scholarly journals Methods to verify parameter equality in nonlinear regression models

2010 ◽  
Vol 67 (2) ◽  
pp. 218-222 ◽  
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.

scholarly journals Stata Tip 128: Marginal Effects in Log-transformed Models: A Trade Application

2017 ◽  
Vol 17 (3) ◽  
pp. 774-778 ◽  
Author(s):  
Luca J. Uberti
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Gravity Equation ◽  
Empirical Literature ◽  
Parameter Estimates ◽  
Nonlinear Regression Models ◽  
Marginal Effects

Since the introduction of the margins command in Stata 11, the empirical literature has increasingly used marginal effects, predictive margins, and adjusted predictions in postestimation analysis. Marginal effects are particularly useful for the interpretation of parameter estimates after logit, probit, poisson, and other nonlinear regression models. If the covariate of interest is in logs, however, obtaining meaningful results from margins, dydx() is not straightforward. In this article, I first illustrate these difficulties in the context of estimation with poisson. I then suggest that a researcher should always compute the derivative of interest and code it manually with margins‘s expression() option. Lastly, I illustrate these problems using the gravity equation from the trade literature.

Reparameterization of weakly nonlinear regression models with constraints

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Lubomír Kubáček ◽  
Gejza Wimmer
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Confidence Regions ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Parameter Estimators

AbstractThere are several ways how to redefine the Bates and Watts curvatures in models with constraints. One of possible approaches is based on a reparametrization of models. It enables us to construct linearization regions for the bias of parameter estimators, for the confidence regions, etc., in an easy way.

scholarly journals NONLINEAR MODELS FOR DESCRIPTION OF CACAO FRUIT GROWTH WITH ASSUMPTION VIOLATIONS

2017 ◽  
Vol 30 (1) ◽  
pp. 250-257 ◽  
Author(s):  
JOEL AUGUSTO MUNIZ ◽  
◽  
MICHERLANIA DA SILVA NASCIMENTO ◽  
TALES JESUS FERNANDES
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Nonlinear Models ◽  
Growth Curves ◽  
Residual Analysis ◽  
Fruit Growth ◽  
Model Fit ◽  
Maturation Stage ◽  
Nonlinear Regression Models ◽  
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.

scholarly journals Empirical Model With Excellent Statistical Properties for Describing Temperature-Dependent Developmental Rates of Insects and Mites

2017 ◽  
Vol 110 (3) ◽  
pp. 302-309 ◽  
Author(s):  
David A. Ratkowsky ◽  
Gadi V. P. Reddy
Keyword(s):  
Nonlinear Regression ◽  
Empirical Model ◽  
Minimum Variance ◽  
Statistical Properties ◽  
Parameter Estimates ◽  
Regression Equations ◽  
Temperature Dependent ◽  
Temperature Range ◽  
Least Squares Estimators ◽  
Development Rates

Abstract Previous empirical models for describing the temperature-dependent development rates for insects include the Briére, Lactin, Beta, and Ratkowsky models. Another nonlinear regression model, not previously considered in population entomology, is the Lobry–Rosso–Flandrois model, the shape of which is very close to that of the Ratkowsky model in the suboptimal temperature range, but which has the added advantage that all four of its parameters have biological meaning. A consequence of this is that initial parameter estimates, needed for solving the nonlinear regression equations, are very easy to obtain. In addition, the model has excellent statistical properties, with the estimators of the parameters being “close-to-linear,” which means that the least squares estimators are close to being unbiased, normally distributed, minimum variance estimators. The model describes the pooled development rates very well throughout the entire biokinetic temperature range and deserves to become the empirical model of general use in this area.

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