Related Experiment Video
Updated: Jan 4, 2026
04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
3.6K
Bayesian power equivalence in latent growth curve models
Angelika M Stefan1, Timo von Oertzen2
1Department of Psychology, University of Amsterdam, The Netherlands.
The British Journal of Mathematical and Statistical Psychology
|November 7, 2019
Summary
This study extends power equivalence to Bayesian hypothesis tests for Latent Growth Curve Models (LGCMs). This allows researchers to achieve equivalent evidence for latent structure constants in Bayesian design analysis, optimizing longitudinal study planning.
Area of Science:
- Social Sciences
- Psychology
- Statistics
Background:
- Longitudinal studies are crucial for time-dependent phenomena but are costly.
- Optimizing design factors in longitudinal studies is essential for efficiency.
- Latent Growth Curve Models (LGCMs) are common for analyzing such data.
Purpose of the Study:
- To extend the concept of power equivalence to Bayesian hypothesis testing.
- To demonstrate the equivalence of Bayes factor design analysis (BFDA) for power-equivalent LGCMs.
- To provide researchers with methods for planning compelling Bayesian evidence.
Main Methods:
- Applied power equivalence to Bayesian hypothesis tests of latent structure constants.
- Utilized Bayes factor design analysis (BFDA) for two power-equivalent LGCMs.
- Extended previous work on power equivalence for frequentist likelihood-ratio tests.
Main Results:
- The notion of power equivalence is applicable to Bayesian hypothesis tests.
- BFDA results are equivalent for power-equivalent LGCMs.
- This equivalence facilitates planning for Bayesian evidence.
Conclusions:
- Researchers can use power equivalence for planning Bayesian hypothesis tests in LGCMs.
- This approach contributes to more efficient Bayesian design analysis.
- It supports the goal of planning for compelling evidence over frequentist power.
Related Concept Videos
01:14Parametric Survival Analysis: Weibull and Exponential Methods
961
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
961
02:33Exponential Equations for Modeling Growth
167
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...
167
01:16Bioequivalence Data: Statistical Interpretation
171
Body:The statistical interpretation of bioequivalence data is a significant aspect of pharmaceutical research. Bioequivalence refers to the absence of any significant difference in the rate and extent to which the active ingredient in pharmaceutical products becomes available at the site of drug action when administered at the same molar dose under similar conditions. This helps determine if different drug products have similar absorption rates, ensuring their interchangeability.Statistical...
171
01:15Assumptions of Survival Analysis
361
Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
361
00:57Population Growth
27.7K
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.
27.7K
01:29Exponential Equations with Logarithms: Problem Solving
130
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...
130