2b. Item-pool dimensionality (EFA)

NoteWhere am I in the pipeline?

Overview

This page hosts Stage 1 — item-pool dimensionality for the DisInforMeter predictor batteries. Two waves carry the bulk of the dimensionality evidence: Study 1 fielded the broadest exploratory item pool, and Study 4 fielded the deployed multinational predictor pool (the version that downstream CFAs and structural models work from). The cross-study evidence on first-order structure consolidates on 4a Measurement architecture; per-study pages then estimate Stage 2 (first-order measurement) and Stages 3 / 5 / 6 / 7 / 8 against the structure documented here.

Per the eight-stage pipeline locked in R/roadmap_helpers.R::progress_matrix(), Stage 1 asks whether the empirical correlation structure can plausibly support the registered CFA partition. The diagnostics on this page are exploratory; they are reported alongside, not in place of, the registered CFA solutions. The CFA specifications in R/sem_specs.R are not re-specified on the basis of EFA findings — the EFA simply gives empirical context for how strongly the deployed partition is supported by the off-diagonal correlation structure.

Stage 1 in the pipeline

Stage 1 is exploratory dimensionality work on the predictor item pool. The FIMI criterion is excluded — Stage 4 (outcome operationalisation) treats FIMI separately on 03d and 4b. For each wave we report:

  • Sampling adequacy: overall KMO (psych::KMO) and item-level MSA; Bartlett’s test of sphericity (psych::cortest.bartlett). Low MSA on any item is flagged; a Bartlett rejection is necessary (not sufficient) for EFA to be meaningful.
  • Factor-count diagnostics: parallel analysis with the 95th-percentile rule (psych::fa.parallel, n.iter = 50) and Velicer’s MAP across 1–8 factors (psych::vss, fm = "ml", rotate = "oblimin").
  • Factor extraction: maximum-likelihood EFA with oblimin rotation (psych::fa, fm = "ml") at the registered factor count. Loadings with |λ| < .30 are suppressed in the printed table to keep the structure readable. The full unsuppressed loading matrix is written to outputs/tables/.

The registered factor counts are taken directly from the lavaan specifications:

  • S1: the thirteen first-order latents in S1_full (CET, EXPL, MOR, GAY, ABANF, MIGR, ABANH, KNOW, FREE, PRAGR, PRAGCH, SUPR, SUPCH; S1 legacy: USE/SAFE/LONE/ANXR/ANXK/SUPK). FIMI is the criterion and is excluded.
  • S4: the six first-order predictor latents in S4_deploy_cfa (GEN, THREAT, ABAND, FEAR, SUPF, SUPFCH; S4 legacy: PRAG/SUPR/SUPCH — note that S4 SUPF / SUPFCH are affective admiration via the fru* / fch* items, not the S1/S5 belief composites). FIMI is the criterion and is excluded.

S1 item pool dimensionality

The Study 1 predictor item pool comprises 73 items across 13 first-order constructs (ABANF, ABANH, ABANM, CET, EXPL, GAY, KNOW, MIGR, MOR, PRAGCH, PRAGR, SUPCH, SUPR), drawn from the cached S1_full lavaan specification. FIMI news items are excluded.

S1 predictor pool: sampling adequacy and sphericity
Statistic Value
Items 73
N (pairwise) 681
N (complete-case) 681
Overall KMO (MSA) 0.980
Bartlett chi-square 53 829.1
Bartlett df 2628
Bartlett p <0.001
S1 item-level KMO measures of sampling adequacy
Construct Item MSA
ABANF unp1 0.984
ABANF unp6 0.988
ABANF unp7 0.986
ABANF unp8 0.986
ABANH aban1 0.976
ABANH aban2 0.976
ABANH aban3 0.987
ABANH aban4 0.978
ABANH aban5 0.977
ABANM cen1 0.989
ABANM cen2 0.972
ABANM cen3 0.957
ABANM cen4 0.986
ABANM cen5 0.963
CET poi3 0.989
CET poi6 0.985
CET poi7 0.985
EXPL exp1 0.990
EXPL exp2 0.986
EXPL exp3 0.987
EXPL exp4 0.987
GAY lgb1 0.974
GAY lgb2 0.968
GAY lgb3 0.975
GAY lgb4 0.976
KNOW aban6 0.940
KNOW aban7 0.924
KNOW aban8 0.967
MIGR unp3 0.962
MIGR unp4 0.949
MOR dec1 0.979
MOR dec2 0.979
MOR dec3 0.988
MOR dec4 0.985
MOR dec5 0.986
PRAGCH pkin1 0.985
PRAGCH pkin2 0.989
PRAGCH pkin3 0.974
PRAGCH pkin4 0.978
PRAGCH pkin5 0.985
PRAGCH pkin6 0.973
PRAGR pru1 0.987
PRAGR pru2 0.989
PRAGR pru3 0.982
PRAGR pru4 0.985
PRAGR pru5 0.989
PRAGR pru6 0.974
SUPCH ski1 0.979
SUPCH ski10 0.980
SUPCH ski11 0.985
SUPCH ski2 0.978
SUPCH ski3 0.979
SUPCH ski4 0.964
SUPCH ski5 0.968
SUPCH ski6 0.963
SUPCH ski7 0.973
SUPCH ski8 0.974
SUPCH ski9 0.982
SUPR sru1 0.979
SUPR sru10 0.985
SUPR sru11 0.981
SUPR sru12 0.980
SUPR sru13 0.981
SUPR sru14 0.981
SUPR sru15 0.984
SUPR sru2 0.984
SUPR sru3 0.984
SUPR sru4 0.986
SUPR sru5 0.975
SUPR sru6 0.988
SUPR sru7 0.985
SUPR sru8 0.987
SUPR sru9 0.985

