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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
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Generalized AIC and chi-squared statistics for path models consistent with directed acyclic graphs.

Bill Shipley1, Jacob C Douma2

  • 1Département de biologie, Université de Sherbrooke, Sherbrooke, Quebec, J1K 2R1, Canada.

Ecology
|December 20, 2019
PubMed
Summary
This summary is machine-generated.

Researchers present methods for calculating generalized chi-square and Akaike Information Criterion statistics in piecewise structural equation modeling (SEM). This approach simplifies complex models by decomposing them into manageable submodels for robust statistical analysis.

Keywords:
Akaike Information Criteriond-separationdirected acyclic graphmaximum likelihoodmodel selectionpath analysispiecewise SEM

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Area of Science:

  • Statistics
  • Ecology
  • Biostatistics

Background:

  • Structural equation modeling (SEM) is a powerful statistical technique for analyzing complex relationships between variables.
  • Piecewise SEM, which avoids latent variables and represents causal structures as directed acyclic graphs (DAGs), offers a more accessible approach.
  • Existing methods for calculating goodness-of-fit statistics in piecewise SEM can be complex and computationally intensive.

Purpose of the Study:

  • To develop and explain a method for obtaining a generalized maximum-likelihood chi-square statistic for piecewise SEM.
  • To provide a straightforward approach for calculating a full-model Akaike Information Criterion (AIC) statistic for piecewise SEM.
  • To facilitate the statistical evaluation and comparison of piecewise SEMs, enhancing their practical application in scientific research.

Main Methods:

  • Decomposition of the full piecewise SEM into a Markov network of submodels.
  • Each submodel can accommodate diverse distributional assumptions and functional relationships.
  • Utilizing maximum-likelihood estimation methods for parameter estimates within each submodel.

Main Results:

  • A generalized chi-square statistic is derived as a function of the difference between the model's maximum likelihood and its saturated equivalent.
  • The full-model AIC is computed by aggregating the AIC statistics from individual submodels.
  • These statistics provide robust measures for assessing the overall fit and parsimony of piecewise SEMs.

Conclusions:

  • The proposed methods offer a computationally efficient and statistically sound framework for analyzing piecewise SEMs.
  • These statistics enable rigorous model evaluation, aiding researchers in selecting the best-fitting causal network.
  • The approach enhances the utility of piecewise SEM in diverse scientific fields by simplifying model assessment.