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

a whole retention object as n_factors names the component that holds the counts

Code
  cat(bad_n_factors(ret))
Output
  `n_factors` must be a single count, not an <efa_retain> object.
  i Its `$n_factors` holds 3 suggested counts; supply one of them.

Code
  cat(bad_n_factors(suppressMessages(efa_ekc(cm, N = 500))))
Output
  `n_factors` must be a single count, not an <efa_retention> object.
  i Its `$n_factors` holds 1 suggested count; supply it.

print.efa output is stable (PAF, promax)

Code
  print(efa_psych)
Output

  EFA performed with estimator = 'PAF' and rotation = 'promax'.

  -- Rotated Loadings ------------------------------------------------------------

         F1     F2     F3    h2    u2
  V1 <num> <num> <num> <num> <num>
  V2 <num> <num> <num> <num> <num>
  V3 <num> <num> <num> <num> <num>
  V4 <num> <num> <num> <num> <num>
  V5 <num> <num> <num> <num> <num>
  V6 <num> <num> <num> <num> <num>
  V7 <num> <num> <num> <num> <num>
  V8 <num> <num> <num> <num> <num>
  V9 <num> <num> <num> <num> <num>
  V10 <num> <num> <num> <num> <num>
  V11 <num> <num> <num> <num> <num>
  V12 <num> <num> <num> <num> <num>
  V13 <num> <num> <num> <num> <num>
  V14 <num> <num> <num> <num> <num>
  V15 <num> <num> <num> <num> <num>
  V16 <num> <num> <num> <num> <num>
  V17 <num> <num> <num> <num> <num>
  V18 <num> <num> <num> <num> <num>

  -- Factor Intercorrelations ----------------------------------------------------

        F1 F2 F3
  F1 <num>
  F2 <num> <num>
  F3 <num> <num> <num>

  -- Variances Accounted for -----------------------------------------------------

                       F1 F2 F3
  SS loadings <num> <num> <num>
  Prop Tot Var <num> <num> <num>
  Cum Prop Tot Var <num> <num> <num>
  Prop Comm Var <num> <num> <num>
  Cum Prop Comm Var <num> <num> <num>

  -- Model Fit -------------------------------------------------------------------

  CAF: <num>
  SRMR: <num>
  df: 102

print.efa output is stable (ML, promax)

Code
  print(efa_ml_moderate)
Output

  EFA performed with estimator = 'ML' and rotation = 'promax'.

  -- Rotated Loadings ------------------------------------------------------------

        F1    F2    F3    h2    u2
  V1 <num> <num> <num> <num> <num>
  V2 <num> <num> <num> <num> <num>
  V3 <num> <num> <num> <num> <num>
  V4 <num> <num> <num> <num> <num>
  V5 <num> <num> <num> <num> <num>
  V6 <num> <num> <num> <num> <num>
  V7 <num> <num> <num> <num> <num>
  V8 <num> <num> <num> <num> <num>
  V9 <num> <num> <num> <num> <num>
  V10 <num> <num> <num> <num> <num>
  V11 <num> <num> <num> <num> <num>
  V12 <num> <num> <num> <num> <num>
  V13 <num> <num> <num> <num> <num>
  V14 <num> <num> <num> <num> <num>
  V15 <num> <num> <num> <num> <num>
  V16 <num> <num> <num> <num> <num>
  V17 <num> <num> <num> <num> <num>
  V18 <num> <num> <num> <num> <num>

  -- Factor Intercorrelations ----------------------------------------------------

        F1 F2 F3
  F1 <num>
  F2 <num> <num>
  F3 <num> <num> <num>

  -- Variances Accounted for -----------------------------------------------------

                       F1 F2 F3
  SS loadings <num> <num> <num>
  Prop Tot Var <num> <num> <num>
  Cum Prop Tot Var <num> <num> <num>
  Prop Comm Var <num> <num> <num>
  Cum Prop Comm Var <num> <num> <num>

  -- Model Fit -------------------------------------------------------------------

  χ²(102) = <num>, p = <num>
  CFI: <num>
  TLI: <num>
  RMSEA [90% CI]: <num> [ <num>; <num>]
  AIC: <num>
  BIC: <num>
  ECVI: <num>
  CAF: <num>
  SRMR: <num>

summary.efa output is stable (PAF, promax)

Code
  print(summary(efa_psych))
Output

  EFA performed with estimator = 'PAF' and rotation = 'promax'.

