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Comparing logit & probit coefficients between nested models.

Richard Williams1, Abigail Jorgensen1

  • 1University of Notre Dame, 4060 Jenkins Nanovic Halls, Department of Sociology, University of Notre Dame, Notre Dame, IN, 46556, USA.

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|December 5, 2022
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Summary
This summary is machine-generated.

Interpreting nested models with logit or probit techniques for binary dependent variables can be misleading. Naïve coefficient comparisons may inaccurately represent variable effects, necessitating alternative methods for accurate social science research.

Keywords:
Karlson/ Holm/ Breen methodLogit & probitMarginal effectsNested modelsY-standardization

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Area of Science:

  • Social Sciences
  • Statistics
  • Econometrics

Background:

  • Social scientists analyze how variable effects change when controlling for others.
  • Nested models are common for exploring mediating or confounding relationships.
  • Logit and probit models are frequently used for binary dependent variables in social science.

Purpose of the Study:

  • To highlight the interpretive problems of nested models with binary dependent variables using logit/probit.
  • To explain why naive coefficient comparisons can lead to erroneous conclusions.
  • To evaluate proposed solutions for accurate interpretation.

Main Methods:

  • Discussion of the theoretical underpinnings of coefficient interpretation in nested logit/probit models.
  • Illustration of potential consequences through examples.
  • Explanation and evaluation of alternative methods: Linear Probability Models, Y-standardization, Karlson/Holm/Breen method, and marginal effects.

Main Results:

  • Naive comparisons of coefficients in nested logit/probit models can produce misleading results.
  • These misinterpretations can include showing effects where none exist, hiding existing effects, or reversing the direction of effects.
  • The study demonstrates the practical implications of these interpretive challenges.

Conclusions:

  • Standard coefficient comparisons in nested logit/probit models are unreliable for binary outcomes.
  • Researchers must employ appropriate methods like marginal effects or the Karlson/Holm/Breen method for valid interpretation.
  • Careful methodological choices are crucial for accurate causal inference in social science research.