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

a failing group names the group and hands the cause on unaltered

Code
  cat(conditionMessage(e))
Output
  The `efa_fit()` fit failed for group "a".
  Caused by error:
  ! `estimator = "DWLS"` requires a polychoric asymptotic covariance.
  x You supplied a correlation matrix, so no asymptotic covariance can be estimated.
  i Supply raw ordinal data with `cor_method = "poly"` or `"tetra"`.

print and format render the efa_group report

Code
  print(mg)
Output
  -- Multigroup exploratory factor analysis --------------------------------------

  2 groups (age_6_8, age_14_19) · 3 factors · PAF extraction · varimax rotation
  Aligned to a symmetric consensus target.
  N: age_6_8 = 825, age_14_19 = 1685

  -- Factor congruence -----------------------------------------------------------

  Tucker's congruence between the aligned group loadings (matched factors):

                         F1 F2 F3
  age_6_8 vs age_14_19 <num> <num> <num>

  -- Loading differences ---------------------------------------------------------

  Absolute loading differences by group pair (salience threshold |Δ| ≥ <num>):

                        mean  median   min   max  rmse  flagged
  age_6_8 vs age_14_19 <num> <num> <num> <num> <num> <flagged>

  -- Approximate invariance ------------------------------------------------------

  Congruence bands (Lorenzo-Seva & ten Berge, 2006: ≥ <num> equal, ≥ <num> fair):

                          F1 F2 F3
  age_6_8 vs age_14_19  equal  equal  equal

Code
  print(mg_ident)
Output
  -- Multigroup exploratory factor analysis --------------------------------------

  3 groups (a, b, c) · 2 factors · PAF extraction · varimax rotation
  Aligned to a symmetric consensus target.
  N: a = 500, b = 500, c = 500

  -- Factor congruence -----------------------------------------------------------

  Tucker's congruence between the aligned group loadings (matched factors):

            F1 F2
  a vs b <num> <num>
  a vs c <num> <num>
  b vs c <num> <num>

  -- Loading differences ---------------------------------------------------------

  Absolute loading differences by group pair (salience threshold |Δ| ≥ <num>):

          mean  median   min   max  rmse  flagged
  a vs b <num> <num> <num> <num> <num> <flagged>
  a vs c <num> <num> <num> <num> <num> <flagged>
  b vs c <num> <num> <num> <num> <num> <flagged>

  -- Approximate invariance ------------------------------------------------------

  Congruence bands (Lorenzo-Seva & ten Berge, 2006: ≥ <num> equal, ≥ <num> fair):

            F1 F2
  a vs b  equal  equal
  a vs c  equal  equal
  b vs c  equal  equal

Code
  print(mg_ob)
Output
  -- Multigroup exploratory factor analysis --------------------------------------

  2 groups (age_6_8, age_14_19) · 3 factors · PAF extraction · promax rotation
  Aligned to reference group age_6_8.
  N: age_6_8 = 825, age_14_19 = 1685

  -- Factor congruence -----------------------------------------------------------

  Tucker's congruence between the aligned group loadings (matched factors):

                         F1 F2 F3
  age_6_8 vs age_14_19 <num> <num> <num>

  -- Loading differences ---------------------------------------------------------

  Absolute loading differences by group pair (salience threshold |Δ| ≥ <num>):

                        mean  median   min   max  rmse  flagged
  age_6_8 vs age_14_19 <num> <num> <num> <num> <num> <flagged>

print reports the bootstrap congruence intervals and verdicts

Code
  print(mg)
Output
  -- Multigroup exploratory factor analysis --------------------------------------

  2 groups (g1, g2) · 1 factor · PAF extraction · unrotated
  Aligned to a symmetric consensus target.
  N: g1 = 405, g2 = 405

  -- Factor congruence -----------------------------------------------------------

  Tucker's congruence between the aligned group loadings (matched factors):

             F1
  g1 vs g2 <num>

  i 95% percentile bootstrap CIs (50 replicates) are in `$congruence$matched_ci`.

