3. Models — Overview

NoteWhere am I in the pipeline?
  • Inputs: Cleaned item batteries from Data Preparation and the harmonised mapping in outputs/item_mapping_mini.csv.
  • This page: Modelling reference only. The inventory of registered SEM specifications, lavaan operators, item-level mapping across waves, model-purpose taxonomy, model-complexity counts, and the diagram conventions used by the per-study figures. Estimation results, fitted path diagrams, and cross-study syntheses live elsewhere.
  • Hands off to: Study 1, Study 2, Study 3, the live multinational Study 4, the live validation Study 5, and the cross-study 4a Measurement architecture page.

Overview

The DisInforMeter is evaluated across five ingested waves (S1–S5). Each wave is modelled on its own page. This page is the shared modelling reference: every model card, operator explanation, item mapping, and diagram-convention legend cited from a per-study page resolves back here. Estimation results and fitted path diagrams live with each study; cross-study syntheses live in 4a Measurement architecture (architecture, evolution, consolidated fit summary) and the 4b-4e synthesis pages.

The work follows four principles:

  • One source of truth for model syntax. Every lavaan specification is registered in R/sem_specs.R and rendered both as a documentation card (below) and as a fitted model on the per-study pages. When an item is dropped or renamed, the change happens once, in the spec file.
  • Purpose before results. The catalogue distinguishes first-order measurement validation, higher-order construct representation, outcome operationalisation, structural prediction, scale reduction/deployment adaptation, invariance, and external validation. A model can contain more than one syntax element, but the report keeps these scientific questions separate.
  • Cards over comments. Each registered model becomes a collapsible card with a one-paragraph description, the structural paths extracted automatically from the syntax, and the full lavaan string. The card lives in the rendered HTML, not in folded R source.
  • Data-driven diagrams. Path diagrams are produced from fitted lavaan objects rather than redrawn by hand: standardized estimates feed reusable Graphviz layouts in figures/sem_templates/, exported to SVG (HTML) and PDF (LaTeX/Word). Layouts are held fixed across model variants so figures compare directly. The conventions are documented at the bottom of this page; the diagrams themselves render on the per-study pages.

Analysis stages

The catalogue is organised around the analytic purpose a registered specification serves, not the lavaan syntax it happens to use. The same model can carry measurement loadings, a higher-order representation, and a structural-prediction path, and those purposes are interpreted separately on the per-study pages.

  • First-order measurement validation. Reconstruct the latent blocks (threat, abandonment, pragmatic accommodation, foreign-power admiration, and FIMI where administered) as defined in the harmonised specifications, adapting only where survey instruments differ across waves.
  • Higher-order construct representation. Compare correlated first-order factors, reflective second-order factors (=~), pure formative composites (<~), and hybrid formative–reflective / MIMIC-style specifications (=~ + ~) as alternative representations of the broader DisInforMeter dimensions. This is a construct-representation question, not a FIMI prediction result.
  • Outcome operationalisation before prediction. Treat Full FIMI as the named primary criterion in waves that administer the news battery, with Russian-origin, Chinese-origin, and Short FIMI as planned sensitivity/comparability operationalisations. Prediction comparisons are interpreted only after the relevant FIMI score has been named.
  • Structural prediction models. Estimate first-order and higher-order paths to the harmonised FIMI criterion(s) using robust maximum likelihood (MLR) with full information maximum likelihood (FIML) for missing data. Standardized structural coefficients and latent R² are reported separately from measurement diagnostics.
  • Scale reduction and deployment adaptation. Document each brief/deployment model and the trade-off between item economy and retained prediction.
  • Invariance and external validation. Configural/metric/scalar invariance across waves and countries; nomological-network checks against external anchor scales.

Data sources

Wrangled item-level sample sizes available for modelling and validation pages
Study Respondents
Study 1 — Lithuania (Dec 2024) 681
Study 2 — Lithuania (Mar 2025) 582
Study 3 — Germany (May 2025) 782
Study 4 — Cross-national (Dec 2025) 8,040
Study 5 — Lithuania validation (Mar–Apr 2026) 248

S1–S4 are fully modelled in the current SEM pages. S4 is ingested with cleaned items in data/wrangled_data/ and its modelling page now reports the multinational deployment CFA, country invariance ladder, harmonised FIMI prediction variants, combined-item bridge checks, and external-anchor probes. S5 is ingested and live for measurement, deployment-item checks, exploratory S2/S5 invariance, and nomological-network validation, but it does not administer FIMI.

Model specifications

The full set of registered SEM models is stored in R/sem_specs.R as a single named catalogue. Each entry carries the study it belongs to, a model-family tag, a one-paragraph description, and the canonical lavaan syntax string. Centralising the syntax means every per-study page refers to one source of truth. The syntax catalogue is not itself a result table: the same model can contain measurement loadings, higher-order representation paths, and structural prediction paths, and those purposes are interpreted separately in the per-study results.

Registered SEM specifications. Each row links to the model card below for syntax and structural paths.
study model_id model_label family
S1 S1_block_ideology Ideological grievances predict FIMI First-order blocks
S1 S1_block_abandon State abandonment / knowledge (no ABANM) First-order blocks
S1 S1_block_abandon_free State abandonment + censorship First-order blocks
S1 S1_block_russia Russia / China admiration (beliefs) First-order blocks
S1 S1_full Full first-order structural model Full SEM
S1 S1_second_hybrid Second-order (hybrid formative–reflective / MIMIC, stabilised) Higher-order (hybrid MIMIC)
S1 S1_second_formative Second-order (pure formative composite, `<~`) Higher-order (pure formative composite)
S1 S1_second_reflective Second-order (fully reflective) Higher-order (reflective)
S1 S1_brief S1 brief structural test Abbreviated
S1 S1_second_twostep_measurement Two-step measurement CFA Two-step measurement CFA
S1 S1_second_twostep_struct Two-step structural (factor-score regression) Two-step structural
S2 S2_main S2 hybrid MIMIC composites plus FIMI layer Higher-order (hybrid MIMIC)
S2 S2_main_formative S2 pure formative composites plus FIMI layer (`<~`) Higher-order (pure formative composite)
S2 S2_brief S2 brief validation model Abbreviated
S3 S3_main Germany replication: hybrid MIMIC composites Higher-order (hybrid MIMIC)
S3 S3_main_formative Germany: pure formative composites plus FIMI layer (`<~`) Higher-order (pure formative composite)
S3 S3_brief Germany brief validation Abbreviated
S4 S4_deploy_cfa S4 deployed short-form measurement CFA Abbreviated
S4 S4_pred_full S4 full FIMI prediction Full SEM
S4 S4_pred_russian S4 Russian-origin FIMI prediction Full SEM
S4 S4_pred_chinese S4 Chinese-origin FIMI prediction Full SEM
S4 S4_pred_short S4 short FIMI prediction Full SEM
S5 S5_long_mimic S5 hybrid MIMIC measurement-only model (exploratory) Higher-order (hybrid MIMIC)
S5 S5_long_cfa S5 long-form measurement CFA Measurement
S5 S5_brief_cfa S5 brief measurement CFA Abbreviated
S5 S5_S2_long_invariance_meta Temporal invariance vs. Study 2 (descriptive) Invariance

