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Circular interpretation of regression coefficients.

Jolien Cremers1, Kees Tim Mulder1, Irene Klugkist1,2

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Summary

New measures simplify interpreting predictor effects in projected normal regression models for social scientists. Average slope (AS) and slope at mean (SAM) are recommended for circular data analysis.

Keywords:
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Area of Science:

  • Statistics
  • Social Sciences
  • Bayesian Modeling

Background:

  • Interpreting predictor effects in projected normal regression models can be complex.
  • Social scientists need accessible methods for analyzing circular data.

Purpose of the Study:

  • To simplify the interpretation of predictor effects in Bayesian projected normal regression models.
  • To introduce new measures for assessing marginal effects in circular regression.

Main Methods:

  • Introduction of three novel measures: slope at inflection point (bc), average slope (AS), and slope at mean (SAM).
  • Development of methods to differentiate between location (mean) and accuracy (spread) effects in circular outcomes.
  • A simulation study to evaluate the performance of the new measures and methods.

Main Results:

  • The new measures and methods effectively distinguish location and accuracy effects when location effects are clear.
  • Slope at mean (SAM) and average slope (AS) are preferred when data deviates from the inflection point.
  • Performance varies when location and accuracy effects are not clearly distinguishable, with SAM showing promise.

Conclusions:

  • The proposed measures enhance the utility of projected normal regression models for social science research.
  • The distinction between location and accuracy effects provides deeper insights into circular data.
  • Slope at mean (SAM) is a robust measure, particularly recommended for complex scenarios.