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Related Concept Videos

Variation01:19

Variation

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An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
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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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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
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Defining R-squared measures for mixed-effects location scale models.

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  • 1Department of Public Health Sciences, The University of Chicago, Chicago, Illinois, USA.

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Summary
This summary is machine-generated.

This study introduces novel effect size measures for mixed-effects location scale (MELS) models, enhancing the interpretation of health behavior research. The developed framework and R function aid researchers in analyzing complex longitudinal data.

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Ecological momentary assessment and modern technologies generate intensive longitudinal data, revealing within- and between-subject variability in health outcomes.
  • Existing two-level mixed-effects location scale (MELS) models accommodate covariate and random subject effects on outcome means and variability.
  • Standardized effect size measures for MELS models are currently lacking, hindering comprehensive data interpretation.

Purpose of the Study:

  • To extend existing effect size frameworks for multilevel models to MELS models.
  • To develop interpretable effect size measures that account for random subject effects on both location and scale.
  • To provide a practical tool for researchers utilizing MELS models.

Main Methods:

  • Extension of Rights and Sterba's measures framework, based on model-implied variances, to MELS models.
  • Application of the framework to MELS models with covariate-influenced random intercepts and random intercepts combined with random slopes.
  • Development of an R function (R2MELS) for calculating and visualizing effect size measures.

Main Results:

  • A validated framework for calculating effect size measures for MELS models was established.
  • The R2MELS function provides summary tables and visualizations for these novel effect size measures.
  • Demonstration of the framework's utility through simulation studies and real-world health behavior and depression data.

Conclusions:

  • The proposed measures offer a standardized approach to quantifying effect sizes in MELS models.
  • These measures enhance the interpretability of findings from intensive longitudinal health research.
  • The R2MELS function facilitates the application and understanding of these effect size measures in practice.