The purpose crosswalk below is the guardrail for interpreting the catalogue. A registered syntax can contain several lavaan operators, but the table separates its primary conceptual stage from any FIMI prediction layer, higher-order representation, or scale-reduction/deployment role.

Model-purpose crosswalk. Each registered model appears exactly once; prediction and higher-order representation are shown as separate layers.
Study Model ID Family Primary conceptual stage FIMI prediction layer Higher-order representation Short/deployment model
S1 S1_block_abandon First-order blocks 2. First-order measurement validation Yes - S1 Full FIMI criterion No No
S1 S1_block_abandon_free First-order blocks 2. First-order measurement validation Yes - S1 Full FIMI criterion No No
S1 S1_block_ideology First-order blocks 2. First-order measurement validation Yes - S1 Full FIMI criterion No No
S1 S1_block_russia First-order blocks 2. First-order measurement validation Yes - S1 Full FIMI criterion No No
S1 S1_second_twostep_measurement Two-step measurement CFA 2. First-order measurement validation No No No
S1 S1_second_hybrid Higher-order (hybrid MIMIC) 3. Higher-order construct modelling Yes - S1 Full FIMI criterion Yes No
S1 S1_second_formative Higher-order (pure formative composite) 3. Higher-order construct modelling Yes - S1 Full FIMI criterion Yes No
S1 S1_second_reflective Higher-order (reflective) 3. Higher-order construct modelling Yes - S1 Full FIMI criterion Yes No
S1 S1_full Full SEM 5. Structural prediction models Yes - S1 Full FIMI criterion No No
S1 S1_second_twostep_struct Two-step structural 5. Structural prediction models Yes - S1 Full FIMI criterion Yes (factor-score composite) No
S1 S1_brief Abbreviated 6. Scale reduction and deployment adaptation Yes - short FIMI criterion Reduced composite Yes
S2 S2_main Higher-order (hybrid MIMIC) 3. Higher-order construct modelling Yes - harmonised Full FIMI criterion Yes No
S2 S2_main_formative Higher-order (pure formative composite) 3. Higher-order construct modelling Yes - harmonised Full FIMI criterion Yes No
S2 S2_brief Abbreviated 6. Scale reduction and deployment adaptation Yes - short FIMI criterion Reduced composite Yes
S3 S3_main Higher-order (hybrid MIMIC) 3. Higher-order construct modelling Yes - harmonised Full FIMI criterion Yes No
S3 S3_main_formative Higher-order (pure formative composite) 3. Higher-order construct modelling Yes - harmonised Full FIMI criterion Yes No
S3 S3_brief Abbreviated 6. Scale reduction and deployment adaptation Yes - short FIMI criterion Reduced composite Yes
S4 S4_pred_chinese Full SEM 5. Structural prediction models Yes - Chinese-origin FIMI criterion No No
S4 S4_pred_full Full SEM 5. Structural prediction models Yes - harmonised Full FIMI criterion No No
S4 S4_pred_russian Full SEM 5. Structural prediction models Yes - Russian-origin FIMI criterion No No
S4 S4_pred_short Full SEM 5. Structural prediction models Yes - short FIMI criterion No No
S4 S4_deploy_cfa Abbreviated 6. Scale reduction and deployment adaptation No No Yes
S5 S5_long_cfa Measurement 2. First-order measurement validation No No No
S5 S5_long_mimic Higher-order (hybrid MIMIC) 3. Higher-order construct modelling No Yes No
S5 S5_brief_cfa Abbreviated 6. Scale reduction and deployment adaptation No No Yes
S5 S5_S2_long_invariance_meta Invariance 7. Measurement invariance No No No

Model cards

Each card below documents one registered model. The header gives the model_id, the human-readable label, the study it is fitted to, and the family it belongs to. The lavaan syntax is shown verbatim and can be copied straight into a lavaan::sem() call. Cards are collapsed by default — click any header to inspect the full specification.

Study: S1 · Family: Abbreviated

Two-indicator-per-latent abbreviated S1 model used as a scale-reduction and deployment-adaptation probe. Each composite (THREAT, FEAR, ABAND, RULE) is reduced to its strongest two items from S1_second_hybrid (the hybrid formative–reflective / MIMIC specification); FIMI is reduced to the source-balanced four-item Short FIMI criterion (news4, news9, news14, news15) so retained prediction can be checked separately.

Structural paths

  • FIMI ~ THREAT + ABAND + FEAR + RULE
THREAT =~ lgb3 + exp1
  FEAR   =~ pru3 + pkin3
  ABAND  =~ unp8 + aban1
  RULE   =~ ski2 + sru2

  FIMI =~ news4 + news9 + news14 + news15

  FIMI ~ THREAT + ABAND + FEAR + RULE

Study: S1 · Family: First-order blocks

Companion S1 block isolating state-abandonment heart (ABANH), perceived state knowledge (KNOW), and the two pragmatism subscales (PRAGR, PRAGCH). ABANM (media-censorship abandonment) is omitted to test whether censorship perceptions are required to recover the abandonment effect.

