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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
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Diagnostics for repeated measurements in linear mixed effects models.

Jungwon Mun1, Mary J Lindstrom

  • 1Department of Mathematics and Statistics, California State Polytechnic University at Pomona, 3801 W. Temple ave., Pomona, CA 91768, USA. stat.chris@gmail.com

Statistics in Medicine
|September 13, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for detecting unusual data points in complex statistical models. The studentized residual sum of squares (TRSS) plots effectively identify discordant subjects and observations, improving model accuracy.

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Current methods for detecting discordant data in linear mixed effects models often adapt single-level regression techniques.
  • Generalizations of deletion-based approaches, like Cook's distance, have limitations when applied to complex models.
  • There is a need for improved methods to identify discordant subjects and observations in longitudinal studies.

Purpose of the Study:

  • To address the limitations of existing methods for detecting discordant subjects and observations in linear mixed effects models.
  • To propose a novel non-deletion subject-level method using studentized residual sum of squares (TRSS) plots.
  • To introduce an observation-level deletion method based on TRSS plots for identifying discordant observations.

Main Methods:

  • Development of studentized residual sum of squares (TRSS) plots for subject-level analysis.
  • Application of TRSS plots to create a new deletion method for observation-level discordance.
  • Utilizing revised residuals to enhance the evaluation of discordant data effects on parameter estimation, including variance components.

Main Results:

  • TRSS plots successfully identified discordant subjects that were missed by modified Cook's distance and local influence methods.
  • The proposed TRSS-based methods provide more detailed information on repeated measurements.
  • The methods efficiently evaluate the impact of discordant subjects and observations on parameter and variance component estimation.

Conclusions:

  • Studentized residual sum of squares (TRSS) plots offer a superior approach for detecting discordant subjects in linear mixed effects models.
  • The proposed TRSS-based methods enhance the analysis of longitudinal data by effectively identifying problematic data points.
  • TRSS plots represent a valuable advancement in diagnostic techniques for mixed-effects modeling, with potential for further extensions.