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Related Concept Videos

Wave Parameters01:10

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
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

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...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...

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Updated: Jun 20, 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

Wavelet-based functional mixed models.

Jeffrey S Morris1, Raymond J Carroll

  • 1University of Texas MD Anderson Cancer Center, Houston, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|September 18, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new functional mixed model for analyzing curve data. The Bayesian wavelet approach offers flexible, adaptive modeling for complex functional data with local features.

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Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Scientific studies increasingly generate functional data, where curves are the primary units of observation.
  • Existing methods may not adequately capture the complexity and irregularity of such functional datasets.

Purpose of the Study:

  • To generalize the linear mixed model to a functional mixed model framework.
  • To develop a Bayesian wavelet-based approach for fitting functional mixed models.

Main Methods:

  • A Bayesian wavelet-based approach is used for model fitting.
  • The methodology allows for flexible modeling of arbitrary function forms and covariance structures.
  • Nonparametric estimation of fixed and random-effects functions and covariance matrices is performed.

Main Results:

  • The method provides adaptive regularization for functional fixed effects and random-effect functions.
  • Posterior samples enable pointwise or joint Bayesian inference and prediction.
  • The approach is particularly suitable for irregular functional data with local features like peaks.

Conclusions:

  • The proposed functional mixed model offers a flexible and adaptive framework for analyzing complex functional data.
  • The Bayesian wavelet approach effectively handles irregular data structures and local features.
  • This methodology enhances the analysis of curve-sampled data in scientific research.