Structural paths

  • FIMI ~ ABANH + KNOW + PRAGR + PRAGCH
ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  KNOW  =~ aban6 + aban7 + aban8

  PRAGR =~ pru1 + pru2 + pru3 + pru4 + pru5 + pru6
  PRAGCH =~ pkin1 + pkin2 + pkin3 + pkin4 + pkin5 + pkin6

  FIMI =~ news1 + news2 + news3 + news4 + news5 +
          news6 + news7 + news8 + news9 + news10 +
          news11 + news12 + news13 + news14 + news15

  FIMI ~ ABANH + KNOW + PRAGR + PRAGCH

Study: S1 · Family: First-order blocks

Same as S1_block_abandon but adds the ABANM (media-censorship abandonment) latent. Pre-registered comparison: does adding ABANM improve fit and structural strength enough to justify keeping it in the full S1 SEM.

Structural paths

  • FIMI ~ ABANH + KNOW + ABANM + PRAGR + PRAGCH
ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  KNOW  =~ aban6 + aban7 + aban8
  ABANM =~ cen1 + cen2 + cen3 + cen4 + cen5

  PRAGR  =~ pru1 + pru2 + pru3 + pru4 + pru5 + pru6
  PRAGCH =~ pkin1 + pkin2 + pkin3 + pkin4 + pkin5 + pkin6

  FIMI =~ news1 + news2 + news3 + news4 + news5 +
          news6 + news7 + news8 + news9 + news10 +
          news11 + news12 + news13 + news14 + news15

  FIMI ~ ABANH + KNOW + ABANM + PRAGR + PRAGCH

Study: S1 · Family: First-order blocks

First S1 measurement block. Treats the six ideological-grievance subscales (CET, EXPL, MOR, GAY, ABANF, MIGR) as reflective latents and regresses FIMI on them directly. Used to gauge whether the grievance battery alone carries meaningful structural signal before the abandonment and admiration blocks are added.

Structural paths

  • FIMI ~ CET + EXPL + MOR + GAY + ABANF + MIGR
CET    =~ poi3 + poi6 + poi7
  EXPL   =~ exp1 + exp2 + exp3 + exp4
  MOR    =~ dec1 + dec2 + dec3 + dec4 + dec5
  GAY    =~ lgb1 + lgb2 + lgb3 + lgb4
  ABANF  =~ unp1 + unp6 + unp7 + unp8
  MIGR   =~ unp3 + unp4

  FIMI =~ news1 + news2 + news3 + news4 + news5 +
          news6 + news7 + news8 + news9 + news10 +
          news11 + news12 + news13 + news14 + news15

  FIMI ~ CET + EXPL + MOR + GAY + ABANF + MIGR

Study: S1 · Family: First-order blocks

S1 block for the two foreign-power belief-superiority subscales (SUPR, SUPCH; legacy S1 labels SUPR / SUPK), with FIMI paths included after the block measurement is specified. Establishes baseline measurement quality for the long admiration batteries before they are folded into the full SEM.

Structural paths

  • FIMI ~ SUPR + SUPCH
SUPR  =~ sru1 + sru2 + sru3 + sru4 + sru5 +
           sru6 + sru7 + sru8 + sru9 + sru10 +
           sru11 + sru12 + sru13 + sru14 + sru15

  SUPCH =~ ski1 + ski2 + ski3 + ski4 + ski5 +
           ski6 + ski7 + ski8 + ski9 + ski10 +
           ski11

  FIMI =~ news1 + news2 + news3 + news4 + news5 +
          news6 + news7 + news8 + news9 + news10 +
          news11 + news12 + news13 + news14 + news15

  FIMI ~ SUPR + SUPCH

Study: S1 · Family: Full SEM

All thirteen first-order S1 latents simultaneously regress on the S1 FIMI criterion. This is the reference first-order structural prediction model for Study 1; higher-order specifications address the separate construct-representation question.

Structural paths

  • FIMI ~ CET + EXPL + MOR + GAY + ABANF + MIGR + ABANH + KNOW + ABANM + PRAGR + PRAGCH + SUPR + SUPCH
CET   =~ poi3 + poi6 + poi7
  EXPL  =~ exp1 + exp2 + exp3 + exp4
  MOR   =~ dec1 + dec2 + dec3 + dec4 + dec5
  GAY   =~ lgb1 + lgb2 + lgb3 + lgb4
  ABANF =~ unp1 + unp6 + unp7 + unp8
  MIGR  =~ unp3 + unp4

  ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  KNOW  =~ aban6 + aban7 + aban8
  ABANM =~ cen1 + cen2 + cen3 + cen4 + cen5

  PRAGR  =~ pru1 + pru2 + pru3 + pru4 + pru5 + pru6
  PRAGCH =~ pkin1 + pkin2 + pkin3 + pkin4 + pkin5 + pkin6

  SUPR  =~ sru1 + sru2 + sru3 + sru4 + sru5 +
           sru6 + sru7 + sru8 + sru9 + sru10 +
           sru11 + sru12 + sru13 + sru14 + sru15

  SUPCH =~ ski1 + ski2 + ski3 + ski4 + ski5 +
           ski6 + ski7 + ski8 + ski9 + ski10 +
           ski11

  FIMI =~ news1 + news2 + news3 + news4 + news5 +
          news6 + news7 + news8 + news9 + news10 +
          news11 + news12 + news13 + news14 + news15

  FIMI ~ CET + EXPL + MOR + GAY + ABANF + MIGR +
          ABANH + KNOW + ABANM + PRAGR + PRAGCH + SUPR + SUPCH

Study: S1 · Family: Higher-order (hybrid MIMIC)

