ThSQCA Reproducible Code (English)

In ThSQCA: Threshold-Sweep QCA

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

This document provides reproducible code for ThSQCA analyses.
It is designed to be inserted directly into a research article's appendix
or provided as supplementary analysis documentation. All code is fully executable and ordered for reproducibility.

Note (v1.3.2): New Section 12 provides complete reproducible code for Fiss (2011) core/peripheral classification using compute_fiss_core(), generate_fiss_chart(), and print_fiss_summary().

Note (v1.2.0): If you previously used intermediate solutions (with dir.exp), please re-run your analyses. Version 1.2.0 fixed a bug where intermediate solutions were incorrectly extracted. Reports now also display the Solution Type and include optional QCA package output for verification.

---

1. Load Packages

library(ThSQCA)
library(QCA)

---

2. Load Data

# Adjust the file name as needed
library(ThSQCA)
data("sample_data")
dat <- sample_data

# Outcome and conditions
outcome  <- "Y"
conditions <- c("X1", "X2", "X3")

# Quick inspection
str(dat)
summary(dat)

---

3. Baseline Thresholds

thrY_base <- 7
thrX_base <- 7

# Fixed X thresholds (for OTS)
thrX_vec <- c(
  X1 = thrX_base,
  X2 = thrX_base,
  X3 = thrX_base
)
thrX_vec

---

3.5. Three Types of QCA Solutions (New in v1.1.0)

As of v1.1.0, ThSQCA defaults match the QCA package:

| Solution Type | include | dir.exp | When to Use | |--------------|-----------|-----------|-------------| | Complex (default) | "" | NULL | Conservative analysis | | Parsimonious | "?" | NULL | Maximum simplification | | Intermediate | "?" | c(1,1,...) | Theory-driven (most common) |

# Example: Three solution types at single threshold
thrX <- c(X1 = 7, X2 = 7, X3 = 7)

# Complex (default)
res_comp <- otSweep(dat, "Y", c("X1", "X2", "X3"), sweep_range = 7, thrX = thrX)
cat("Complex:", res_comp$summary$expression, "\n")

# Parsimonious
res_pars <- otSweep(dat, "Y", c("X1", "X2", "X3"), sweep_range = 7, thrX = thrX,
                    include = "?")
cat("Parsimonious:", res_pars$summary$expression, "\n")

# Intermediate
res_int <- otSweep(dat, "Y", c("X1", "X2", "X3"), sweep_range = 7, thrX = thrX,
                   include = "?", dir.exp = c(1, 1, 1))
cat("Intermediate:", res_int$summary$expression, "\n")

---

4. CTS, single condition (ctSweepS)

Sweep a single condition X (example: X3).

Default: Complex Solution

sweep_var   <- "X3"   # Condition (X) whose threshold is swept
sweep_range <- 6:9    # Candidate threshold values to evaluate
thrY         <- 7     # Outcome (Y) threshold (fixed)
thrX_default <- 7     # Threshold for other X conditions (fixed)

# Default: Complex solution (include = "", dir.exp = NULL)
res_cts <- ctSweepS(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_var      = "X3",
  sweep_range    = 6:9,
  thrY           = 7,
  thrX_default   = 7,
  return_details = TRUE
)

summary(res_cts)

Intermediate Solution (Theory-Driven)

# Intermediate solution: specify include = "?" and dir.exp
res_cts_int <- ctSweepS(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_var      = "X3",
  sweep_range    = 6:9,
  thrY           = 7,
  thrX_default   = 7,
  include        = "?",
  dir.exp        = c(1, 1, 1),
  return_details = TRUE
)

summary(res_cts_int)

Export:

write.csv(res_cts$summary, file = "ThSQCA_CTS_results.csv", row.names = FALSE)

---

5. CTS, multiple conditions (ctSweepM)

Sweep multiple X thresholds simultaneously.

Default: Complex Solution

# Create a sweep list specifying thresholds for each condition
sweep_list <- list(
  X1 = 6:7,
  X2 = 6:7,
  X3 = 6:7
)

# Default: Complex solution
res_mcts <- ctSweepM(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_list     = sweep_list,
  thrY           = 7,
  return_details = TRUE
)

summary(res_mcts)

Intermediate Solution (Theory-Driven)

# Intermediate solution: specify include = "?" and dir.exp
res_mcts_int <- ctSweepM(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_list     = sweep_list,
  thrY           = 7,
  include        = "?",
  dir.exp        = c(1, 1, 1),
  return_details = TRUE
)

summary(res_mcts_int)

Export:

write.csv(res_mcts$summary, file = "ThSQCA_CTS_multi_results.csv", row.names = FALSE)

---

6. OTS (otSweep)

Sweep only the outcome threshold (Y).

