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Does the ADF fit function decrease when the kurtosis increases?

Ulf Henning Olsson1, Tron Foss, Sigurd V Troye

  • 1Department of Economics, Norwegian School of Management, Sandvika, Norway. ulf.h.olsson@bi.no

The British Journal of Mathematical and Statistical Psychology
|November 25, 2003
PubMed
Summary

Excessive kurtosis in data significantly impacts asymptotically distribution-free (ADF) fit functions. Higher kurtosis levels decrease ADF fit values, affecting factor model assessment.

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Area of Science:

  • Psychometrics
  • Statistics
  • Quantitative Psychology

Background:

  • Asymptotically distribution-free (ADF) fit functions are crucial for structural equation modeling (SEM).
  • Data kurtosis, a measure of 'tailedness,' can influence statistical test results.
  • Understanding kurtosis effects on ADF fit is vital for accurate model evaluation.

Purpose of the Study:

  • To investigate how univariate kurtosis affects asymptotically distribution-free (ADF) fit functions.
  • To analyze the impact of varying kurtosis levels on fit indices in misspecified factor models.

Main Methods:

  • Numerical calculations were performed on 13 different factor models.
  • The study formally proved the monotonic relationship between kurtosis and ADF fit function probability limits.

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Main Results:

  • The probability limit F(0) of the ADF fit function significantly decreases with increasing kurtosis.
  • This effect was observed across 13 tested factor models.
  • A formal proof confirmed that F(0) monotonically decreases as kurtosis increases.

Conclusions:

  • Excessive kurtosis in observed data can lead to misleadingly poor fit for misspecified factor models when using ADF fit functions.
  • Researchers should consider data kurtosis when interpreting ADF fit indices in SEM.
  • The findings highlight the importance of assessing data distributional properties for robust statistical inference.