Parallel analysis and scree plot for the S1 predictor pool. Retained factor count = number of empirical eigenvalues exceeding the 95th-percentile simulated eigenvalues.
Parallel analysis suggests that the number of factors =  7  and the number of components =  NA
S1 Velicer's MAP across candidate factor counts (smaller is better)
# factors MAP
1 0.0295
2 0.0179
3 0.0124
4 0.0115
5 0.0095
6 0.0087
7 0.0082
8 0.0081
S1 oblimin-rotated 13-factor ML solution; |λ|
Item Construct ML1 ML3 ML8 ML2 ML9 ML6 ML7 ML5 ML4 ML10 ML11 ML12 ML13
unp1 ABANF 0.40
unp6 ABANF 0.36
unp7 ABANF 0.40
unp8 ABANF
aban1 ABANH 0.83
aban2 ABANH 0.84
aban3 ABANH 0.57
aban4 ABANH 0.71
aban5 ABANH 0.67
cen1 ABANM 0.31
cen2 ABANM 0.69
cen3 ABANM 0.90
cen4 ABANM 0.46
cen5 ABANM 0.86
poi3 CET
poi6 CET 0.52
poi7 CET 0.59
exp1 EXPL 0.57
exp2 EXPL 0.58
exp3 EXPL 0.44
exp4 EXPL 0.39
lgb1 GAY 0.66
lgb2 GAY 0.94
lgb3 GAY 0.82
lgb4 GAY 0.85
aban6 KNOW 0.88
aban7 KNOW 0.94
aban8 KNOW 0.39 0.31
unp3 MIGR 0.78
unp4 MIGR 0.72
dec1 MOR 0.82
dec2 MOR 0.79
dec3 MOR 0.62
dec4 MOR 0.52
dec5 MOR 0.42
pkin1 PRAGCH 0.53
pkin2 PRAGCH 0.35
pkin3 PRAGCH 0.64
pkin4 PRAGCH 0.62
pkin5 PRAGCH 0.41
pkin6 PRAGCH 0.61
pru1 PRAGR 0.40
pru2 PRAGR 0.43
pru3 PRAGR 0.50
pru4 PRAGR 0.50
pru5 PRAGR 0.46
pru6 PRAGR 0.60
ski1 SUPCH 0.40 0.30
ski10 SUPCH 0.66
ski11 SUPCH 0.49
ski2 SUPCH 0.53
ski3 SUPCH 0.53
ski4 SUPCH 0.73
ski5 SUPCH 0.82
ski6 SUPCH 0.78
ski7 SUPCH 0.68
ski8 SUPCH 0.56
ski9 SUPCH 0.70
sru1 SUPR 0.69
sru10 SUPR 0.68
sru11 SUPR 0.67
sru12 SUPR 0.38
sru13 SUPR 0.65
sru14 SUPR 0.59
sru15 SUPR 0.62
sru2 SUPR 0.66
sru3 SUPR 0.71
sru4 SUPR 0.62
sru5 SUPR 0.36
sru6 SUPR 0.66
sru7 SUPR 0.64
sru8 SUPR 0.42
sru9 SUPR 0.62
S1 variance accounted for by each oblimin-rotated factor
metric ML1 ML3 ML8 ML2 ML9 ML6 ML7 ML5 ML4 ML10 ML11 ML12 ML13
SS loadings 9.437 6.479 5.280 4.949 4.534 4.457 4.087 2.998 2.775 2.731 2.450 2.303 1.242
Proportion Var 0.129 0.089 0.072 0.068 0.062 0.061 0.056 0.041 0.038 0.037 0.034 0.032 0.017
Cumulative Var 0.129 0.218 0.290 0.358 0.420 0.481 0.537 0.578 0.616 0.654 0.687 0.719 0.736
Proportion Explained 0.176 0.121 0.098 0.092 0.084 0.083 0.076 0.056 0.052 0.051 0.046 0.043 0.023
Cumulative Proportion 0.176 0.296 0.395 0.487 0.571 0.654 0.730 0.786 0.838 0.888 0.934 0.977 1.000

Parallel analysis retains 7 factors. Velicer’s MAP minimises at 8 factors. The registered S1 first-order partition (S1_full) specifies 13 latents. The EFA is reported at 13 factors to keep the comparison aligned with the registered specification; the parallel-analysis and MAP counts are noted for transparency and are not used to re-specify the CFA.