Higher-order S1 specification mirroring the original LISREL design. Each composite is reflectively identified by one or two direct indicators (e.g. ABAND =~ unp8 + aban1) and simultaneously regressed on its first-order parents (ABAND ~ ABANH + ABANF). This is a hybrid formative–reflective (MIMIC-style) construct-representation specification — the ~ operator is a structural regression between latents, not the lavaan formative operator <~. A separate prediction layer regresses FIMI on the four composites. Stabilisation: the pure-MIMIC parameterisation (without residual freeings) failed to converge on this wave under MLR / FIML at both std.lv = TRUE and std.lv = FALSE. The catalogued spec frees 24 residual covariances between each direct affective indicator and the other indicators in the first-order block from which it is drawn (e.g. unp8 ~~ unp1, unp8 ~~ unp6, unp8 ~~ unp7), substantively justified because the direct indicators are borrowed from the parent blocks and continue to carry within-block content variance. Under that freeing the model converges in ~35 s under MLR / FIML and produces a positive-definite vcov for the structural FIMI ~ paths. lavaan does flag a borderline non-positive-definite theta (observed-variable residual covariance matrix) — a Heywood-adjacent symptom of the 24 freed residual covariances bumping up against the same first-order multicollinearity that prevented pure-MIMIC convergence — so the model is read with that caveat rather than as a clean replacement for the pure formative or two-step variants. The post-fit fitMeasures / modindices pipeline is heavy under MLR for a model with this many free parameters (the robust-correction matrix inversion is the bottleneck), so the per-study page caches the extraction outputs to a sidecar file on first render and reads from it thereafter; subsequent renders of 3a and the cross-study consumers (4a, 4c) are fast. First-order parent multicollinearity (worst |r| up to .88 between ABANH/ABANF and PRAGR/PRAGCH) remains large enough to keep individual ABAND ~ ABANH + ABANF etc. weights unstable, so the pure formative (S1_second_formative) and two-step (S1_second_twostep_struct) readings remain on the page as complementary representations.

Structural paths

  • ABAND ~ ABANH + ABANF
  • FEAR ~ PRAGR + PRAGCH
  • THREAT ~ EXPL + GAY + MIGR
  • RULE ~ SUPR + SUPCH
  • FIMI ~ THREAT + FEAR + ABAND + RULE
ABANH =~ aban2 + aban3 + aban4 + aban5
  ABANF =~ unp1 + unp6 + unp7
  ABAND =~ unp8 + aban1
  ABAND ~ ABANH + ABANF

  PRAGR  =~ pru4 + pru2 + pru1 + pru5 + pru6
  PRAGCH =~ pkin4 + pkin2 + pkin1 + pkin5 + pkin6
  FEAR   =~ pru3 + pkin3
  FEAR ~ PRAGR + PRAGCH

  EXPL   =~ poi3 + poi6 + exp3 + exp4 + dec1 + dec4
  GAY    =~ lgb1 + lgb2 + lgb4
  MIGR   =~ unp3 + unp4
  THREAT =~ lgb3 + exp1
  THREAT ~ EXPL + GAY + MIGR

  SUPR  =~ sru1 + sru3 + sru4 + sru6 + sru7 + sru9 + sru10 + sru11 + sru12 + sru13 + sru14 + sru15
  SUPCH =~ ski1 + ski3 + ski4 + ski5 + ski6 + ski7 + ski8 + ski9 + ski10 + ski11
  RULE  =~ ski2 + sru2
  RULE ~ SUPR + SUPCH

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8 + news9 + news10 + news11 + news12 + news13 + news14 + news15
  FIMI ~ THREAT + FEAR + ABAND + RULE

  # Direct ABAND indicators ~~ their first-order block siblings:
  unp8 ~~ unp1
  unp8 ~~ unp6
  unp8 ~~ unp7
  aban1 ~~ aban2
  aban1 ~~ aban3
  aban1 ~~ aban4
  aban1 ~~ aban5

  # Direct FEAR indicators ~~ their first-order block siblings:
  pru3 ~~ pru1
  pru3 ~~ pru2
  pru3 ~~ pru4
  pru3 ~~ pru5
  pru3 ~~ pru6
  pkin3 ~~ pkin1
  pkin3 ~~ pkin2
  pkin3 ~~ pkin4
  pkin3 ~~ pkin5
  pkin3 ~~ pkin6

  # Direct THREAT indicators ~~ their first-order block siblings:
  lgb3 ~~ lgb1
  lgb3 ~~ lgb2
  lgb3 ~~ lgb4
  exp1 ~~ exp2
  exp1 ~~ exp3
  exp1 ~~ exp4

  # Direct RULE indicators ~~ their first-order block siblings:
  ski2 ~~ ski1
  ski2 ~~ ski3
  ski2 ~~ ski4
  ski2 ~~ ski5
  ski2 ~~ ski6
  ski2 ~~ ski7
  ski2 ~~ ski8
  ski2 ~~ ski9
  ski2 ~~ ski10
  ski2 ~~ ski11
  sru2 ~~ sru1
  sru2 ~~ sru3
  sru2 ~~ sru4
  sru2 ~~ sru5
  sru2 ~~ sru6
  sru2 ~~ sru7
  sru2 ~~ sru8
  sru2 ~~ sru9
  sru2 ~~ sru10
  sru2 ~~ sru11
  sru2 ~~ sru12
  sru2 ~~ sru13
  sru2 ~~ sru14
  sru2 ~~ sru15

Study: S1 · Family: Higher-order (pure formative composite)

Pure formative higher-order specification: each composite is built from its first-order parents via the lavaan formative operator <~ (e.g. THREAT <~ 1*EXPL + GAY + MIGR). The first formative weight in each composite is fixed to 1 (anchored composite scaling) so the model is identified under std.lv = TRUE; without the anchor the optimizer collapses to a degenerate all-zero solution. FIMI is reflectively measured by the full 15-item battery and provides the structural prediction layer (FIMI ~ THREAT + FEAR + ABAND + RULE) that closes the identification of the four composites. Sibling to S1_second_hybrid (stabilised hybrid MIMIC) and S1_second_reflective (fully reflective); the three representations triangulate the S1 higher-order construct space.

