fix(aefa): 현행 mirt 모델 선택 수식과 종료성 복원

R/kaefa-package.r

@@ -22,10 +22,12 @@
 #'
 #' The kaefa may inspect this issues from the MMMM or MM
 #' in statistical learning theory perspectives using model
-#' selection criteria like the DIC (Kang, 2008; Kang, Cohen, & Sung, 2009;
-#' Jiao, Kamata, Wang, & Jin, 2012; Jiao & Zhang, 2015) with maximising
-#' generalisability of the number of factor decisions in every calibration
-#' (Kang, 2008; Preacher, Zhang, Kim, & Mels, 2013).
+#' likelihood-based model-selection criteria such as AIC, AICc, BIC, and
+#' sample-size-adjusted BIC. Posterior DIC (Spiegelhalter et al., 2002) is
+#' accepted only when the fitted model actually supplies it; DIC is not
+#' reconstructed from AIC. These criteria support generalisable factor-count
+#' decisions in each calibration (Kang, 2008; Preacher, Zhang, Kim, & Mels,
+#' 2013).
 #'
 #' If researcher provide of demographical information in kaefa,
 #' kaefa will inspect the optimal number of factor and optimal IRT model,

README.Rmd

@@ -22,7 +22,7 @@ The goal of kaefa is to improve researchers' ability to identify unexplained fac
 The automated exploratory factor analysis (aefa) framework implements a **greedy search algorithm** to efficiently explore the model space and find improved model configurations. The algorithm iteratively:
 
 1. Evaluates multiple model candidates with different factor structures and item response models
-2. Selects the best model based on information criteria (DIC, AIC, BIC, etc.)
+2. Selects the best model using AIC by default, with AICc, BIC, and sample-size-adjusted BIC available. DIC is used only when a fitted model actually supplies posterior DIC; it is never approximated with AIC.
 3. Assesses item fit and removes poorly fitting items one at a time
 4. Re-estimates the model until convergence to a locally optimal solution
 
@@ -32,6 +32,8 @@ This greedy approach enables efficient exploration of the model space while seek
 
 - Preacher, K. J., Zhang, G., Kim, C., & Mels, G. (2013). Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective. Multivariate Behavioral Research, 48(1), 28-56. https://doi.org/10.1080/00273171.2012.710386
 - Jennrich, R. I., & Bentler, P. M. (2011). Exploratory bi-factor analysis. Psychometrika, 76(4), 537-549. https://doi.org/10.1007/s11336-011-9218-4
+- Hurvich, C. M., & Tsai, C.-L. (1989). Regression and time series model selection in small samples. Biometrika, 76(2), 297-307. https://doi.org/10.1093/biomet/76.2.297
+- Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B, 64(4), 583-639. https://doi.org/10.1111/1467-9868.00353
 
 ## Installation
 

README.md

@@ -18,8 +18,9 @@ find improved model configurations. The algorithm iteratively:
 
 1.  Evaluates multiple model candidates with different factor structures
     and item response models
-2.  Selects the best model based on information criteria (DIC, AIC, BIC,
-    etc.)
+2.  Selects the best model using AIC by default, with AICc, BIC, and
+    sample-size-adjusted BIC available. DIC is used only when a fitted model
+    actually supplies posterior DIC; it is never approximated with AIC.
 3.  Assesses item fit and removes poorly fitting items one at a time
 4.  Re-estimates the model until convergence to a locally optimal
     solution
@@ -38,6 +39,13 @@ research (Preacher, Zhang, Kim, & Mels, 2013; Jennrich & Bentler, 2011).
 - Jennrich, R. I., & Bentler, P. M. (2011). Exploratory bi-factor
   analysis. Psychometrika, 76(4), 537-549.
   <https://doi.org/10.1007/s11336-011-9218-4>
+- Hurvich, C. M., & Tsai, C.-L. (1989). Regression and time series model
+  selection in small samples. Biometrika, 76(2), 297-307.
+  <https://doi.org/10.1093/biomet/76.2.297>
+- Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A.
+  (2002). Bayesian measures of model complexity and fit. Journal of the
+  Royal Statistical Society: Series B, 64(4), 583-639.
+  <https://doi.org/10.1111/1467-9868.00353>
 
 ## Installation
 

docs/papers/README.md

@@ -86,10 +86,43 @@ cited with its DOI. Open-access / preprint links are noted where available.
 
