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Simple Ways to Interpret Effects in Modeling Binary Data

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Trends and Challenges in Categorical Data Analysis

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

Abstract

Traditional methods for the analysis of binary response data are generalized linear models that employ logistic or probit link functions. Unfortunately, effect measures for these type of models do not have a straightforward interpretation. Hence, in this paper we survey probability-based effect measures that can be simpler to understand than logistic and probit regression model parameters and their corresponding effect measures, such as odds ratios. For describing the effect of an explanatory variable while adjusting for others, it is sometimes possible to employ the identity and log link functions to generate simple effect measures. When such link functions are inappropriate, one can still construct analogous effect measures. For comparing groups that are levels of categorical explanatory variables or relevant values for quantitative explanatory variables, such measures can be based on average differences or log-ratios of the probability modeled. For quantitative explanatory variables, they can also be based on average instantaneous rates of change for the probability. We also propose analogous measures for interpreting effects in models with nonlinear predictors, such as generalized additive models. We illustrate the measures for two examples and show how to implement them with R software.

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Acknowledgements

The authors appreciate helpful comments from two referees and from Pablo Inchausti and Maria Kateri.

Author information

Authors and Affiliations

  1. Department of Statistics, University of Florida, Gainesville, FL, USA

    Alan Agresti

  2. Department of Economics and Management, University of Pavia, Pavia, Italy

    Claudia Tarantola

  3. Istat and La Sapienza University, Rome, Italy

    Roberta Varriale

Authors
  1. Alan Agresti
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  2. Claudia Tarantola
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  3. Roberta Varriale
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Corresponding author

Correspondence to Alan Agresti .

Editor information

Editors and Affiliations

  1. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Maria Kateri

  2. Department of Statistics, London School of Econ. & Polit. Science, London, UK

    Irini Moustaki

Appendix

Appendix

This appendix provides the source code for the R analyses described in the text.

Table A1 R code for fitting logistic and linear probability models to the younger-age Istat sample and finding the average partial effect for the logistic regression model
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Table A2 R code for finding average log-ratio partial effect and bootstrap SE and bootstrap CI for the logistic regression model applied to the older-age Istat sample
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Table A3 R code for GAM fit for using width and color as predictors of whether a female horseshoe crab has any satellites
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Table A4 R code for finding the average partial effects for width and for color for the logistic regression model and for the generalized additive model for the presence of horseshoe crab satellites
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Table A5 R code for using a bootstrap to find confidence intervals for the average partial effects for width and for color for the generalized additive model for the presence of horseshoe crab satellites
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Table A6 R code for using a bootstrap to find confidence intervals for the average partial effects for width and for color for the generalized additive model for the presence of horseshoe crab satellites
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Agresti, A., Tarantola, C., Varriale, R. (2023). Simple Ways to Interpret Effects in Modeling Binary Data. In: Kateri, M., Moustaki, I. (eds) Trends and Challenges in Categorical Data Analysis. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-031-31186-4_5

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