Structural paths

  • FIMI ~ THREAT + FEAR + ABAND + RULE
ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANF =~ unp1 + unp6 + unp7 + unp8

  PRAGR  =~ pru1 + pru2 + pru3 + pru4 + pru5 + pru6
  PRAGCH =~ pkin1 + pkin2 + pkin3 + pkin4 + pkin5 + pkin6

  EXPL =~ exp1 + exp2 + exp3 + exp4
  GAY  =~ lgb1 + lgb2 + lgb3 + lgb4
  MIGR =~ unp3 + unp4

  SUPR  =~ sru1 + sru2 + sru3 + sru4 + sru5 + sru6 + sru7 + sru8 + sru9 + sru10 + sru11 + sru12 + sru13 + sru14 + sru15
  SUPCH =~ ski1 + ski2 + ski3 + ski4 + ski5 + ski6 + ski7 + ski8 + ski9 + ski10 + ski11

  ABAND  <~ 1*ABANH + ABANF
  FEAR   <~ 1*PRAGR + PRAGCH
  THREAT <~ 1*EXPL + GAY + MIGR
  RULE   <~ 1*SUPR + SUPCH

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8 + news9 + news10 + news11 + news12 + news13 + news14 + news15
  FIMI ~ THREAT + FEAR + ABAND + RULE

Study: S1 · Family: Higher-order (reflective)

Fully reflective higher-order S1 specification: the four composites (THREAT, ABAND, FEAR, RULE) are reflective latents identified by their first-order factors via =~ (e.g. ABAND =~ ABANH + ABANF). Provides a contrast with the hybrid MIMIC and pure formative variants and is more permissive of multicollinearity, at the cost of conflating measurement and aggregation.

Structural paths

  • FIMI ~ THREAT + FEAR + ABAND + RULE
ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANF =~ unp1 + unp6 + unp7 + unp8
  ABAND =~ ABANH + ABANF

  PRAGR  =~ pru1 + pru2 + pru3 + pru4 + pru5 + pru6
  PRAGCH =~ pkin1 + pkin2 + pkin3 + pkin4 + pkin5 + pkin6
  FEAR   =~ PRAGR + PRAGCH

  EXPL   =~ exp1 + exp2 + exp3 + exp4
  GAY    =~ lgb1 + lgb2 + lgb3 + lgb4
  MIGR   =~ unp3 + unp4
  THREAT =~ EXPL + GAY + MIGR

  SUPR  =~ sru1 + sru2 + sru3 + sru4 + sru5 + sru6 + sru7 + sru8 + sru9 + sru10 + sru11 + sru12 + sru13 + sru14 + sru15
  SUPCH =~ ski1 + ski2 + ski3 + ski4 + ski5 + ski6 + ski7 + ski8 + ski9 + ski10 + ski11
  RULE  =~ SUPR + SUPCH

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8 + news9 + news10 + news11 + news12 + news13 + news14 + news15
  FIMI ~ THREAT + FEAR + ABAND + RULE

Study: S1 · Family: Two-step measurement CFA

Step 1 of the rescue solution for the hybrid MIMIC S1 collapse. A pure measurement CFA with the same first-order structure but no structural regressions, fitted with std.lv = TRUE and MLR/FIML. Factor scores from this fit feed the structural step (S1_second_twostep_struct).

Measurement-only specification (no structural regressions).

ABANH =~ aban2 + aban3 + aban4 + aban5
  ABANF =~ unp1 + unp6 + unp7
  ABAND =~ unp8 + aban1

  PRAGR  =~ pru4 + pru2 + pru1 + pru5 + pru6
  PRAGCH =~ pkin4 + pkin2 + pkin1 + pkin5 + pkin6
  FEAR   =~ pru3 + pkin3

  EXPL   =~ poi3 + poi6 + exp3 + exp4 + dec1 + dec4
  GAY    =~ lgb1 + lgb2 + lgb4
  MIGR   =~ unp3 + unp4
  THREAT =~ lgb3 + exp1

  SUPR  =~ sru1 + sru3 + sru4 + sru6 + sru7 + sru9 + sru10 +
           sru11 + sru12 + sru13 + sru14 + sru15
  SUPCH =~ ski1 + ski3 + ski4 + ski5 + ski6 + ski7 +
           ski8 + ski9 + ski10 + ski11
  RULE  =~ ski2 + sru2

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 +
          news8 + news9 + news10 + news11 + news12 + news13 + news14 + news15

Study: S1 · Family: Two-step structural

Step 2 of the rescue solution. The composite-level regressions (ABAND/FEAR/THREAT/RULE on their first-order parents; FIMI on the four composites) are re-estimated as ordinary ~ regressions on factor scores extracted from S1_second_twostep_measurement. This is not a lavaan formative model — ~ is a regression operator, not the formative <~ — but the factor-score approach approximates the composite logic while side-stepping the latent-level multicollinearity that caused the hybrid MIMIC variant (S1_second_hybrid) to produce Heywood cases.

Structural paths

  • ABAND ~ ABANH + ABANF
  • FEAR ~ PRAGR + PRAGCH
  • THREAT ~ EXPL + GAY + MIGR
  • RULE ~ SUPR + SUPCH
  • FIMI ~ THREAT + FEAR + ABAND + RULE
ABAND  ~ ABANH + ABANF
  FEAR   ~ PRAGR + PRAGCH
  THREAT ~ EXPL  + GAY + MIGR
  RULE   ~ SUPR  + SUPCH
  FIMI   ~ THREAT + FEAR + ABAND + RULE

Study: S2 · Family: Abbreviated

Three-indicator-per-composite reduced deployment model derived from S2_main. Drops the formative aggregation and uses the four composites directly as reflective latents. FIMI uses the source-balanced four-item Short FIMI criterion (news2, news5, news7, news8). Functions as the prototype reduced instrument carried forward to S3; retained criterion prediction is interpreted as a separate check.

