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    Area of Science:

    • Statistics
    • Quantitative Psychology
    • Econometrics

    Background:

    • Conditional relations, where one predictor's effect depends on another, are crucial in many research hypotheses.
    • Multiplicative interactions are commonly used to test these conditional relations in fixed- and random-effects regression.
    • Probing interactions, often via simple slopes, is necessary to fully understand conditional effects, but existing methods have limitations.

    Purpose of the Study:

    • To generalize the Johnson-Neyman (J-N) technique for probing interactions.
    • To extend the J-N technique to accommodate a wider range of interactions in both fixed- and random-effects regression models.
    • To provide a more versatile and comprehensive method for analyzing conditional effects compared to traditional simple slopes analysis.

    Main Methods:

    • Review of existing methods for probing interactions in regression analysis.
    • Development of analytic expressions to extend the Johnson-Neyman (J-N) technique.
    • Application of the generalized J-N technique to fixed- and random-effects regression models with various interaction types.

    Main Results:

    • The study successfully generalizes the Johnson-Neyman (J-N) technique beyond its previous limitations.
    • The expanded J-N technique is applicable to a broader array of interactions, including those in random-effects models.
    • Empirical examples demonstrate the advantages of the generalized J-N technique over simple slopes analysis for probing interactions.

    Conclusions:

    • The generalized Johnson-Neyman (J-N) technique offers a powerful and flexible tool for analyzing complex conditional relations.
    • This advancement facilitates a more thorough understanding of interaction effects in both fixed- and random-effects regression.
    • The proposed method enhances the interpretability of conditional effects, surpassing the utility of simple slopes analysis in many scenarios.