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Generalized linear models (GLMs) in psychology often misinterpret interaction effects for probabilities and counts. This study introduces accurate methods using partial derivatives and discrete differences for correct interpretation.

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Area of Science:

  • Psychology
  • Statistics
  • Biostatistics

Background:

  • Generalized linear models (GLMs) are widely used in psychology to analyze probabilities and counts.
  • Current methods for interpreting interaction effects in GLMs often incorrectly extend linear model approaches.
  • This can lead to inaccurate conclusions regarding the interplay between predictor variables.

Purpose of the Study:

  • To redefine and accurately quantify interaction effects in generalized linear models for probability and count data.
  • To provide researchers with correct methods for estimating and interpreting interactions in these models.
  • To address the limitations of traditional product-term approaches in non-linear models.

Main Methods:

  • Defining interactions as the change in a marginal effect of one variable contingent on another.
  • Utilizing partial derivatives and discrete differences to quantify interaction effects.
  • Applying these methods to simulated data and a real-world dataset (Adolescent Brain Cognitive Development Study).

Main Results:

  • Interaction effects in GLMs for probabilities and counts are not equivalent to product terms.
  • The proposed methods (partial derivatives, discrete differences) accurately capture the non-linear nature of these interactions.
  • Demonstrated correct interpretation of interaction effects in a logistic regression model.

Conclusions:

  • Accurate interpretation of interaction effects in GLMs requires methods beyond simple product terms.
  • The use of partial derivatives and discrete differences is crucial for understanding complex relationships in psychological research.
  • Correctly evaluating interactions enhances the validity of findings from probability and count data analyses.