NONLINEAR MODELS FOR DESCRIPTION OF CACAO FRUIT GROWTH WITH ASSUMPTION VIOLATIONS

ABSTRACT 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.

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Methods to verify parameter equality in nonlinear regression models

Scientia Agricola ◽

10.1590/s0103-90162010000200014 ◽

2010 ◽

Vol 67 (2) ◽

pp. 218-222 ◽

Cited By ~ 3

Author(s):

Lídia Raquel de Carvalho ◽

Sheila Zambello de Pinho ◽

Martha Maria Mischan

Keyword(s):

Nonlinear Regression ◽

Regression Models ◽

Growth Curves ◽

Original Data ◽

Minimum Variance ◽

Ratio Method ◽

Parameter Estimates ◽

Nonlinear Regression Models ◽

Sample Data ◽

Parameter Estimators

In biologic experiments, in which growth curves are adjusted to sample data, treatments applied to the experimental material can affect the parameter estimates. In these cases the interest is to compare the growth functions, in order to distinguish treatments. Three methods that verify the equality of parameters in nonlinear regression models were compared: (i) developed by Carvalho in 1996, performing ANOVA on estimates of parameters of individual fits; (ii) suggested by Regazzi in 2003, using the likelihood ratio method; and (iii) constructing a pooled variance from individual variances. The parametric tests, F and Tukey, were employed when the parameter estimators were near to present the properties of linear model estimators, that is, unbiasedness, normal distribution and minimum variance. The first and second methods presented similar results, but the third method is simpler in calculations and uses all information contained in the original data.

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Optimality criteria for design in nonlinear models with constraints

Tatra Mountains Mathematical Publications ◽

10.2478/v10127-012-0014-z ◽

2012 ◽

Vol 51 (1) ◽

pp. 141-149

Author(s):

Andrej Pázman

Keyword(s):

Nonlinear Regression ◽

Regression Models ◽

Nonlinear Models ◽

Equivalence Theorem ◽

Optimality Criteria ◽

Nonlinear Regression Models

ABSTRACT We shall present different expressions for optimality criteria in nonlinear regression models, and compare them with corresponding expressions in models without constraints. We also present how to formulate the equivalence theorem in models with constraints.

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Gender on the growth of Criollo foals from birth to three years of age

Ciência Rural ◽

10.1590/0103-8478cr20150989 ◽

2017 ◽

Vol 47 (1) ◽

Author(s):

Anelise Maria Hammes Pimentel ◽

Walvonvitis Baes Rodrigues ◽

Charles Ferreira Martins ◽

Nathanael Ramos Montanez ◽

Arione Augusti Boligon ◽

...

Keyword(s):

Regression Models ◽

Nonlinear Models ◽

Body Height ◽

Growth Curves ◽

Experimental Period ◽

Future Research ◽

First Year ◽

Nonlinear Regression Models ◽

Rate Of Increase ◽

First Year Of Life

ABSTRACT: The objective of the present study was to evaluate the effect of gender on the growth of Criollo foals, in order to use this information as a reference for breeding as well as in future research. Body height, thoracic perimeter, and cannon bone perimeter of 75 foals were measured from two farms in Rio Grande do Sul, Brazil (Lat. 32°, 33′, 58″, Long. 53°, 22′, 33″) and from three generations over three years. In both farms, animals were kept under the same range and feeding conditions. Nonlinear regression models were applied to describe the growth curves for the three traits over the experimental period. Cannon bone perimeter was greater in males than in females (P<0.001) but the predicted curves for body height and thoracic perimeter did not differ between genders. For all traits, the highest rate of increase was achieved in the first year of life (body height = 74%, thoracic perimeter = 76%, and cannon bone perimeter = 63% for males and 83% for females). Results of this study indicated that changes in body height and thoracic perimeter can be predicted using nonlinear models in both male and female foals, until they reach three years of age; whereas, changes in cannon bone perimeter should be modeled separately for each gender.

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NONLINEAR MODELS BASED ON QUANTILES IN THE FITTING OF GROWTH CURVES OF PEPPER GENOTYPES

REVISTA BRASILEIRA DE BIOMETRIA ◽

10.28951/rbb.v39i3.505 ◽

2021 ◽

Vol 39 (3) ◽

Author(s):

Ana Carolina Ribeiro de OLIVEIRA ◽

Paulo Roberto CECON ◽

Guilherme Alves PUIATTI ◽

Maria Eduarda da Silva GUIMARÃES ◽

Cosme Damião CRUZ ◽

...

Keyword(s):

Regression Models ◽

Nonlinear Models ◽

Growth Curves ◽

Information Criterion ◽

Ordinary Least Squares ◽

Von Bertalanffy ◽

Absolute Deviation ◽

Nonlinear Regression Models ◽

Curvature Measurements ◽

Best Fit

This study aimed to fit nonlinear regression models to model the growth of the characters fruit length (FL) and fruit width (FW) of pepper genotypes (Capsicum annuum L.) over time using the method of ordinary least squares (OLS); and identify the model with the best fit and compare it to the model obtained via nonlinear quantile regression (QR) in the 0.25, 0.5, and 0.75 quantiles. Three regression models (Logistic, Gompertz, and von Bertalanffy) and four fit quality evaluators were adopted: Akaike information criterion, residual mean absolute deviation, and parametric and intrinsic curvature measurements. Five commercial genotypes of pepper were evaluated. Characters FL and FW were evaluated weekly from seven days after flowering, totaling ten measurements. In the estimation by OLS, the Logistic and von Bertalanffy models were considered adequate according to the quality evaluators. In the comparison between the models above by OLS and QR, the superiority of models obtained by QR was verified for the character FL. For the character FW, QR was efficient in three out of the five genotypes, being a valuable alternative in the study of fruit growth.

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