Structural paths

  • FIMI ~ THREAT + ABAND + FEAR + SUPF
THREAT =~ th9 + th4 + th6
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa4 + pa6
  SUPF   =~ fru2 + fru3 + fru4

  FIMI =~ news2 + news5 + news7 + news8
  FIMI ~ THREAT + ABAND + FEAR + SUPF

Study: S2 · Family: Higher-order (hybrid MIMIC)

Reference S2 higher-order representation with a separate FIMI prediction layer. Each higher-order composite (THREAT, ABAND, FEAR, SUPF) is reflectively identified by direct affective indicators (e.g. THREAT =~ th9 + th4 + th6) and simultaneously regressed on its component first-order factors (THREAT ~ EXPL + GAY + MIGR). This is a hybrid formative–reflective (MIMIC-style) specification, not a pure formative composite — the ~ operator is a structural regression between latents, not the lavaan formative operator <~. FIMI loads on the eight-item news battery (news1–news8) and is then regressed on the four composites. Convergence: the canonical spec converges cleanly under MLR / FIML in ~7 s. Why it fits worse than S2_main_formative: residual diagnostics (modindices ≥ 10) flag substantial within-composite residual correlation that the pure-MIMIC parameterisation does not absorb — the FEAR indicator pair pa4 ~~ pa5 carries MI ≈ 287 and pa1 ~~ pa4 MI ≈ 256 (six FEAR direct indicators loading on a single first-order parent PRAGR concentrate the shared variance into residual correlations), and fru2 ~~ fru3 (MI ≈ 54) and th4 ~~ th6 (MI ≈ 38) flag analogous within-block residuals in SUPF and THREAT. First-order parent multicollinearity is moderate (ABAND parents worst |r| ≈ .80, cond ≈ 12; THREAT parents worst |r| ≈ .68, cond ≈ 7) and does not by itself prevent convergence on this wave. The pure formative variant (S2_main_formative) drops the direct indicators and so sidesteps the within-composite residual issue entirely.

Structural paths

  • THREAT ~ EXPL + GAY + MIGR
  • ABAND ~ ABANF + ABANH + ABANM
  • FEAR ~ PRAGR
  • SUPF ~ SUPR
  • FIMI ~ THREAT + ABAND + FEAR + SUPF
EXPL =~ exp2 + exp3 + exp4 + exp5
  GAY  =~ lgb2 + lgb3 + lgb4
  MIGR =~ mi2 + mi3 + mi4
  THREAT =~ th9 + th4 + th6
  THREAT ~ EXPL + GAY + MIGR

  ABANF =~ unp1 + unp2 + unp3 + unp4
  ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANM =~ cen2 + cen4 + cen5 + cen6
  ABAND =~ ab2 + ab4 + ab7
  ABAND ~ ABANF + ABANH + ABANM

  PRAGR =~ pru1 + pru2 + pru4 + pru5
  FEAR  =~ pa1 + pa2 + pa3 + pa4 + pa5 + pa6
  FEAR  ~ PRAGR

  SUPR =~ sru1 + sru2 + sru3 + sru6 + sru8 + sru9
  SUPF =~ fru2 + fru3 + fru4
  SUPF ~ SUPR

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8
  FIMI ~ THREAT + ABAND + FEAR + SUPF

Study: S2 · Family: Higher-order (pure formative composite)

Pure formative variant of S2_main. Drops the direct affective indicators (th9, th4, th6, etc.) and identifies each higher-order composite from its first-order parents alone via the lavaan formative operator <~ (e.g. THREAT <~ 1*EXPL + GAY + MIGR). Each composite anchors its first formative weight to 1 — without the anchor the un-identified specification collapses to a degenerate all-zero solution under std.lv = TRUE. FIMI remains reflectively measured and the FIMI ~ THREAT + ABAND + FEAR + SUPF prediction layer closes the identification of the composites. Documented alongside S2_main so the conceptual contrast between hybrid MIMIC (=~ + ~) and pure formative (<~) higher-order specifications is preserved in the catalogue.

Structural paths

  • FIMI ~ THREAT + ABAND + FEAR + SUPF
EXPL =~ exp2 + exp3 + exp4 + exp5
  GAY  =~ lgb2 + lgb3 + lgb4
  MIGR =~ mi2 + mi3 + mi4
  THREAT <~ 1*EXPL + GAY + MIGR

  ABANF =~ unp1 + unp2 + unp3 + unp4
  ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANM =~ cen2 + cen4 + cen5 + cen6
  ABAND <~ 1*ABANF + ABANH + ABANM

  PRAGR =~ pru1 + pru2 + pru4 + pru5
  FEAR  <~ 1*PRAGR

  SUPR =~ sru1 + sru2 + sru3 + sru6 + sru8 + sru9
  SUPF <~ 1*SUPR

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8
  FIMI ~ THREAT + ABAND + FEAR + SUPF

Study: S3 · Family: Abbreviated

German reduced-instrument mirror of S2_brief. Same four reflective composites and source-balanced four-item Short FIMI criterion; provides the cross-cultural test of the prototype deployment form and its retained prediction layer.

Structural paths

  • FIMI ~ THREAT + ABAND + FEAR + SUPF
THREAT =~ th9 + th4 + th6
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa2 + pa6
  SUPF   =~ fru1 + fru2 + fru3 + fru4

  FIMI =~ news2 + news5 + news7 + news8
  FIMI ~ THREAT + ABAND + FEAR + SUPF

Study: S3 · Family: Higher-order (hybrid MIMIC)

German cross-cultural replication of S2_main. It carries forward the same hybrid formative–reflective (MIMIC-style) construct representation (each composite is reflectively identified by direct affective indicators and regressed on its first-order parents via ~) and then tests the same FIMI ~ THREAT + ABAND + FEAR + SUPF prediction layer. Differences vs. S2: FEAR uses the German pa2/pa6 indicators, SUPR uses the extended sru1–sru12 battery, and SUPF includes the additional fru1 item. Convergence: clean under MLR / FIML in ~13 s. Why it fits worse than S3_main_formative: the German wave shows the same diagnostic pattern as S2 in a more concentrated form. The SUPF residual fru2 ~~ fru3 carries MI ≈ 77 (vs. 54 in S2), the only direct-indicator pair to clear the MI ≥ 10 threshold on this wave because S3’s two-indicator FEAR (pa2 + pa6) cannot generate the within-FEAR residual cluster seen in S2. First-order parent multicollinearity is consistently higher in the German sample than in the Lithuanian one (THREAT parents worst |r| ≈ .77, cond ≈ 13; ABAND parents worst |r| ≈ .82, cond ≈ 15) — a substantive cross-cultural signal that German respondents fuse the grievance and abandonment first-order factors more tightly than Lithuanian respondents do. The hybrid MIMIC representation absorbs this multicollinearity through unstable ~ weights; the pure formative variant absorbs it as instability in the formative weights instead, with comparable composite-level prediction strength.