Default: Complex Solution

sweep_range_ots <- 6:8

# Default: Complex solution
res_ots <- otSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_range    = sweep_range_ots,
  thrX           = thrX_vec,
  return_details = TRUE
)

summary(res_ots)

Intermediate Solution (Theory-Driven)

# Intermediate solution: specify include = "?" and dir.exp
res_ots_int <- otSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_range    = sweep_range_ots,
  thrX           = thrX_vec,
  include        = "?",
  dir.exp        = c(1, 1, 1),
  return_details = TRUE
)

summary(res_ots_int)

Export:

write.csv(res_ots$summary, file = "ThSQCA_OTS_results.csv", row.names = FALSE)

---

7. DTS (dtSweep)

Two-dimensional sweep: X thresholds × Y thresholds.

Default: Complex Solution

sweep_list_dts_X <- list(
  X1 = 6:7,
  X2 = 6:7,
  X3 = 6:7
)

sweep_range_dts_Y <- 6:7

# Default: Complex solution
res_dts <- dtSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_list_X   = sweep_list_dts_X,
  sweep_range_Y  = sweep_range_dts_Y,
  dir.exp        = c(1, 1, 1),
  return_details = TRUE
)

summary(res_dts)

Intermediate Solution (Theory-Driven)

# Intermediate solution: specify include = "?" and dir.exp
res_dts_int <- dtSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_list_X   = sweep_list_dts_X,
  sweep_range_Y  = sweep_range_dts_Y,
  include        = "?",
  dir.exp        = c(1, 1, 1),
  return_details = TRUE
)

summary(res_dts_int)

Export:

write.csv(res_dts$summary, file = "ThSQCA_DTS_results.csv", row.names = FALSE)

---

8. Using extract_mode (New in v0.2.0)

Extract all solutions or essential prime implicants for robustness analysis.

Extract All Solutions

res_all <- otSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_range    = 6:8,
  thrX           = thrX_vec,
  include        = "?",           # Include logical remainders
  dir.exp        = c(1, 1, 1),    # Intermediate solution
  extract_mode   = "all",
  return_details = TRUE
)

# View results with n_solutions column
head(res_all$summary)

Extract Essential Prime Implicants

res_essential <- otSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_range    = 6:8,
  thrX           = thrX_vec,
  include        = "?",           # Include logical remainders
  dir.exp        = c(1, 1, 1),    # Intermediate solution
  extract_mode   = "essential",
  return_details = TRUE
)

# View results with essential prime implicants, selective terms, and unique terms
head(res_essential$summary)

---

9. Generating Reports (New in v0.2.0)

Create comprehensive markdown reports for documentation.

Full Report

generate_report(res_ots, "ThSQCA_OTS_report_full.md", dat = dat, format = "full")

Simple Report (for manuscripts)

generate_report(res_ots, "ThSQCA_OTS_report_simple.md", dat = dat, format = "simple")

---

10. Negated Outcome Analysis (New in v0.3.0)

Analyze conditions sufficient for the absence of the outcome.

Standard vs Negated Outcome

# Standard: conditions for Y >= threshold (intermediate solution)
res_Y <- otSweep(
  dat            = dat,
  outcome        = "Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_range    = 6:8,
  thrX           = thrX_vec,
  include        = "?",           # Include logical remainders
  dir.exp        = c(1, 1, 1)     # Intermediate solution
)

# Negated: conditions for Y < threshold (intermediate solution)
res_negY <- otSweep(
  dat            = dat,
  outcome        = "~Y",
  conditions     = c("X1", "X2", "X3"),
  sweep_range    = 6:8,
  thrX           = thrX_vec,
  include        = "?",           # Include logical remainders
  dir.exp        = c(1, 1, 1)     # Intermediate solution
)

# Compare results
res_Y$summary
res_negY$summary

# Check negation flag
res_negY$params$negate_outcome
# [1] TRUE

---

11. Accessing Analysis Parameters

All parameters are stored for reproducibility.