   Both have expectation 1 under good fit.
 
+## 5. Corrected Akaike information criterion (`AICc`)
+
+- **Source:** Hurvich, C. M., & Tsai, C.-L. (1989). Regression and time series
+  model selection in small samples. *Biometrika, 76*(2), 297-307.
+  DOI: [10.1093/biomet/76.2.297](https://doi.org/10.1093/biomet/76.2.297)
+- **Canonical equation.** For maximized log-likelihood `logLik`, parameter count
+  `k`, and sample size `n`:
+
+      AIC  = -2 * logLik + 2 * k
+      AICc = AIC + 2 * k * (k + 1) / (n - k - 1)
+
+  Current `mirt` fits supply `AIC` and `logLik` but do not consistently expose
+  `AICc`. Kaefa therefore recovers `k = (AIC + 2 * logLik) / 2` and applies the
+  correction exactly. The statistic is undefined when `n <= k + 1`; kaefa
+  reports that reason rather than returning a fabricated finite score.
+
+## 6. Deviance information criterion (`DIC`) boundary
+
+- **Source:** Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde,
+  A. (2002). Bayesian measures of model complexity and fit. *Journal of the
+  Royal Statistical Society: Series B, 64*(4), 583-639.
+  DOI: [10.1111/1467-9868.00353](https://doi.org/10.1111/1467-9868.00353)
+- **Canonical equation.** With posterior mean deviance `Dbar`, deviance at the
+  posterior mean parameters `D(theta_bar)`, and effective parameter count `pD`:
+
+      pD  = Dbar - D(theta_bar)
+      DIC = Dbar + pD
+
+  DIC is a posterior-deviance criterion. The maximum-likelihood/MAP models
+  produced by current `mirt` versions do not expose the posterior quantities
+  needed to reconstruct it. Kaefa accepts DIC only when the fitted model
+  supplies a finite DIC value and never relabels AIC as DIC.
+
 ## Audit note
 
 kaefa does **not** re-implement `P(theta)`, the MML-EM E-/M-step, `S-X2`, `infit`,
-or `outfit`; those are delegated verbatim to `mirt` and are therefore correct by
-construction (subject to `mirt`'s own validation). The only package-local numeric
-formulas are the fit-based **decision rules** documented above; the `Zh` rule is
-the one that had drifted out of internal consistency and has been restored.
+or `outfit`; those are delegated verbatim to `mirt` and remain subject to
+`mirt`'s validation. Package-local formulas and decision rules are pinned above:
+the `Zh` cutoff, the exact Hurvich-Tsai AICc correction, and the explicit
+posterior-information boundary that prevents DIC from being fabricated.

inst/WORDLIST

@@ -25,6 +25,7 @@
 18637
 20
 200
+2002
 2008
 2009
 2011
@@ -102,6 +103,7 @@ Kang
 LAN
 LCA
 Leiman
+MAP
 MH
 MHRM
 MIRT

inst/shiny-app/README.md

@@ -29,7 +29,7 @@ launchAEFA()
 2. **Configure Model**:
    - Set minimum and maximum number of factors to explore
    - Choose rotation method (bifactorQ recommended for most cases)
-   - Select model selection criteria (DIC is default)
+   - Select model selection criteria (AIC is default for mirt ML/MAP fits)
    - Optionally enable model history saving to inspect candidate models
 
 3. **Run Analysis**: Click the "Run Analysis" button
@@ -56,7 +56,9 @@ following inputs and pass them to `aefa()`:
 - **Rotation method**: select input mapped to `rotate` (e.g., `bifactorQ`,
   `geominQ`, `oblimin`).
 - **Model selection criteria**: select input mapped to
-  `modelSelectionCriteria` (e.g., `DIC`, `AIC`, `AICc`, `BIC`, `saBIC`).
+  `modelSelectionCriteria` (e.g., `AIC`, `AICc`, `BIC`, `saBIC`). DIC is an
+  API-only option and requires a fitted model that actually supplies posterior
+  DIC; the application never substitutes AIC for it.
 - **Model history toggle**: checkbox mapped to `saveModelHistory` (recommended
   for inspecting candidate models).
 

