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On the Use of Elbow Plot Method for Class Enumeration in Factor Mixture Models.

Sedat Sen1, Allan S Cohen2

  • 1Faculty of Education, Harran University, Türkiye.

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Summary
This summary is machine-generated.

The elbow plot method effectively identifies the correct number of latent classes in factor mixture models (FMMs) for two- and three-class conditions. However, its performance declines with more complex models, showing limitations in specific scenarios.

Keywords:
class enumerationelbow plotfactor mixture modelinformation criterion

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Area of Science:

  • * Statistics
  • * Psychometrics
  • * Data Analysis

Background:

  • * Determining the correct number of latent classes is crucial for applying factor mixture models (FMMs).
  • * Previous research has evaluated various information criterion (IC) indices for this purpose.
  • * The effectiveness of the elbow plot method for FMM latent class determination remained unexamined.

Purpose of the Study:

  • * To compare the effectiveness of the elbow plot method against established criteria for selecting the number of latent classes in FMMs.
  • * To evaluate the performance of the elbow plot method across different FMM configurations.

Main Methods:

  • * A simulation study was conducted to assess method performance.
  • * The elbow plot method was compared with the lowest information criterion (IC) value and difference methods.
  • * Five common IC indices were utilized in the analysis.

Main Results:

  • * The elbow plot method successfully detected the generating model in at least 90% of two- and three-class FMM simulations.
  • * Performance decreased in two-factor and four-class FMM conditions.
  • * The elbow plot method generally outperformed the lowest IC value and difference methods for two- and three-class models, but not for four-class models.

Conclusions:

  • * The elbow plot method is a reliable tool for determining latent classes in simpler FMMs (2-3 classes).
  • * Its utility is limited in more complex FMM scenarios (e.g., four classes or two factors).
  • * The difference method showed superior performance in specific complex conditions (two factors, four classes).