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Multicollinearity and misleading statistical results.

Jong Hae Kim1

  • 1Department of Anesthesiology and Pain Medicine, School of Medicine, Daegu Catholic University, Daegu, Korea.

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Summary

Multicollinearity, high intercorrelation between variables, causes unreliable regression results. Variance inflation factor (VIF) and condition indices help detect it, while variance decomposition proportion (VDP) identifies specific multicollinear variables for model stability.

Keywords:
Biomedical researchBiostatisticsMultivariable analysisRegressionStatistical biasStatistical data analysis

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Multicollinearity, high intercorrelation between explanatory variables, distorts multiple regression analysis.
  • This distortion leads to unreliable regression coefficients, probability values, and confidence intervals.

Purpose of the Study:

  • To explain diagnostic tools for multicollinearity: Variance Inflation Factor (VIF), condition index, condition number, and Variance Decomposition Proportion (VDP).
  • To clarify how VDP identifies specific multicollinear variables, unlike VIF or condition indices alone.

Main Methods:

  • Assessing multicollinearity using VIF, condition index, and condition number thresholds (VIF > 5-10, condition index > 10-30).
  • Utilizing Variance Decomposition Proportion (VDP) derived from eigenvectors to pinpoint multicollinear variables.
  • Identifying multicollinearity when VDPs associated with a high condition index (>10-30) exceed 0.8-0.9.

Main Results:

  • VIF and condition indices indicate the presence but not the specific variables involved in multicollinearity.
  • VDPs effectively identify which explanatory variables contribute to multicollinearity.
  • Removing multicollinear variables stabilizes multiple regression models.

Conclusions:

  • Accurate identification of multicollinear variables using VDP is crucial for robust regression analysis.
  • Excluding identified multicollinear variables enhances the statistical stability and reliability of regression models.