of chronic periodontitis with spatially referenced and nonrandomly missing skewed outcomes

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