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Distance-based logistic model for cross-classified categorical data.

José Fernando Vera1

  • 1Department of Statistics and O.R. Faculty of Sciences, University of Granada, Spain.

The British Journal of Mathematical and Statistical Psychology
|January 26, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel distance-based logistic model for analyzing categorical data. The model offers a graphical interpretation of association coefficients using odds ratios, enhancing data analysis and understanding.

Keywords:
categorical predictorcontingency tabledistancesmultinomial baseline-category logit modelodds ratiounfolding

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • Logistic regression models are vital for analyzing categorical response variables in cross-classified data.
  • Interpreting coefficients as odds ratios is common due to their straightforward understanding.

Purpose of the Study:

  • To present a distance-based logistic model for graphical interpretation of association coefficients.
  • To explore the inverse relationship between local odds ratios and distances between predictor and response categories.

Main Methods:

  • Developed a distance-based logistic model for contingency tables.
  • Estimated row and column configurations for polytomous predictor and nominal response variables.
  • Investigated the relationship between distances across different predictor variable codings.

Main Results:

  • The model provides a graphical interpretation of associations via odds ratios.
  • Demonstrated an inverse relationship between local odds ratios and category distances.
  • Monte Carlo experiments validated the estimation procedure's performance.

Conclusions:

  • The distance-based logistic model offers an interpretable alternative for analyzing associations in categorical data.
  • The model's performance is comparable to existing two-step methods.
  • Graphical interpretation aids in understanding complex data relationships.