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

Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

426
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
426
Modeling with Differential Equations01:25

Modeling with Differential Equations

203
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
203
Population Growth00:57

Population Growth

29.5K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
29.5K
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

145
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
145
Quadratic Models01:23

Quadratic Models

302
Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
302
Exponential Equations with Logarithms: Problem Solving01:29

Exponential Equations with Logarithms: Problem Solving

249
In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...
249

You might also read

Related Articles

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

Sort by
Same author

Causal inference for targeted public health interventions: interactions among environmental, social, and economic determinants within the one health framework.

Journal of water and health·2026
Same author

Epidemiology of extrapulmonary tuberculosis, Alameda County, California, 2010-2021.

Journal of clinical tuberculosis and other mycobacterial diseases·2026
Same author

Computer-aided detection for radiological disease severity classification on chest radiograph in children with intra-thoracic tuberculosis.

PLOS global public health·2026
Same author

Associations of accelerometry-derived time in major activity intensities with cognitive outcomes: a compositional data analysis approach.

The journals of gerontology. Series A, Biological sciences and medical sciences·2026
Same author

A multi-omics study reveals pathway-level insights and predictive biomarkers in pediatric TB.

Clinical proteomics·2026
Same author

Platelet-leucocyte interactions drive MMP-mediated tissue damage in tuberculosis.

PLoS pathogens·2026

Related Experiment Video

Updated: Mar 27, 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

3.8K

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

Laura M Grajeda1, Andrada Ivanescu2, Mayuko Saito1,3,4

  • 1Program in Global Disease Control and Epidemiology, Department of International Health, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, USA.

Emerging Themes in Epidemiology
|January 12, 2016
PubMed
Summary

This study introduces advanced statistical models for tracking childhood growth, significantly reducing unexplained variability in height measurements. These linear mixed-effect models with cubic splines offer better estimation and prediction of individual growth trajectories.

Keywords:
Body HeightChild developmentGrowthLinear ModelsLongitudinal studies

More Related Videos

Midface Hypoplasia and Cranial Base Morphology in Syndromic Craniosynostosis: A Comparative Analysis Study Using a Predictive Regression Model
08:03

Midface Hypoplasia and Cranial Base Morphology in Syndromic Craniosynostosis: A Comparative Analysis Study Using a Predictive Regression Model

Published on: November 4, 2025

379
A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

11.2K

Related Experiment Videos

Last Updated: Mar 27, 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

3.8K
Midface Hypoplasia and Cranial Base Morphology in Syndromic Craniosynostosis: A Comparative Analysis Study Using a Predictive Regression Model
08:03

Midface Hypoplasia and Cranial Base Morphology in Syndromic Craniosynostosis: A Comparative Analysis Study Using a Predictive Regression Model

Published on: November 4, 2025

379
A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

11.2K

Area of Science:

  • Pediatric research
  • Biostatistics
  • Longitudinal data analysis

Background:

  • Childhood growth is a critical area in pediatric research, requiring sophisticated statistical models to capture individual developmental trajectories.
  • Accurate modeling of population- and subject-specific growth, velocity, and acceleration necessitates well-defined longitudinal models.
  • Linear mixed-effect models with cubic regression splines offer a robust approach to handle the inherent nonlinearity in growth curves.

Purpose of the Study:

  • To present a stepwise methodology for building complex longitudinal statistical models for childhood growth.
  • To compare the efficacy of cubic regression splines against linear piecewise splines in modeling growth data.
  • To provide reproducible statistical code for analyzing longitudinal height measurements in children.

Main Methods:

  • A stepwise approach was employed, progressing from simple to complex linear mixed-effect models, incorporating random intercepts, slopes, and residual autocorrelation.
  • Cubic regression splines were evaluated against linear piecewise splines, with variations in knot number and placement.
  • The models were applied to longitudinal height data from 215 Peruvian children from birth to four years of age.

Main Results:

  • Linear mixed-effect models with random slopes and autoregressive error terms significantly reduced unexplained variability from 7.34 to 0.81 (p < 0.001).
  • Substantial heterogeneity was observed in individual growth trajectory intercepts and slopes (p < 0.001), along with significant serial correlation (ρ = 0.66, p < 0.001).
  • Cubic regression splines demonstrated superior performance over linear splines in estimation and prediction within the linear mixed-effect framework, yielding biologically meaningful growth velocity and acceleration curves.

Conclusions:

  • The developed stepwise approach and linear mixed-effect models provide effective tools for analyzing longitudinal childhood growth data.
  • The study offers practical solutions for non-statisticians to model complex longitudinal data, enhancing the understanding of child development.
  • Cubic regression splines are recommended for their ability to capture nuanced growth patterns and provide interpretable velocity and acceleration estimates.