Structural paths

  • THREAT ~ EXPL + GAY + MIGR
  • ABAND ~ ABANF + ABANH + ABANM
  • FEAR ~ PRAGR
  • SUPF ~ SUPR
  • FIMI ~ THREAT + ABAND + FEAR + SUPF
EXPL =~ exp2 + exp3 + exp4 + exp5
  GAY  =~ lgb2 + lgb3 + lgb4
  MIGR =~ mi2 + mi3 + mi4
  THREAT =~ th9 + th4 + th6
  THREAT ~ EXPL + GAY + MIGR

  ABANF =~ unp1 + unp2 + unp3 + unp4
  ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANM =~ cen2 + cen4 + cen5 + cen6
  ABAND =~ ab2 + ab4 + ab7
  ABAND ~ ABANF + ABANH + ABANM

  PRAGR =~ pru1 + pru2 + pru4 + pru5
  FEAR  =~ pa2 + pa6
  FEAR  ~ PRAGR

  SUPR =~ sru1 + sru2 + sru3 + sru4 + sru5 + sru6 + sru7 + sru8 + sru9 + sru10 + sru11 + sru12
  SUPF =~ fru1 + fru2 + fru3 + fru4
  SUPF ~ SUPR

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8
  FIMI ~ THREAT + ABAND + FEAR + SUPF

Study: S3 · Family: Higher-order (pure formative composite)

Pure formative variant of S3_main. Drops the direct affective indicators and identifies each higher-order composite from its first-order parents alone via <~ with the first formative weight fixed to 1 (e.g. THREAT <~ 1*EXPL + GAY + MIGR). Keeps the same first-order indicator sets and the same downstream FIMI ~ THREAT + ABAND + FEAR + SUPF prediction layer. Provides the German counterpart to S2_main_formative.

Structural paths

  • FIMI ~ THREAT + ABAND + FEAR + SUPF
EXPL =~ exp2 + exp3 + exp4 + exp5
  GAY  =~ lgb2 + lgb3 + lgb4
  MIGR =~ mi2 + mi3 + mi4
  THREAT <~ 1*EXPL + GAY + MIGR

  ABANF =~ unp1 + unp2 + unp3 + unp4
  ABANH =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANM =~ cen2 + cen4 + cen5 + cen6
  ABAND <~ 1*ABANF + ABANH + ABANM

  PRAGR =~ pru1 + pru2 + pru4 + pru5
  FEAR  <~ 1*PRAGR

  SUPR =~ sru1 + sru2 + sru3 + sru4 + sru5 + sru6 + sru7 + sru8 + sru9 + sru10 + sru11 + sru12
  SUPF <~ 1*SUPR

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8
  FIMI ~ THREAT + ABAND + FEAR + SUPF

Study: S4 · Family: Abbreviated

Multinational deployment measurement model for the S4 short DisInforMeter. It uses the actually fielded S4 indicators, including the compressed/combined deployment items and separate Russia (SUPF, fru*) and China (SUPFCH, fch*) affective-admiration factors. This model is the predictor-side baseline for country invariance before any FIMI prediction paths are interpreted.

Measurement-only specification (no structural regressions).

GEN    =~ gen1 + gen2 + gen3 + gen5 + gen7
  THREAT =~ th6 + th9
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa2 + pa4
  SUPF   =~ fru1 + fru2 + fru3
  SUPFCH =~ fch1 + fch2 + fch3

Study: S4 · Family: Full SEM

Sensitivity model using the three Chinese-origin S2+ news items (news6-news8) as the FIMI criterion while keeping the S4 predictor measurement model fixed.

Structural paths

  • FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH
GEN    =~ gen1 + gen2 + gen3 + gen5 + gen7
  THREAT =~ th6 + th9
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa2 + pa4
  SUPF   =~ fru1 + fru2 + fru3
  SUPFCH =~ fch1 + fch2 + fch3

  FIMI =~ news6 + news7 + news8
  FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH

Study: S4 · Family: Full SEM

Primary Study 4 structural-prediction model. The deployed predictor factors (GEN, THREAT, ABAND, FEAR, SUPF, SUPFCH) predict the harmonised eight-item S2+ FIMI criterion (news1-news8) in the full multinational sample.

Structural paths

  • FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH
GEN    =~ gen1 + gen2 + gen3 + gen5 + gen7
  THREAT =~ th6 + th9
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa2 + pa4
  SUPF   =~ fru1 + fru2 + fru3
  SUPFCH =~ fch1 + fch2 + fch3

  FIMI =~ news1 + news2 + news3 + news4 + news5 + news6 + news7 + news8
  FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH

Study: S4 · Family: Full SEM

Sensitivity model using the five Russian-origin S2+ news items (news1-news5) as the FIMI criterion while keeping the S4 predictor measurement model fixed.

Structural paths

  • FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH
GEN    =~ gen1 + gen2 + gen3 + gen5 + gen7
  THREAT =~ th6 + th9
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa2 + pa4
  SUPF   =~ fru1 + fru2 + fru3
  SUPFCH =~ fch1 + fch2 + fch3

  FIMI =~ news1 + news2 + news3 + news4 + news5
  FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH

Study: S4 · Family: Full SEM

Comparability model using the source-balanced four-item cross-wave Short FIMI criterion (news2, news5, news7, news8) while keeping the S4 predictor measurement model fixed.

Structural paths

  • FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH
GEN    =~ gen1 + gen2 + gen3 + gen5 + gen7
  THREAT =~ th6 + th9
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa2 + pa4
  SUPF   =~ fru1 + fru2 + fru3
  SUPFCH =~ fch1 + fch2 + fch3

  FIMI =~ news2 + news5 + news7 + news8
  FIMI ~ GEN + THREAT + ABAND + FEAR + SUPF + SUPFCH

Study: S5 · Family: Abbreviated

Three-indicator-per-construct reduced deployment form parallel to S2_brief / S3_brief. Because S5 has no FIMI battery, this entry is a pure five-factor measurement model: THREAT, ABAND, FEAR, SUPR, SUPCH. Used to confirm that the brief scale’s measurement structure survives in a fresh Lithuanian validation sample one year on from Study 2.

