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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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A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
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SEM with Missing Data and Unknown Population Distributions Using Two-Stage ML: Theory and Its Application.

Ke-Hai Yuan1, Laura Lu1

  • 1a University of Notre Dame .

Multivariate Behavioral Research
|January 16, 2016
PubMed
Summary

This study introduces a 2-stage maximum likelihood (ML) method for structural equation modeling (SEM) with missing data, which is valid even without assuming a normal distribution. This approach simplifies handling unknown missing data mechanisms by incorporating auxiliary variables.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Structural Equation Modeling (SEM) often encounters missing data, complicating analysis.
  • Traditional Maximum Likelihood (ML) methods may require assumptions of data normality or specific missing data mechanisms.
  • Handling missing data effectively is crucial for accurate statistical inference in SEM.

Purpose of the Study:

  • To present the theory and application of a 2-stage ML procedure for SEM with missing data.
  • To demonstrate the validity of this procedure without assuming a normal population distribution.
  • To provide practical tools (SAS IML and EQS codes) for implementing the 2-stage ML method.

Main Methods:

  • The article details the 2-stage maximum likelihood (ML) procedure for SEM.
  • It explains the statistical conditions for the validity of the 2-stage ML, particularly with missing at random (MAR) data.
  • Auxiliary variables are incorporated to improve the likelihood of MAR mechanisms, especially when unknown.

Main Results:

  • The 2-stage ML procedure is shown to be valid even when the population distribution is unknown.
  • It provides consistent parameter estimates when the missing data mechanism is MAR.
  • The method is demonstrated to be more amenable to including auxiliary variables than direct ML.

Conclusions:

  • The 2-stage ML procedure offers a robust approach to SEM with missing data, not requiring normality assumptions.
  • The provided SAS IML and EQS programs facilitate the practical application of this method.
  • The study aims to enhance understanding and proper use of advanced missing data techniques among researchers and students.