  -- Loading differences ---------------------------------------------------------

  Absolute loading differences by group pair (salience threshold |Δ| ≥ <num>):

            mean  median   min   max  rmse  flagged
  g1 vs g2 <num> <num> <num> <num> <num> <flagged>

  i 1 loading has a bootstrap CI excluding 0 (see `$flags`).

  -- Approximate invariance ------------------------------------------------------

  Congruence bands (Lorenzo-Seva & ten Berge, 2006), read off the CI lower bound:

              F1
  g1 vs g2  equal

print points out an 'equal' verdict that rests on scale-invariance

Code
  print(mg)
Output
  -- Multigroup exploratory factor analysis --------------------------------------

  2 groups (g1, g2) · 2 factors · PAF extraction · varimax rotation
  Aligned to a symmetric consensus target.
  N: g1 = 500, g2 = 500

  -- Factor congruence -----------------------------------------------------------

  Tucker's congruence between the aligned group loadings (matched factors):

              F1 F2
  g1 vs g2 <num> <num>

  -- Loading differences ---------------------------------------------------------

  Absolute loading differences by group pair (salience threshold |Δ| ≥ <num>):

            mean  median   min   max  rmse  flagged
  g1 vs g2 <num> <num> <num> <num> <num> <flagged>

  -- Approximate invariance ------------------------------------------------------

  Congruence bands (Lorenzo-Seva & ten Berge, 2006: ≥ <num> equal, ≥ <num> fair):

              F1 F2
  g1 vs g2  equal  equal

  i Every factor is graded "equal" while the aligned loadings differ by up to
   <num> on average: Tucker's congruence is invariant to a proportional rescaling
  of a factor's loadings, so read the verdicts alongside `$diffs`.

the report wraps its header and splits its tables to the console width

Code
  print(mg)
Output
  -- Multigroup exploratory factor analysis ------------------

  4 groups (age_6_8, age_9_13, age_14_19, age_20_39) · 3
    factors · PAF extraction · varimax rotation
  Aligned to a symmetric consensus target.
  N: age_6_8 = 825, age_9_13 = 1572, age_14_19 = 1685,
    age_20_39 = 1251

  -- Factor congruence ---------------------------------------

  Tucker's congruence between the aligned group loadings
  (matched factors):

                           F1 F2 F3
  age_6_8 vs age_9_13 <num> <num> <num>
  age_6_8 vs age_14_19 <num> <num> <num>
  age_6_8 vs age_20_39 <num> <num> <num>
  age_9_13 vs age_14_19 <num> <num> <num>
  age_9_13 vs age_20_39 <num> <num> <num>
  age_14_19 vs age_20_39 <num> <num> <num>

  -- Loading differences -------------------------------------

  Absolute loading differences by group pair (salience
  threshold |Δ| ≥ <num>):

                          mean  median   min   max  rmse
  age_6_8 vs age_9_13 <num> <num> <num> <num> <num>
  age_6_8 vs age_14_19 <num> <num> <num> <num> <num>
  age_6_8 vs age_20_39 <num> <num> <num> <num> <num>
  age_9_13 vs age_14_19 <num> <num> <num> <num> <num>
  age_9_13 vs age_20_39 <num> <num> <num> <num> <num>
  age_14_19 vs age_20_39 <num> <num> <num> <num> <num>

                          flagged
  age_6_8 vs age_9_13 <flagged>
  age_6_8 vs age_14_19 <flagged>
  age_6_8 vs age_20_39 <flagged>
  age_9_13 vs age_14_19 <flagged>
  age_9_13 vs age_20_39 <flagged>
  age_14_19 vs age_20_39 <flagged>

  -- Approximate invariance ----------------------------------

  Congruence bands (Lorenzo-Seva & ten Berge, 2006: ≥ <num>
  equal, ≥ <num> fair):

                            F1 F2 F3
  age_6_8 vs age_9_13     equal  equal  equal
  age_6_8 vs age_14_19    equal  equal  equal
  age_6_8 vs age_20_39    equal  equal  equal
  age_9_13 vs age_14_19   equal  equal  equal
  age_9_13 vs age_20_39   equal  equal  equal
  age_14_19 vs age_20_39  equal  equal  equal