inst/shiny-app/app.R

@@ -53,8 +53,8 @@ ui <- fluidPage(
                   selected = "bifactorQ"),
 
       selectInput("modelSelection", "Model Selection Criteria:",
-                  choices = c("DIC", "AIC", "AICc", "BIC", "SABIC"),
-                  selected = "DIC"),
+                  choices = c("AIC", "AICc", "BIC", "SABIC"),
+                  selected = "AIC"),
 
       checkboxInput("saveHistory", "Save Model History", TRUE),
 
@@ -139,7 +139,7 @@ ui <- fluidPage(
                  tags$ul(
                    tags$li(strong("Minimum/Maximum Factors:"), "Set the range of factors to explore. The algorithm will test models with different numbers of factors and select the best one."),
                    tags$li(strong("Rotation Method:"), "Choose the rotation method for factor loadings. 'bifactorQ' is recommended for most cases."),
-                   tags$li(strong("Model Selection Criteria:"), "Choose the criteria for selecting the best model. 'DIC' (Deviance Information Criterion) is the default.")
+                   tags$li(strong("Model Selection Criteria:"), "Choose the criterion for selecting the best model. AIC is the default for the maximum-likelihood/MAP models fitted by mirt; AICc applies the finite-sample correction.")
                  ),
 
                  h4("Step 3: Run the Analysis"),

tests/testthat/helper-test-data.R

@@ -80,7 +80,16 @@ create_binary_test_data <- function(n_items = 10, n_obs = 100) {
 }
 
 .merge_test_defaults <- function(defaults, dots) {
-  utils::modifyList(defaults, dots)
+  dot_names <- names(dots)
+  if (is.null(dot_names)) {
+    dot_names <- rep("", length(dots))
+  }
+
+  is_named <- !is.na(dot_names) & nzchar(dot_names)
+  positional <- dots[!is_named]
+  named <- dots[is_named]
+
+  c(positional, utils::modifyList(defaults, named))
 }
 
 .skip_expensive_ci_calls <- function(function_name) {

tests/testthat/test-aefa-advanced-parameters.R

@@ -4,6 +4,8 @@
 
 context("AEFA Advanced Parameter Interactions and Combinations")
 
+.ensure_kaefa_namespace()
+
 expect_valid_aefa <- function(result) {
   expect_false(inherits(result, "try-error"))
   expect_s3_class(result, "aefa")
@@ -15,16 +17,15 @@ expect_valid_aefa <- function(result) {
 # Test Suite 1: Model Selection Criteria Variations
 # ============================================================
 
-test_that("aefa respects different model selection criteria - DIC", {
-  test_data <- create_test_data(n_items = 5, n_obs = 100)
-
-  result <- try(aefa(test_data, 
-                     minExtraction = 1, 
-                     maxExtraction = 1,
-                     modelSelectionCriteria = "DIC"), 
-                silent = TRUE)
-
-  expect_valid_aefa(result)
+test_that("DIC is not fabricated for mirt ML/MAP fits", {
+  expect_error(
+    kaefa:::.aefaFitCriterionValue(
+      list(AIC = 120, logLik = -50),
+      criterion = "DIC",
+      sample_size = 100
+    ),
+    "posterior deviance draws.*never replaced by AIC"
+  )
 })
 
 test_that("aefa respects different model selection criteria - AIC", {

tests/testthat/test-aefa-greedy-algorithm.R

@@ -90,7 +90,7 @@ test_that("aefa greedy search evaluates model candidates", {
       expect_true(is.list(result$itemFitTrials))
       last_model <- result$estModelTrials[[length(result$estModelTrials)]]
       if (isS4(last_model) && "Fit" %in% slotNames(last_model)) {
-        fit_values <- c(last_model@Fit$AIC, last_model@Fit$BIC, last_model@Fit$DIC)
+        fit_values <- c(last_model@Fit$AIC, last_model@Fit$BIC, last_model@Fit$SABIC)
         expect_true(any(is.finite(fit_values)),
                     info = "Selected model should include information criteria values")
       }
@@ -107,7 +107,7 @@ test_that("aefa greedy search evaluates model candidates", {
 test_that("aefa uses information criteria for model selection", {
   test_data <- create_test_data(n_items = 6, n_obs = 100)
 
