Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

359
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
359
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

438
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...
438
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

7.1K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
7.1K
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

1.5K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
1.5K
Regression Analysis01:11

Regression Analysis

7.2K
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:
7.2K
Multiple Regression01:25

Multiple Regression

3.3K
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...
3.3K

You might also read

Related Articles

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

Sort by
Same journal

Enhancing Environmental Performance for Green Building Projects: Assessment Study due to the Applicability of Industry 4.0 Technologies.

TheScientificWorldJournal·2026
Same journal

Ethnobotanical Survey of Medicinal Plants Utilized by Traditional Healers in Managing Respiratory Tract Infections in the Kagera Region, Tanzania.

TheScientificWorldJournal·2026
Same journal

Solvent Extraction of Metals in the Circular Economy: Enhancing Resource Efficiency and Sustainability.

TheScientificWorldJournal·2026
Same journal

Agronomic Performance and Nutritive Value Evaluation of Desho Grass Varieties Under Supplementary Irrigation in Western Oromia, Ethiopia.

TheScientificWorldJournal·2026
Same journal

Physicians' and Hospital Administrators' Perspectives of Diagnosis-Related Groups (DRGs) in High-Income Countries: A Systematic Review.

TheScientificWorldJournal·2026
Same journal

The Eco-Friendly Preparation of Se, Zn, and Ag MONPs and Their Current Medical Applications and Drug Delivery for AD Diseases.

TheScientificWorldJournal·2026

Related Experiment Video

Updated: May 2, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

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

Published on: July 3, 2020

2.9K

A stochastic restricted principal components regression estimator in the linear model.

Daojiang He1, Yan Wu1

  • 1Department of Statistics, Anhui Normal University, Wuhu 241000, China.

Thescientificworldjournal
|March 4, 2014
PubMed
Summary

We introduce a new stochastic restricted principal components (SRPC) regression estimator to address multicollinearity in linear models with stochastic restrictions. This SRPC estimator combines ordinary mixed estimator and principal components regression methods for improved performance.

More Related Videos

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
09:44

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

Published on: October 16, 2018

13.3K
Machine Learning-Based Cough Tone Classification: Diagnostic Exploration of Chronic Obstructive Pulmonary Disease and Respiratory Tract Infections
06:22

Machine Learning-Based Cough Tone Classification: Diagnostic Exploration of Chronic Obstructive Pulmonary Disease and Respiratory Tract Infections

Published on: September 19, 2025

751

Related Experiment Videos

Last Updated: May 2, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

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

Published on: July 3, 2020

2.9K
Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
09:44

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

Published on: October 16, 2018

13.3K
Machine Learning-Based Cough Tone Classification: Diagnostic Exploration of Chronic Obstructive Pulmonary Disease and Respiratory Tract Infections
06:22

Machine Learning-Based Cough Tone Classification: Diagnostic Exploration of Chronic Obstructive Pulmonary Disease and Respiratory Tract Infections

Published on: September 19, 2025

751

Area of Science:

  • Statistics
  • Econometrics
  • Regression Analysis

Background:

  • Multicollinearity poses a significant challenge in linear regression models, potentially leading to unstable coefficient estimates.
  • Stochastic linear restrictions on regression coefficients are common in various applied fields.
  • Existing estimators may not adequately handle multicollinearity in the presence of such restrictions.

Purpose of the Study:

  • To propose a novel estimator, the stochastic restricted principal components (SRPC) regression estimator.
  • To address the issue of multicollinearity in linear models when stochastic linear restrictions are present.
  • To derive conditions under which the proposed SRPC estimator outperforms existing methods.

Main Methods:

  • The proposed SRPC estimator is constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator.
  • The mean squared error matrix criterion is used to establish conditions for estimator superiority.
  • A numerical example and Monte Carlo simulations are employed for performance evaluation.

Main Results:

  • Necessary and sufficient conditions for the superiority of the SRPC estimator over OME and PCR are derived.
  • The SRPC estimator demonstrates improved performance in mitigating multicollinearity under stochastic restrictions.
  • Simulation results validate the theoretical findings regarding the estimator's effectiveness.

Conclusions:

  • The proposed SRPC regression estimator offers a valuable tool for handling multicollinearity in linear models with stochastic restrictions.
  • The derived conditions provide guidance for selecting the appropriate estimator.
  • The study highlights the practical utility of the SRPC estimator through numerical and simulation analyses.