Bridging Log-Odds Ratios and Correspondence Analysis via Closeness-of-Concordance Measures.

lorbridge

Overview

lorbridge provides a unified analytical framework that connects two worlds that clinical and medical researchers often treat separately: conventional logistic regression and geometric correspondence analysis.

The Problem

When a logistic regression model produces a log-odds ratio (LOR) of 1.47 for a predictor, most clinical faculty find it difficult to judge whether this represents a small, moderate, or large association — because the log-odds ratio scale is unbounded and asymmetric. The exponentiated form (odds ratio = 4.35) is easier to communicate but still not directly comparable across predictors or across studies.

The Solution

Building on Kim and Grochowalski (2019), lorbridge re-expresses every LOR from binary and multinomial logistic regression as a cosine theta estimate — a measure bounded between −1 and +1, interpretable exactly like a Pearson correlation. A cosine theta of +0.68 is immediately recognisable as a strong positive association to any researcher familiar with correlations, without requiring statistical training in odds ratios or log-transformations.

In addition to cosine theta, lorbridge computes three further closeness-of-concordance measures (CCMs) — Yule's Q, Yule's Y, and r_meta (a meta-analytic correlation) — all on the same −1 to +1 scale, with bootstrap confidence intervals throughout.

The Bridge to Correspondence Analysis

The same cosine theta metric connects logistic regression output to the geometry of Singly-Ordered Nonsymmetric Correspondence Analysis (SONSCA) and Doubly-Ordered Nonsymmetric Correspondence Analysis (DONSCA). These methods extend conventional correspondence analysis to tables where one or both variable orderings carry substantive meaning — for example, a table of racial groups (nominal rows) by discretised IQ or Vocabulary Meaning score bins (ordered columns).

SONSCA and DONSCA produce geometric biplots that make complex categorical relationships immediately visible, while the cosine theta values anchored at user-specified reference categories provide a single, interpretable effect-size summary for each pairwise contrast — directly comparable to the LOR-derived CCMs from the logistic regression in the same analysis.

Who Is This For?

lorbridge is designed for:

• Clinical and medical researchers who routinely report odds ratios and want an intuitive, correlation-like effect-size companion measure
• Methodologists working with ordered categorical data who want to connect logistic regression and correspondence analysis in a single coherent workflow
• Graduate students and faculty learning to interpret association strength beyond p-values and raw odds ratios

Methodological Lineage

This package implements and extends methods from:

• Kim, S.-K., & Grochowalski, J. H. (2019) — the original cosine theta bridge between LORs and CA geometry
• Kim, S.-K. (2020, 2021, 2022) — clinical applications of matched and nonsymmetric CA in psychiatric and pediatric research
• Kim, S.-K. (2024) — factor analytic profile analysis and interpretable machine learning for biomedical data

Installation

# From CRAN (once published):
install.packages("lorbridge")

# Development version from GitHub:
# install.packages("remotes")
remotes::install_github("sekangakim/lorbridge")

Quick Start

library(lorbridge)
data(lorbridge_data)

## --- Binary logistic regression: continuous predictor ---
res_cont <- blr_continuous(
  outcome   = lorbridge_data$minority,
  predictor = lorbridge_data$VM
)
print(res_cont$summary_table[, c("LOR","OR","OR_lo","OR_hi","p","r_meta")])

## --- Binary logistic regression: categorical predictor ---
res_cat <- blr_categorical(
  outcome   = lorbridge_data$minority,
  predictor = lorbridge_data$VMbin,
  ref_level = "VM4"
)
print(res_cat$results[, c("Category","LOR","OR","p","YuleQ","cos_theta")])

## --- SONSCA pairwise CCMs ---
data(tab_IQ)
sonsca_ccm(tab_IQ,
           row_k = "Race1", bin_j = "IQ1",
           row_anchor = "Race2", col_anchor = "IQ4")

## --- DONSCA cosine theta ---
data(tab_IQ_VM)
fit <- donsca_fit(tab_IQ_VM)
donsca_cosines(fit, col_anchor_idx = 4, row_anchor_idx = 4)

Package Structure

Datasets

References

Kim, S.-K., & Grochowalski, J. H. (2019). Gaining from discretization of continuous data: The correspondence analysis biplot approach. Behavior Research Methods, 51(2), 589–601. https://doi.org/10.3758/s13428-018-1161-1

Kim, S.-K. (2020). Test treatment effect differences in repeatedly measured symptoms with binary values: The matched correspondence analysis approach. Behavior Research Methods, 52, 1480–1490. https://doi.org/10.3758/s13428-019-01328-9

Kim, S.-K., McKay, D., Murphy, T. K., Bussing, R., McNamara, J. P., Goodman, W. K., & Storch, E. C. (2021). Age moderated–anxiety mediation for multimodal treatment outcome among children with obsessive-compulsive disorder: An evaluation with correspondence analysis. Journal of Affective Disorders, 282, 766–775. https://doi.org/10.1016/j.jad.2020.12.198

Kim, S.-K. (2022). Assessment of improvement in anxiety severity for children with autism spectrum disorders: The matched correspondence analysis approach. Journal of Psychiatric Research, 145, 175–181. https://doi.org/10.1016/j.jpsychires.2021.12.004

Kim, S.-K. (2024). Factorization of person response profiles to identify summative profiles carrying central response patterns. Psychological Methods, 29(4), 723–730. https://doi.org/10.1037/met0000568

Author

Se-Kang Kim, Ph.D. Professor (Tenured), Division of Pediatric Psychology Baylor College of Medicine, Houston, TX [email protected] ORCID: 0000-0003-0928-3396

License

GPL-3 © Se-Kang Kim.