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The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
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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...
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Sometimes we want to see how people change over time, as in studies of human development and lifespan. When we test the same group of individuals repeatedly over an extended period of time, we are conducting longitudinal research. Longitudinal research is a research design in which data-gathering is administered repeatedly over an extended period of time. For example, we may survey a group of individuals about their dietary habits at age 20, retest them a decade later at age 30, and then again...
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Related Experiment Video

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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Bayesian analysis of longitudinal multitrait-multimethod data with ordinal response variables.

Jana Holtmann1, Tobias Koch2, Johannes Bohn1

  • 1Department of Education and Psychology, Free University Berlin, Germany.

The British Journal of Mathematical and Statistical Psychology
|January 25, 2017
PubMed
Summary
This summary is machine-generated.

A new Bayesian multilevel model accurately estimates construct validity over time in longitudinal multitrait-multimethod (MTMM) studies. This method effectively analyzes changes in constructs and method effects using ordinal data.

Keywords:
Bayesian statisticsMonte Carlo simulationmultilevel item response theorymultitrait-multimethod measurementsubjective well-being

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Area of Science:

  • Psychometrics
  • Quantitative Psychology
  • Longitudinal Data Analysis

Background:

  • Multitrait-multimethod (MTMM) studies are crucial for assessing construct validity.
  • Longitudinal MTMM designs face challenges in modeling complex data structures and method effects over time.
  • Existing models may not adequately handle ordinal response variables and multilevel data simultaneously.

Purpose of the Study:

  • To propose a novel multilevel latent state graded response model for longitudinal MTMM designs.
  • To enable the examination of construct validity, change, and stability of constructs and method effects over time.
  • To demonstrate the utility of Bayesian estimation for these complex longitudinal models.

Main Methods:

  • Development of a multilevel latent state graded response model for MTMM data.
  • Application of Bayesian estimation techniques to address estimation challenges.
  • Conducting a Monte Carlo simulation study to assess parameter recovery and estimation accuracy.
  • Empirical application to longitudinal well-being data (life satisfaction, subjective happiness).

Main Results:

  • The proposed Bayesian model accurately estimates parameters even with low convergent validity.
  • Sufficient accuracy was achieved with 250 clusters and over two observations per cluster.
  • The model successfully assessed changes and stability in life satisfaction and subjective happiness in young adults.

Conclusions:

  • Bayesian estimation is a viable and effective approach for complex longitudinal multilevel MTMM models.
  • The developed model provides a robust framework for analyzing construct validity and change over time.
  • Guidelines for empirical application and a discussion of the Bayesian approach's advantages and limitations are provided.