# View stored parameters
res_ots$params

# Example output:
# $outcome
# [1] "Y"
# $conditions
# [1] "X1" "X2" "X3"
# $thrX
# X1 X2 X3 
#  7  7  7 
# $incl.cut
# [1] 0.8
# $n.cut
# [1] 1
# $pri.cut
# [1] 0

---

Configuration Charts (New in v0.5.0)

Configuration charts are now automatically included in reports. You can also generate them separately:

# From path strings
paths <- c("A*B*~C", "A*D")
chart <- config_chart_from_paths(paths)
cat(chart)

For reports:

# Charts are included by default
generate_report(result, "report.md", dat = dat, format = "full")

# Use LaTeX symbols for academic papers
generate_report(result, "report.md", dat = dat, chart_symbol_set = "latex")

---

References

For more information on ThS-QCA methodology, see:

• Ragin, C. C. (2008). Redesigning Social Inquiry: Fuzzy Sets and Beyond. University of Chicago Press. DOI: 10.7208/chicago/9780226702797.001.0001
• Duşa, A. (2019). QCA with R: A Comprehensive Resource. Springer. DOI: 10.1007/978-3-319-75668-4
• Oana, I.-E., & Schneider, C. Q. (2024). A Robustness Test Protocol for Applied QCA: Theory and R Software Application. Sociological Methods & Research, 53(1), 57–88. DOI: 10.1177/00491241211036158

---

12. Fiss (2011) Core/Peripheral Classification (New in v1.3.2)

This section provides fully reproducible code for Fiss-style four-symbol configuration charts. Run sections 1–6 first to ensure res_ots_int is available.

12.1 Compute Core/Peripheral Classification

# Requires: include = "?", dir.exp specified, return_details = TRUE
# res_ots_int was created in Section 6 above.

res_fiss <- compute_fiss_core(
  res_ots_int,
  conditions = c("X1", "X2", "X3")
)

# Inspect available thresholds
names(res_fiss$fiss_core)

12.2 Print Per-Threshold Summary

# English
print_fiss_summary(res_fiss, thr_key = "7")

# Japanese
print_fiss_summary(res_fiss, thr_key = "7", language = "ja")

Output (ThSQCA 2.0.8, QCA 3.25):

=== Fiss Core/Peripheral Classification (thrY = 7) ===
Parsimonious : X3 + X1*X2
Intermediate : X3 + X1*X2

[Term T1]  X3
  Core present    :  X3

[Term T2]  X1*X2
  Core present    :  X1, X2

Here the parsimonious and intermediate solutions coincide, so every condition is core. In general, each term of the intermediate solution is compared with the parsimonious term(s) contained in it: their conditions are core and the other conditions of the term are peripheral, as in the solution tables of Fiss (2011). See the section "Relation to Fiss (2011)" in ?compute_fiss_core for tied parsimonious solutions and other details. compute_fiss_core() accepts results of otSweep() and ctSweepS().

12.3 Generate Four-Symbol Chart

# Unicode (Markdown / screen)
cat(generate_fiss_chart(res_fiss, symbol_set = "unicode"))

# LaTeX (for PDF/journal submission)
cat(generate_fiss_chart(res_fiss, symbol_set = "latex"))

# ASCII (maximum compatibility)
cat(generate_fiss_chart(res_fiss, symbol_set = "ascii"))

Symbol legend:

| Symbol (unicode) | LaTeX | ASCII | Meaning | |-----------------|-------|-------|---------| | ● | $\bullet$ | O | Core condition present | | ⊗ | $\otimes$ | X | Core condition absent | | ⊙ | $\odot$ | o | Peripheral condition present | | ⊘ | $\oslash$ | x | Peripheral condition absent | | (blank) | (blank) | (blank) | Don't care |

12.4 Include in Report

# Full report with Fiss four-symbol charts
generate_report(
  res_fiss,
  output_file       = "ThSQCA_Fiss_report.md",
  format            = "full",
  dat               = dat,
  include_fiss_core = TRUE,       # activates four-symbol charts
  chart_symbol_set  = "unicode",
  include_raw_output = TRUE
)

12.5 Accessing the Classification Data

# Access raw classification data frame for a given threshold
classif_7 <- res_fiss$fiss_core[["7"]]$classification
classif_7

# Filter core conditions only
classif_7[classif_7$type == "core" & classif_7$status != "dontcare", ]

# Filter peripheral conditions only
classif_7[classif_7$type == "peripheral" & classif_7$status != "dontcare", ]

# Parsimonious and intermediate expressions
res_fiss$fiss_core[["7"]]$parsim_expression
res_fiss$fiss_core[["7"]]$interm_expression

12.6 Note on Computational Cost

compute_fiss_core() runs QCA::minimize() once per threshold (to count the tied parsimonious solutions, and as a fallback when the stored solution does not record its derivation). The total computation time is therefore approximately double that of the original sweep. For large sweeps (many thresholds or conditions), this is worth keeping in mind.

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13. Session Information

sessionInfo()

ThSQCA documentation built on Sept. 26, 2026, 5:07 p.m.