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TSQCA: Threshold-Sweep Qualitative Comparative Analysis in R

Yuki Toyoda

TL;DR

TSQCA reframes calibration thresholds in Qualitative Comparative Analysis as explicit analytical variables and provides automated threshold-sweep tools in R to map how sufficient configurations evolve across substantively meaningful outcome and condition levels. By integrating with the QCA package and delivering structured S3 results, configuration charts, and Markdown reports, TSQCA enables reproducible, cross-threshold exploration rather than ad hoc robustness checks. The approach reveals hierarchical sufficiency patterns and supports transparent reporting of threshold-driven changes, EPIs, and SPIs across multiple solutions. This has practical impact by making threshold sensitivity a standard, scalable part of QCA workflows, guiding more informed threshold setting and interpretation. The package thus complements existing QCA tools, offering a forward-facing exploratory framework that enhances transparency and comparability in configurational analysis.

Abstract

Qualitative Comparative Analysis (QCA) requires researchers to choose calibration and dichotomization thresholds, and these choices can substantially affect truth tables, minimization, and resulting solution formulas. Despite this dependency, threshold sensitivity is often examined only in an ad hoc manner because repeated analyses are time-intensive and error-prone. We present TSQCA, an R package that automates threshold-sweep analyses by treating thresholds as explicit analytical variables. It provides four sweep functions (otSweep, ctSweepS, ctSweepM, dtSweep) to explore outcome thresholds, single-condition thresholds, multi-condition threshold grids, and joint outcome-condition threshold spaces, respectively. TSQCA integrates with the established CRAN package QCA for truth table construction and Boolean minimization, while returning structured S3 objects with consistent print/summary methods and optional detailed results. The package also supports automated Markdown report generation and configuration-chart output to facilitate reproducible documentation of cross-threshold results.

TSQCA: Threshold-Sweep Qualitative Comparative Analysis in R

TL;DR

TSQCA reframes calibration thresholds in Qualitative Comparative Analysis as explicit analytical variables and provides automated threshold-sweep tools in R to map how sufficient configurations evolve across substantively meaningful outcome and condition levels. By integrating with the QCA package and delivering structured S3 results, configuration charts, and Markdown reports, TSQCA enables reproducible, cross-threshold exploration rather than ad hoc robustness checks. The approach reveals hierarchical sufficiency patterns and supports transparent reporting of threshold-driven changes, EPIs, and SPIs across multiple solutions. This has practical impact by making threshold sensitivity a standard, scalable part of QCA workflows, guiding more informed threshold setting and interpretation. The package thus complements existing QCA tools, offering a forward-facing exploratory framework that enhances transparency and comparability in configurational analysis.

Abstract

Qualitative Comparative Analysis (QCA) requires researchers to choose calibration and dichotomization thresholds, and these choices can substantially affect truth tables, minimization, and resulting solution formulas. Despite this dependency, threshold sensitivity is often examined only in an ad hoc manner because repeated analyses are time-intensive and error-prone. We present TSQCA, an R package that automates threshold-sweep analyses by treating thresholds as explicit analytical variables. It provides four sweep functions (otSweep, ctSweepS, ctSweepM, dtSweep) to explore outcome thresholds, single-condition thresholds, multi-condition threshold grids, and joint outcome-condition threshold spaces, respectively. TSQCA integrates with the established CRAN package QCA for truth table construction and Boolean minimization, while returning structured S3 objects with consistent print/summary methods and optional detailed results. The package also supports automated Markdown report generation and configuration-chart output to facilitate reproducible documentation of cross-threshold results.
Paper Structure (53 sections, 1 equation, 2 figures, 6 tables)

This paper contains 53 sections, 1 equation, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. The threshold dependency problem in QCA
  3. Existing approaches and their limitations
  4. Contributions of TSQCA
  5. Paper organization
  6. Theoretical background
  7. Calibration and threshold dependency
  8. The concept of hierarchical sufficiency
  9. Relationship to existing robustness research
  10. Package design
  11. Design philosophy
  12. Relationship to the QCA package
  13. Package structure
  14. S3 methods
  15. Function overview
  16. ...and 38 more sections

Figures (2)

  • Figure 1: Conceptual illustration of hierarchical sufficiency across outcome thresholds. As the outcome threshold increases from thrY = 5 to thrY = 9, the number of sufficient paths decreases from three (M1, M2, M3) to none. This figure is schematic and intended to illustrate the general logic of hierarchical sufficiency; actual empirical results vary by dataset.
  • Figure 2: TSQCA workflow diagram. The package takes raw data and threshold range specifications as input, then iterates through each threshold value. At each iteration, TSQCA calls QCA::truthTable() and QCA::minimize() from the QCA package to perform standard QCA analysis. Results are aggregated across all thresholds and returned as an S3 object containing both a summary table for cross-threshold comparison and detailed results for each threshold.