Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...

Regression Analysis

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:

Regression Toward the Mean

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Multiple Regression

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics.

PloS one·2021

Same author

A randomized triple-blind crossover trial of a hydrocolloid-containing dentifrice as a controlled-release system for fluoride.

Clinical oral investigations·2018

See all related articles

Search research articles

Related Experiment Video

Updated: Sep 2, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Bootstrap-based inferential improvements to the simplex nonlinear regression model.

Alisson de Oliveira Silva¹, Jonas Weverson de Ararújo Silva², Patrícia L Espinheira³

¹Instituto Federal de Educação, Ciência e Tecnologia da Paraíba, João Pessoa, Brazil.

|August 9, 2022

Summary

Maximum likelihood estimation (MLE) for nonlinear simplex regression models can be unreliable in small samples. Bootstrap methods, particularly bootstrap intervals, offer improved accuracy for parameter estimation and inference in these models.

More Related Videos

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Published on: June 25, 2019

Related Experiment Videos

Last Updated: Sep 2, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Published on: June 25, 2019

Area of Science:

Statistics
Econometrics
Biostatistics

Background:

Traditional maximum likelihood estimation (MLE) offers asymptotic properties but can be inadequate for small sample sizes in nonlinear regression.
The nonlinear simplex regression model presents unique challenges for accurate parameter estimation and inference.

Purpose of the Study:

To evaluate the performance of point and interval estimators for the nonlinear simplex regression model.
To introduce bootstrap-based corrections to enhance maximum likelihood estimators (MLEs).
To compare traditional confidence intervals with bootstrap and percentile confidence intervals.

Main Methods:

Maximum Likelihood Estimation (MLE) for nonlinear simplex regression.
Development of bootstrap-based corrections for MLEs.
Construction of percentile and bootstrap confidence intervals.
Numerical evaluation of estimator performance.

Main Results:

Traditional MLE performance is suboptimal in small samples.
Bootstrap-corrected estimators demonstrate superior performance.
Bootstrap confidence intervals show enhanced accuracy and reliability.
The bootstrap method proved decisive in a real-data application.

Conclusions:

Bootstrap methods, especially bootstrap intervals, are recommended for parameter estimation in nonlinear simplex regression.
The proposed bootstrap approach improves inference accuracy over traditional methods.
The findings have implications for statistical modeling in various scientific fields.