  -- Model Diagnostics -----------------------------------------------------------

  Factors: 3
  Variables: 18
  N: 500
  Heywood cases: 0
  Cross-loading items (|loading| >= <num>): 0
  Items without salient loading (|loading| >= <num>): 0
  Factors with fewer than 3 salient indicators: 0
  Items with primary-loading gap < <num>: 1
  Largest |residual|: <num>
  Factor intercorrelations > <num>: none

  -- Rotated Loadings ------------------------------------------------------------

         F1     F2     F3    h2    u2
  V1 <num> <num> <num> <num> <num>
  V2 <num> <num> <num> <num> <num>
  V3 <num> <num> <num> <num> <num>
  V4 <num> <num> <num> <num> <num>
  V5 <num> <num> <num> <num> <num>
  V6 <num> <num> <num> <num> <num>
  V7 <num> <num> <num> <num> <num>
  V8 <num> <num> <num> <num> <num>
  V9 <num> <num> <num> <num> <num>
  V10 <num> <num> <num> <num> <num>
  V11 <num> <num> <num> <num> <num>
  V12 <num> <num> <num> <num> <num>
  V13 <num> <num> <num> <num> <num>
  V14 <num> <num> <num> <num> <num>
  V15 <num> <num> <num> <num> <num>
  V16 <num> <num> <num> <num> <num>
  V17 <num> <num> <num> <num> <num>
  V18 <num> <num> <num> <num> <num>

  -- Factor Intercorrelations ----------------------------------------------------

        F1 F2 F3
  F1 <num>
  F2 <num> <num>
  F3 <num> <num> <num>

  -- Structure Matrix ------------------------------------------------------------

        F1 F2 F3
  V1 <num> <num> <num>
  V2 <num> <num> <num>
  V3 <num> <num> <num>
  V4 <num> <num> <num>
  V5 <num> <num> <num>
  V6 <num> <num> <num>
  V7 <num> <num> <num>
  V8 <num> <num> <num>
  V9 <num> <num> <num>
  V10 <num> <num> <num>
  V11 <num> <num> <num>
  V12 <num> <num> <num>
  V13 <num> <num> <num>
  V14 <num> <num> <num>
  V15 <num> <num> <num>
  V16 <num> <num> <num>
  V17 <num> <num> <num>
  V18 <num> <num> <num>

  -- Simple Structure Diagnostics ------------------------------------------------

  Items with primary-loading gap < <num>:
  * V11: F2 = <num>, F3 = <num>


  -- Variances Accounted for -----------------------------------------------------

                       F1 F2 F3
  SS loadings <num> <num> <num>
  Prop Tot Var <num> <num> <num>
  Cum Prop Tot Var <num> <num> <num>
  Prop Comm Var <num> <num> <num>
  Cum Prop Comm Var <num> <num> <num>

  -- Model Fit -------------------------------------------------------------------

  CAF: <num>
  SRMR: <num>
  df: 102

  -- Residual Diagnostics --------------------------------------------------------

  Residual cutoff: |r| > <num>
  Number of large residuals: 0
  Largest absolute residual: <num>

  No absolute residuals > <num> occurred.

  Inspect the residual matrix for details (e.g., with residuals()).

summary.efa output is stable (ML, promax)

Code
  print(summary(efa_ml_moderate))
Output

  EFA performed with estimator = 'ML' and rotation = 'promax'.

  -- Model Diagnostics -----------------------------------------------------------

  Factors: 3
  Variables: 18
  N: 500
  Heywood cases: 0
  Cross-loading items (|loading| >= <num>): 0
  Items without salient loading (|loading| >= <num>): 0
  Factors with fewer than 3 salient indicators: 0
  Items with primary-loading gap < <num>: 0
  Largest |residual|: <num>
  Factor intercorrelations > <num>: none

  -- Rotated Loadings ------------------------------------------------------------

        F1    F2    F3    h2    u2
  V1 <num> <num> <num> <num> <num>
  V2 <num> <num> <num> <num> <num>
  V3 <num> <num> <num> <num> <num>
  V4 <num> <num> <num> <num> <num>
  V5 <num> <num> <num> <num> <num>
  V6 <num> <num> <num> <num> <num>
  V7 <num> <num> <num> <num> <num>
  V8 <num> <num> <num> <num> <num>
  V9 <num> <num> <num> <num> <num>
  V10 <num> <num> <num> <num> <num>
  V11 <num> <num> <num> <num> <num>
  V12 <num> <num> <num> <num> <num>
  V13 <num> <num> <num> <num> <num>
  V14 <num> <num> <num> <num> <num>
  V15 <num> <num> <num> <num> <num>
  V16 <num> <num> <num> <num> <num>
  V17 <num> <num> <num> <num> <num>
  V18 <num> <num> <num> <num> <num>

  -- Factor Intercorrelations ----------------------------------------------------

        F1 F2 F3
  F1 <num>
  F2 <num> <num>
  F3 <num> <num> <num>

  -- Structure Matrix ------------------------------------------------------------

        F1 F2 F3
  V1 <num> <num> <num>
  V2 <num> <num> <num>
  V3 <num> <num> <num>
  V4 <num> <num> <num>
  V5 <num> <num> <num>
  V6 <num> <num> <num>
  V7 <num> <num> <num>
  V8 <num> <num> <num>
  V9 <num> <num> <num>
  V10 <num> <num> <num>
  V11 <num> <num> <num>
  V12 <num> <num> <num>
  V13 <num> <num> <num>
  V14 <num> <num> <num>
  V15 <num> <num> <num>
  V16 <num> <num> <num>
  V17 <num> <num> <num>
  V18 <num> <num> <num>