S4 item pool dimensionality

The Study 4 deployed predictor pool comprises 19 items across 6 first-order constructs (GEN, THREAT, ABAND, FEAR, SUPF, SUPFCH; S4 legacy: PRAG/SUPR/SUPCH), drawn from the registered S4_deploy_cfa specification. FIMI news items are excluded.

S4 deployed predictor pool: sampling adequacy and sphericity
Statistic Value
Items 19
N (pairwise) 8,040
N (complete-case) 8,040
Overall KMO (MSA) 0.893
Bartlett chi-square 103 570.7
Bartlett df 171
Bartlett p <0.001
S4 item-level KMO measures of sampling adequacy
Construct Item MSA
ABAND ab2 0.903
ABAND ab4 0.876
ABAND ab7 0.915
FEAR pa1 0.765
FEAR pa2 0.929
FEAR pa4 0.756
GEN gen1 0.867
GEN gen2 0.881
GEN gen3 0.892
GEN gen5 0.892
GEN gen7 0.892
SUPF fru1 0.911
SUPF fru2 0.904
SUPF fru3 0.913
SUPFCH fch1 0.887
SUPFCH fch2 0.879
SUPFCH fch3 0.915
THREAT th6 0.941
THREAT th9 0.956

Parallel analysis and scree plot for the S4 deployed predictor pool.
Parallel analysis suggests that the number of factors =  5  and the number of components =  NA
S4 Velicer's MAP across candidate factor counts (smaller is better)
# factors MAP
1 0.0766
2 0.0361
3 0.0324
4 0.0346
5 0.0306
6 0.0370
7 0.0470
8 0.0575
S4 oblimin-rotated 6-factor ML solution; |λ|
Item Construct ML5 ML4 ML3 ML2 ML1 ML6
ab2 ABAND 0.70
ab4 ABAND 0.77
ab7 ABAND 0.68
pa1 FEAR 0.78
pa2 FEAR 0.39
pa4 FEAR 0.89
gen1 GEN 0.62
gen2 GEN 0.63
gen3 GEN 0.53
gen5 GEN 0.95
gen7 GEN 0.31 0.61
fru1 SUPF 0.79
fru2 SUPF 0.90
fru3 SUPF 0.84
fch1 SUPFCH 0.89
fch2 SUPFCH 0.55 0.31
fch3 SUPFCH 0.59
th6 THREAT 0.61
th9 THREAT 0.32
S4 variance accounted for by each oblimin-rotated factor
metric ML5 ML4 ML3 ML2 ML1 ML6
SS loadings 3.059 2.783 1.934 1.776 1.681 0.958
Proportion Var 0.161 0.146 0.102 0.093 0.088 0.050
Cumulative Var 0.161 0.307 0.409 0.503 0.591 0.642
Proportion Explained 0.251 0.228 0.159 0.146 0.138 0.079
Cumulative Proportion 0.251 0.479 0.638 0.784 0.921 1.000

Parallel analysis retains 5 factors. Velicer’s MAP minimises at 5 factors. The registered S4_deploy_cfa specifies 6 first-order latents (GEN, THREAT, ABAND, FEAR, SUPF, SUPFCH). The EFA is reported at 6 factors so it is directly comparable to the registered solution; the parallel-analysis and MAP counts are noted for transparency. The EFA is not used to re-specify the CFA.

How dimensionality decisions flow into Stage 2 / 3

Stage 1 dimensionality on this page feeds two downstream stages.

  • Stage 2 — first-order measurement validation estimates the registered first-order CFAs on each wave. For S1 this happens on 03a Study 1 (block CFAs and S1_full); for S4 on 03d Study 4 (S4_deploy_cfa). Cross-wave first-order synthesis lives on 4a Measurement architecture.
  • Stage 3 — higher-order construct representation sits on top of the validated first-order partition. For S1 the higher-order representation choice is explored on 03a (reflective second-order, pure formative <~, hybrid MIMIC, two-step rescue). S4 inherits the S2 / S3 representation; see the inheritance note on 03d and the cross-study comparison on 4a.

The EFA results here are reported for transparency and to surface any item-level MSA or empirical-eigenvalue surprises ahead of the registered CFA estimation. They are not used to re-specify R/sem_specs.R.