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Related Concept Videos

Randomized Experiments01:13

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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 squares (OLS)...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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...
Group Design02:01

Group Design

The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except for one difference— experimental manipulation. The experimental group gets the experimental manipulation—that is, the treatment or variable being tested—and the control group does not. Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between the two are due to...
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...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...

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Related Experiment Video

Updated: Jun 10, 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

Fixed and random effects selection in mixed effects models.

Joseph G Ibrahim1, Hongtu Zhu, Ramon I Garcia

  • 1Department of Biostatistics, University of North Carolina, McGavran Greenberg Hall, Chapel Hill, North Carolina 27599-7420, USA. ibrahim@bios.unc.edu

Biometrics
|July 29, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for selecting important fixed and random effects in mixed effects models using penalized likelihood estimation. The approach ensures accurate variable selection for complex statistical models.

Related Experiment Videos

Last Updated: Jun 10, 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

Area of Science:

  • Statistics
  • Statistical Modeling
  • Econometrics

Background:

  • Mixed effects models are widely used in various scientific fields to analyze clustered or longitudinal data.
  • Selecting appropriate fixed and random effects is crucial for model interpretability and predictive accuracy.
  • Existing methods may struggle with high-dimensional data or complex model structures.

Purpose of the Study:

  • To develop a robust variable selection procedure for mixed effects models.
  • To simultaneously select both fixed and random effects.
  • To propose a model selection criterion for choosing penalty parameters in penalized likelihood estimation.

Main Methods:

  • Utilized maximum penalized likelihood (MPL) estimation.
  • Employed smoothly clipped absolute deviation (SCAD) and adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions.
  • Introduced the IC(Q) statistic for selecting penalty parameters.

Main Results:

  • MPL estimates demonstrated consistency, sparsity, and asymptotic normality.
  • The IC(Q) statistic-based procedure consistently selected important fixed and random effects.
  • The methodology proved general, applicable to generalized linear mixed models and illustrated with real data.

Conclusions:

  • The proposed MPL approach with SCAD/ALASSO penalties offers a powerful tool for variable selection in mixed effects models.
  • The IC(Q) statistic provides a reliable method for tuning penalty parameters.
  • This methodology enhances the analysis of complex data structures across various scientific disciplines.