  -- Variances Accounted for -----------------------------------------------------

                       F1 F2 F3
  SS loadings <num> <num> <num>
  Prop Tot Var <num> <num> <num>
  Cum Prop Tot Var <num> <num> <num>
  Prop Comm Var <num> <num> <num>
  Cum Prop Comm Var <num> <num> <num>

  -- Model Fit -------------------------------------------------------------------

  χ²(102) = <num>, p = <num>
  CFI: <num>
  TLI: <num>
  RMSEA [90% CI]: <num> [ <num>; <num>]
  AIC: <num>
  BIC: <num>
  ECVI: <num>
  CAF: <num>
  SRMR: <num>

  -- Residual Diagnostics --------------------------------------------------------

  Residual cutoff: |r| > <num>
  Number of large residuals: 0
  Largest absolute residual: <num>

  No absolute residuals > <num> occurred.

  Inspect the residual matrix for details (e.g., with residuals()).

print/summary.efa omit the inapplicable tables for a rotated single factor

Code
  print(efa_1fac)
Output

  EFA performed with estimator = 'PAF' and rotation = 'promax'.

  -- Rotated Loadings ------------------------------------------------------------

        F1    h2    u2
  V1 <num> <num> <num>
  V2 <num> <num> <num>
  V3 <num> <num> <num>
  V4 <num> <num> <num>
  V5 <num> <num> <num>
  V6 <num> <num> <num>
  V7 <num> <num> <num>
  V8 <num> <num> <num>
  V9 <num> <num> <num>
  V10 <num> <num> <num>
  V11 <num> <num> <num>
  V12 <num> <num> <num>
  V13 <num> <num> <num>
  V14 <num> <num> <num>
  V15 <num> <num> <num>
  V16 <num> <num> <num>
  V17 <num> <num> <num>
  V18 <num> <num> <num>

  -- Variances Accounted for -----------------------------------------------------

  No variance-accounted table available.

  -- Model Fit -------------------------------------------------------------------

  CAF: <num>
  SRMR: <num>
  df: 135

Code
  print(summary(efa_1fac))
Output

  EFA performed with estimator = 'PAF' and rotation = 'promax'.

  -- Model Diagnostics -----------------------------------------------------------

  Factors: 1
  Variables: 18
  N: 500
  Heywood cases: 0
  Cross-loading items (|loading| >= <num>): 0
  Items without salient loading (|loading| >= <num>): 0
  Factors with fewer than 3 salient indicators: 0
  Items with primary-loading gap < <num>: 0
  Largest |residual|: <num>

  -- Rotated Loadings ------------------------------------------------------------

        F1    h2    u2
  V1 <num> <num> <num>
  V2 <num> <num> <num>
  V3 <num> <num> <num>
  V4 <num> <num> <num>
  V5 <num> <num> <num>
  V6 <num> <num> <num>
  V7 <num> <num> <num>
  V8 <num> <num> <num>
  V9 <num> <num> <num>
  V10 <num> <num> <num>
  V11 <num> <num> <num>
  V12 <num> <num> <num>
  V13 <num> <num> <num>
  V14 <num> <num> <num>
  V15 <num> <num> <num>
  V16 <num> <num> <num>
  V17 <num> <num> <num>
  V18 <num> <num> <num>

  -- Variances Accounted for -----------------------------------------------------

  No variance-accounted table available.

  -- Model Fit -------------------------------------------------------------------

  CAF: <num>
  SRMR: <num>
  df: 135

  -- Residual Diagnostics --------------------------------------------------------

  Residual cutoff: |r| > <num>
  Number of large residuals: 9
  Largest absolute residual: <num>

  Largest residuals:
  * V10 ~~ V12: <num>
  * V1 ~~ V6: <num>
  * V9 ~~ V10: <num>
  * V14 ~~ V17: <num>
  * V8 ~~ V10: <num>
  * V1 ~~ V4: <num>
  * V13 ~~ V17: <num>
  * V17 ~~ V18: <num>
  * V4 ~~ V5: <num>

  Inspect the residual matrix for details (e.g., with residuals()).

the Heywood warning names the affected variables

Code
  for (est in c("ML", "ULS")) {
    cat("--", est, "--\n")
    withCallingHandlers(efa_fit(R_bnd, 1, N = 200, estimator = est), efa_heywood = function(
      w) cat(conditionMessage(w), "\n"), warning = function(w) invokeRestart(
      "muffleWarning"))
  }
Output
  -- ML --
  Heywood case detected for "item1": the solution is improper (a communality at or above 1, or a uniqueness fixed at the estimation boundary).
  i Interpret the affected loadings and uniquenesses with caution. 
  -- ULS --
  Heywood case detected for "item1": the solution is improper (a communality at or above 1, or a uniqueness fixed at the estimation boundary).
  i Interpret the affected loadings and uniquenesses with caution.