scholarly journals Analysis of Nonlinear Regression Models: A Cautionary Note

Dose-Response ◽  
2005 ◽  
Vol 3 (3) ◽  
pp. dose-response.0 ◽  
Author(s):  
Shyamal D. Peddada ◽  
Joseph K. Haseman
Keyword(s):  
Confidence Intervals ◽  
Regression Models ◽  
Nonlinear Models ◽  
Nonlinear Function ◽  
Standard Errors ◽  
True Parameter ◽  
Nonlinear Regression Models ◽  
Confidence Levels ◽  
Regression Parameters ◽  
Large Sample Theory

Regression models are routinely used in many applied sciences for describing the relationship between a response variable and an independent variable. Statistical inferences on the regression parameters are often performed using the maximum likelihood estimators (MLE). In the case of nonlinear models the standard errors of MLE are often obtained by linearizing the nonlinear function around the true parameter and by appealing to large sample theory. In this article we demonstrate, through computer simulations, that the resulting asymptotic Wald confidence intervals cannot be trusted to achieve the desired confidence levels. Sometimes they could underestimate the true nominal level and are thus liberal. Hence one needs to be cautious in using the usual linearized standard errors of MLE and the associated confidence intervals.

Nested Nonlinear Regression Models

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Regression Models ◽  
Free Choice ◽  
Model Building ◽  
Linear Models ◽  
Nonlinear Models ◽  
Real Data ◽  
Nonlinear Regression Models ◽  
Stepwise Method ◽  
Forward Stepwise ◽  
Nested Regression

Stepwise fitting of nonlinear nested regression models is considered in this chapter. The forward stepwise method of linear model building is used as far as possible. With linear models this is straightforward as there is in principle a free choice of the order that individual terms or factors are selected for inclusion. The only real issue is that sufficient submodels are examined to ensure that those finally selected really are amongst the best. The nonlinear case is not so straightforward, as embeddedness and parameter indeterminacy issues impose restrictions on the order in which steps can be taken to build a valid model, as certain parameters can only be meaningfully included if other specific parameters are definitely present. A systematic way of building valid nonlinear models of increasing complexity is described and illustrated by two examples using real data. A brief review of non-nested model building is also given.

scholarly journals Pairwise comparisons for parallel profile models with mixed effects

2012 ◽  
Vol 51 (1) ◽  
pp. 67-73
Author(s):  
Hiroto Hyakutake
Keyword(s):  
Confidence Intervals ◽  
Random Effects ◽  
Nonlinear Models ◽  
Mixed Effects ◽  
Repeated Measurements ◽  
Pairwise Comparisons ◽  
Simultaneous Confidence Intervals ◽  
Regression Parameters ◽  
The Mean ◽  
Linear And Nonlinear

ABSTRACT There are several linear and nonlinear models for analyzing repeated measurements. The mean response for an individual depends on the regression parameters specific to that individual. One of the simple forms is the sum of vectors of fixed parameters and random effects. When the models with mixed effects for several groups are parallel, pairwise comparisons of level differences are considered. For the comparisons, approximate simultaneous confidence intervals are given.

scholarly journals Optimality criteria for design in nonlinear models with constraints

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.

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

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.

scholarly journals Profile Likelihood for Estimation and Confidence Intervals

2007 ◽  
Vol 7 (3) ◽  
pp. 376-387 ◽  
Author(s):  
Patrick Royston
Keyword(s):  
Maximum Likelihood ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimate ◽  
Regression Models ◽  
Nonlinear Models ◽  
Profile Likelihood ◽  
Likelihood Estimate ◽  
Sampling Distribution

Normal-based confidence intervals for a parameter of interest are inaccurate when the sampling distribution of the estimate is nonnormal. The technique known as profile likelihood can produce confidence intervals with better coverage. It may be used when the model includes only the variable of interest or several other variables in addition. Profile-likelihood confidence intervals are particularly useful in nonlinear models. The command pllf computes and plots the maximum likelihood estimate and profile likelihood–based confidence interval for one parameter in a wide variety of regression models.

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

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.

scholarly journals Research Methods in Weed Science: Statistics

Weed Science ◽  
2015 ◽  
Vol 63 (SP1) ◽  
pp. 166-187 ◽  
Author(s):  
Christian Ritz ◽  
Andrew R. Kniss ◽  
Jens C. Streibig
Keyword(s):  
Biological Sciences ◽  
Statistical Analysis ◽  
Research Methods ◽  
Confidence Intervals ◽  
Driving Force ◽  
Standard Errors ◽  
Weed Science ◽  
Regression Parameters ◽  
Experimental Variability ◽  
Correct Picture

There are various reasons for using statistics, but perhaps the most important is that the biological sciences are empirical sciences. There is always an element of variability that can only be dealt with by applying statistics. Essentially, statistics is a way to summarize the variability of data so that we can confidently say whether there is a difference among treatments or among regression parameters and tell others about the variability of the results. To that end, we must use the most appropriate statistics to get a “correct” picture of the experimental variability, and the best way of doing that is to report the size of the parameters or the means and their associated standard errors or confidence intervals. Simply declaring that the yields were 1 or 2 ton ha−1does not mean anything without associated standard errors for those yields. Another driving force is that no journal will accept publications without the data having been subjected to some kind of statistical analysis.

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