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

a failing component fit names its imputation and keeps the original condition

Code
  efa_mi(raw, n_factors = 1, estimator = "PAF", rotation = "none")
Message
  i `x` is not a correlation matrix; computing correlations from the raw data.
Condition
  Error in `efa_mi()`:
  ! Imputation 2 could not be fitted.
  i Inspect `data_list[[2]]`, then re-fit or replace it.
  Caused by error:
  ! The correlation matrix could not be computed from the raw data.
  x Column "V3" has zero variance.
  i A constant variable correlates with nothing; drop it before the analysis.

bootstrap arrays are pooled into MI SEs and CIs

Code
  print(summary(pooled_boot))
Output

  Pooled EFA across 2 imputations performed with estimator = 'ML' and
    rotation = 'none'.
  Pooling settings: align_unrotated = 'signed_tucker_congruence',
    fit_pool_method = 'D2'.

  -- Pooled Model Diagnostics ----------------------------------------------------

  Factors: 1
  Variables: 8
  N: 250
  Imputations: 2
  Pooling: align_unrotated = 'signed_tucker_congruence', fit_pool_method = 'D2'
  Bootstrap samples per imputation: 6
  Valid target-rotated samples: 6 out of 6 per imputation
  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>

  -- Unrotated Loadings ----------------------------------------------------------

              F1    h2    u2
  fun <num> <num> <num>
  friends <num> <num> <num>
  enjoy <num> <num> <num>
  hurt <num> <num> <num>
  part <num> <num> <num>
  commonly <num> <num> <num>
  chances <num> <num> <num>
  attracted <num> <num> <num>

  -- 95% bootstrap/MI CIs for salient unrotated loadings -------------------------

  Variable   Factor  est    lower  upper
  fun        F1 <num> <num> <num>
  friends    F1 <num> <num> <num>
  enjoy      F1 <num> <num> <num>
  hurt       F1 <num> <num> <num>
  part       F1 <num> <num> <num>
  commonly   F1 <num> <num> <num>
  chances    F1 <num> <num> <num>
  attracted  F1 <num> <num> <num>

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

                  F1
  SS loadings <num>
  Prop Tot Var <num>

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

  D2-pooled χ²(20) = <num>, p = <num>
  CFI (avg. over imputations) [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  TLI (avg. over imputations) [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  RMSEA [90% CI] [95% bootstrap/MI-CI]: <num> [ <num>; <num>] [ <num>, <num>]
  AIC [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  BIC [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  ECVI [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  CAF [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  SRMR [95% bootstrap/MI-CI]: <num> [ <num>, <num>]
  Note: the pooled χ² is the D2 statistic; its p uses the D2 reference F(20, <num>),
  not the χ²(20) tail.
  Note: CFI and TLI are averaged over the imputations, not formed from the
  separately pooled model and baseline statistics in `mi_diagnostics`.

  Note: Bootstrap/MI CIs based on 6 bootstrap samples per imputation.

  -- MI Uncertainty Summary ------------------------------------------------------

  Largest available FMI: <num>
  Median available FMI: <num>
  Largest available RIV: <num>
  Median available RIV: <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.efa_mi output is stable (PAF, promax)

Code
  print(pooled_obl)
Output

  Pooled EFA across 3 imputations performed with estimator = 'PAF' and
    rotation = 'promax'.
  Pooling settings: target_method = 'first_target',
    align_unrotated = 'signed_tucker_congruence', fit_pool_method = 'D2'.

  -- 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_mi output is stable (ML, unrotated)

Code
  print(pooled_none)
Output

  Pooled EFA across 3 imputations performed with estimator = 'ML' and
    rotation = 'none'.
  Pooling settings: align_unrotated = 'signed_tucker_congruence',
    fit_pool_method = 'D2'.

  -- Unrotated Loadings ----------------------------------------------------------

              F1    h2    u2
  fun <num> <num> <num>
  friends <num> <num> <num>
  enjoy <num> <num> <num>
  hurt <num> <num> <num>
  part <num> <num> <num>
  commonly <num> <num> <num>
  chances <num> <num> <num>
  attracted <num> <num> <num>

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

                  F1
  SS loadings <num>
  Prop Tot Var <num>

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

  D2-pooled χ²(20) = <num>, p = <num>
  CFI (avg. over imputations): <num>
  TLI (avg. over imputations): <num>
  RMSEA [90% CI]: <num> [ <num>; <num>]
  AIC: <num>
  BIC: <num>
  ECVI: <num>
  CAF: <num>
  SRMR: <num>
  Note: the pooled χ² is the D2 statistic; its p uses the D2 reference F(20, <num>),
  not the χ²(20) tail.
  Note: CFI and TLI are averaged over the imputations, not formed from the
  separately pooled model and baseline statistics in `mi_diagnostics`.

summary.efa_mi output is stable (PAF, promax)

Code
  print(summary(pooled_obl))
Output

  Pooled EFA across 3 imputations performed with estimator = 'PAF' and
    rotation = 'promax'.
  Pooling settings: target_method = 'first_target',
    align_unrotated = 'signed_tucker_congruence', fit_pool_method = 'D2'.

  -- Pooled Model Diagnostics ----------------------------------------------------

  Factors: 3
  Variables: 18
  N: 500
  Imputations: 3
  Pooling: target_method = 'first_target',
    align_unrotated = 'signed_tucker_congruence', fit_pool_method = 'D2'
  Alignment: method = 'first_target', converged
  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_mi output is stable (ML, unrotated)

Code
  print(summary(pooled_none))
Output

  Pooled EFA across 3 imputations performed with estimator = 'ML' and
    rotation = 'none'.
  Pooling settings: align_unrotated = 'signed_tucker_congruence',
    fit_pool_method = 'D2'.

  -- Pooled Model Diagnostics ----------------------------------------------------

  Factors: 1
  Variables: 8
  N: 810
  Imputations: 3
  Pooling: align_unrotated = 'signed_tucker_congruence', fit_pool_method = 'D2'
  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>

  -- Unrotated Loadings ----------------------------------------------------------

              F1    h2    u2
  fun <num> <num> <num>
  friends <num> <num> <num>
  enjoy <num> <num> <num>
  hurt <num> <num> <num>
  part <num> <num> <num>
  commonly <num> <num> <num>
  chances <num> <num> <num>
  attracted <num> <num> <num>

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

                  F1
  SS loadings <num>
  Prop Tot Var <num>

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

  D2-pooled χ²(20) = <num>, p = <num>
  CFI (avg. over imputations): <num>
  TLI (avg. over imputations): <num>
  RMSEA [90% CI]: <num> [ <num>; <num>]
  AIC: <num>
  BIC: <num>
  ECVI: <num>
  CAF: <num>
  SRMR: <num>
  Note: the pooled χ² is the D2 statistic; its p uses the D2 reference F(20, <num>),
  not the χ²(20) tail.
  Note: CFI and TLI are averaged over the imputations, not formed from the
  separately pooled model and baseline statistics in `mi_diagnostics`.

  -- 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()).