-  # The function should select best model based on DIC, AIC, BIC, etc.
+  # The function should select the best model using a criterion supplied by mirt.
   result <- try(aefa(test_data, minExtraction = 1, maxExtraction = 2), silent = TRUE)
 
   if (!inherits(result, "try-error") && !is.null(result)) {

tests/testthat/test-model-selection-criteria.R

@@ -0,0 +1,68 @@
+.ensure_kaefa_namespace()
+
+test_that("AICc preserves the Hurvich-Tsai small-sample correction", {
+  fit <- list(AIC = 120, logLik = -50)
+  parameter_count <- 10
+  expected <- 120 + (2 * parameter_count * (parameter_count + 1)) /
+    (100 - parameter_count - 1)
+
+  expect_equal(
+    kaefa:::.aefaFitCriterionValue(fit, "AICc", sample_size = 100),
+    expected,
+    tolerance = 1e-12
+  )
+})
+
+test_that("model-supplied criteria are preserved exactly", {
+  fit <- list(AIC = 120, AICc = 123.5, BIC = 140, SABIC = 130, DIC = 117.25)
+
+  expect_identical(kaefa:::.aefaFitCriterionValue(fit, "AIC", 100), 120)
+  expect_identical(kaefa:::.aefaFitCriterionValue(fit, "AICc", 100), 123.5)
+  expect_identical(kaefa:::.aefaFitCriterionValue(fit, "BIC", 100), 140)
+  expect_identical(kaefa:::.aefaFitCriterionValue(fit, "saBIC", 100), 130)
+  expect_identical(kaefa:::.aefaFitCriterionValue(fit, "DIC", 100), 117.25)
+})
+
+test_that("invalid information-criterion substitutions fail visibly", {
+  fit <- list(AIC = 120, logLik = -50)
+
+  expect_error(
+    kaefa:::.aefaFitCriterionValue(fit, "DIC", 100),
+    "DIC is unavailable"
+  )
+  expect_error(
+    kaefa:::.aefaFitCriterionValue(fit, "CAIC", 100),
+    "not an alias for corrected AIC"
+  )
+  expect_error(
+    kaefa:::.aefaFitCriterionValue(fit, "AICc", 11),
+    "AICc is undefined"
+  )
+})
+
+test_that("candidate selection retains original indices after skipped fits", {
+  expect_identical(kaefa:::.aefaBestScoreIndex(c(Inf, 20, 10)), 3L)
+  expect_identical(kaefa:::.aefaBestScoreIndex(c(NA, Inf)), NA_integer_)
+})
+
+test_that("item exclusions require a new name present in the fitted model", {
+  expect_identical(
+    kaefa:::.aefaValidNewItemExclusions(
+      excluded = "Item1",
+      proposed = c("Item1", "Item2", "missing", NA_character_),
+      available = c("Item1", "Item2", "Item3")
+    ),
+    "Item2"
+  )
+  expect_identical(
+    kaefa:::.aefaValidNewItemExclusions("Item1", "Item1", c("Item1", "Item2")),
+    character()
+  )
+})
+
+test_that("local worker selection survives unavailable CPU telemetry", {
+  expect_identical(kaefa:::.aefaParallelProcessorCount(NULL, 12), 4L)
+  expect_identical(kaefa:::.aefaParallelProcessorCount(c(10, 20), 12), 4L)
+  expect_identical(kaefa:::.aefaParallelProcessorCount(5, 12), 1L)
+  expect_identical(kaefa:::.aefaParallelProcessorCount(80, NA_real_), 1L)
+})

tests/testthat/test-shiny-app.R

@@ -191,7 +191,7 @@ test_that("Model selection criteria choices are valid", {
   ui_html <- as.character(ui)
 
   # Check for expected model selection criteria
-  expected_criteria <- c("DIC", "AIC", "AICc", "BIC", "SABIC")
+  expected_criteria <- c("AIC", "AICc", "BIC", "SABIC")
 
   for (criterion in expected_criteria) {
     expect_true(

tests/testthat/test-test-bootstrap-contract.R

@@ -31,3 +31,17 @@ test_that("test file lookup uses explicit base package helpers", {
     perl = TRUE
   ))
 })
+
+test_that("test defaults preserve positional data and override named options", {
+  data_arg <- data.frame(item = 1:3)
+
+  merged <- .merge_test_defaults(
+    list(NCYCLES = 120, BURNIN = 40),
+    list(data_arg, BURNIN = 10)
+  )
+
+  expect_identical(merged[[1]], data_arg)
+  expect_identical(names(merged)[[1]], "")
+  expect_identical(merged$NCYCLES, 120)
+  expect_identical(merged$BURNIN, 10)
+})