Methods to verify parameter equality in nonlinear regression models

Abstract

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.

Seasonal changes in soil physical properties under long-term no-tillage

“…Statistical comparisons between van Genuchten parameters from different samplings was carried out using procedures described in Carvalho et al (2010), with the likelihood ratio test (p < 0.05). This method tested the following hypotheses: (a) the van Genuchten parameters are equal in successive samplings; and (b) one or more van Genuchten parameters are different in successive samplings.…”

Modelling of lysine requirement in broiler breeder hens based on daily nitrogen retention and efficiency of dietary lysine utilization

“…Based on these hypotheses, the following models were adjusted: = unrestricted model, where the two parameters (NMR or NR max T and b) were adjusted for each period; 1 = restricted model, where the NMR or NR max T parameter is common for both periods; 2 = restricted model, where the b parameter is common for both periods; 3 = restricted model, with all parameters common for both periods. The likelihood ratio test was used to test these hypotheses according to statistical procedures proposed by Regazzi (2003) and Carvalho et al (2010).…”