efa_power.md
In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

printed output is stable

Code
  print(efa_power(df = 100, N = 200))
Output

  -- RMSEA power analysis --------------------------------------------------------

  Test of close fit: H0 RMSEA ≤ .050 vs. H1 RMSEA = .080.
  alpha = .050 · df = 100

  Power = .955 at N = 200.
  Critical value χ²(100) = 183.967 · noncentrality H0 = 49.750, H1 = 127.360.

Code
  print(efa_power(df = 100, power = 0.8))
Output

  -- RMSEA power analysis --------------------------------------------------------

  Test of close fit: H0 RMSEA ≤ .050 vs. H1 RMSEA = .080.
  alpha = .050 · df = 100

  Required N = 132 for a power of .800 (achieved .802).
  Critical value χ²(100) = 163.977 · noncentrality H0 = 32.750, H1 = 83.840.

Code
  print(efa_power(df = 100, N = 200, type = "notclose", group = 2))
Output

  -- RMSEA power analysis --------------------------------------------------------

  Test of not-close fit: H0 RMSEA ≥ .050 vs. H1 RMSEA = .010.
  alpha = .050 · df = 100 · groups = 2

  Power = .429 at N = 200 (total; 100 per group).
  Critical value χ²(100) = 97.795 · noncentrality H0 = 24.875, H1 = .995.

a criterion that fails on every replicate is reported, not dropped

Code
  print(sim)
Output

  -- EFA power simulation --------------------------------------------------------

  18 variables · 3 factors · N = 6 · 3 datasets
  Estimation: PAF · rotation: varimax
  Model error: none. The population is exact, so the hit-rate and recovery are
  optimistic; set `target_rmsea` for realism.

  Retention hit-rate P(k-hat = 3)
  * MAP: NA (n = 0)

  Structure recovery (Tucker congruence ≥ .950)
  * recovery rate (min congruence): NA (n = 0)
  * recovery rate (mean congruence): NA (n = 0)
  * median min congruence: NA

  Convergence
  * fits completed: .000 (0/3)
  * converged (of completed): NA
  * Heywood cases (of completed): NA

simulation-mode printed output is stable

Code
  print(sim)
Output

  -- EFA power simulation --------------------------------------------------------

  18 variables · 3 factors · N = 200 · 10 datasets
  Estimation: PAF · rotation: promax
  Model error: none. The population is exact, so the hit-rate and recovery are
  optimistic; set `target_rmsea` for realism.

  Retention hit-rate P(k-hat = 3)
  * EKC_BvA2017: <num> (n = 10)
  * MAP_TR2: <num> (n = 10)
  * MAP_TR4: <num> (n = 10)

  Structure recovery (Tucker congruence ≥ <num>)
  * recovery rate (min congruence): <num> (n = 10)
  * recovery rate (mean congruence): <num> (n = 10)
  * median min congruence: <num>

  Convergence
  * fits completed: <num> (10/10)
  * converged (of completed): <num>
  * Heywood cases (of completed): <num>