Measurement-only specification (no structural regressions).

THREAT =~ th9 + th4 + th6
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa4 + pa6
  SUPR   =~ sru1 + sru2 + sru3
  SUPCH  =~ ski1 + ski2 + ski3

Study: S5 · Family: Higher-order (hybrid MIMIC)

Hybrid MIMIC sibling of S5_long_cfa, fitted as a measurement-only model because S5 fields no FIMI battery. The S2 / S3 composites (THREAT, ABAND, FEAR) are reflectively identified by their direct affective indicators (th9 + th4 + th6, ab2 + ab4 + ab7, pa1 + pa4 + pa6) and simultaneously regressed on their S5 first-order parents (THREAT on EXPL/GAY/MIGR; ABAND on ABANF/ABANH/ABANM; FEAR on PRAGR). The remaining S5 first-order constructs (CET, PRAGCH, SUPF, SUPFCH, SUPR, SUPCH) appear as reflective latents only — S5 does not field a higher-order composite indicator for foreign-power admiration, so SUPR and SUPCH do not get a MIMIC layer. Exploratory: the model converges in ~9 s under MLR / FIML but the vcov is borderline non-positive-definite (smallest eigenvalue ≈ -2.5e-14, numerically zero) and lavaan flags a single negative observed-variable residual variance, consistent with S5’s lack of a downstream prediction layer to absorb the composites’ residual variance (the S2 / S3 hybrids rely on FIMI ~ THREAT + ABAND + FEAR + SUPF to close the structural side of identification). Catalogued so the cross-wave temporal-invariance ladder (S2 ↔︎ S5) can probe the hybrid MIMIC parameterisation as well as the reflective measurement model, with the caveat that S5’s measurement-only fit is not a substitute for the joint measurement-plus-prediction estimation available on S2 / S3.

Structural paths

  • THREAT ~ EXPL + GAY + MIGR
  • ABAND ~ ABANF + ABANH + ABANM
  • FEAR ~ PRAGR
EXPL   =~ exp2 + exp3 + exp4 + exp5
  GAY    =~ lgb2 + lgb3 + lgb4
  MIGR   =~ mi2 + mi3 + mi4
  THREAT =~ th9 + th4 + th6
  THREAT ~  EXPL + GAY + MIGR

  ABANF  =~ unp1 + unp2 + unp3 + unp4
  ABANH  =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANM  =~ cen2 + cen4 + cen5 + cen6
  ABAND  =~ ab2 + ab4 + ab7
  ABAND  ~  ABANF + ABANH + ABANM

  PRAGR  =~ pru1 + pru2 + pru4 + pru5
  FEAR   =~ pa1 + pa4 + pa6
  FEAR   ~  PRAGR

  CET    =~ cet1 + cet2 + cet3 + cet4
  PRAGCH =~ pkin1 + pkin2 + pkin4 + pkin5
  SUPF   =~ sup1 + sup2 + sup3 + sup4
  SUPFCH =~ sup5 + sup6 + sup7 + sup8
  SUPR   =~ sru1 + sru2 + sru3 + sru6 + sru8 + sru9
  SUPCH  =~ ski1 + ski2 + ski3 + ski6 + ski8 + ski9

Study: S5 · Family: Invariance

Descriptive catalogue entry naming the cross-time invariance ladder fitted by 03e-study5-lithuania.qmd. The actual configural → metric → scalar fits use S5_brief_cfa as the measurement model and stack the S2 and S5 frames on a common indicator subset (THREAT/ABAND/FEAR triplets — SUPR/SUPCH indicators differ across waves so the ladder is restricted to the shared predictors). Results are written to outputs/tables/s5_s2_invariance.csv and treated as exploratory.

Measurement-only specification (no structural regressions).

THREAT =~ th9 + th4 + th6
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa4 + pa6
  SUPR   =~ sru1 + sru2 + sru3
  SUPCH  =~ ski1 + ski2 + ski3

Study: S5 · Family: Measurement

Pure measurement model for the Study 5 validation wave (n = 248 Lithuanian VU SONA pool). Sixteen reflective predictor latents reuse the S2/S3 indicator vocabulary and add CET, SUPF (Russia affective admiration, sup1–sup4 — identical content to S2/S3 SUPF), SUPFCH (China affective admiration, sup5–sup8, newly modelled in this wave), and SUPCH (China beliefs, ski*) for the constructs newly available in Study 5. No FIMI factor (S5 deliberately omits the news-headline battery). All latents are free to covary; structural paths are tested elsewhere via factor-score correlations against the validation anchors.

Measurement-only specification (no structural regressions).

EXPL   =~ exp2 + exp3 + exp4 + exp5
  GAY    =~ lgb2 + lgb3 + lgb4
  MIGR   =~ mi2 + mi3 + mi4
  THREAT =~ th9 + th4 + th6
  CET    =~ cet1 + cet2 + cet3 + cet4
  ABANF  =~ unp1 + unp2 + unp3 + unp4
  ABANH  =~ aban1 + aban2 + aban3 + aban4 + aban5
  ABANM  =~ cen2 + cen4 + cen5 + cen6
  ABAND  =~ ab2 + ab4 + ab7
  FEAR   =~ pa1 + pa4 + pa6
  PRAGR  =~ pru1 + pru2 + pru4 + pru5
  PRAGCH =~ pkin1 + pkin2 + pkin4 + pkin5
  SUPF   =~ sup1 + sup2 + sup3 + sup4
  SUPFCH =~ sup5 + sup6 + sup7 + sup8
  SUPR   =~ sru1 + sru2 + sru3 + sru6 + sru8 + sru9
  SUPCH  =~ ski1 + ski2 + ski3 + ski6 + ski8 + ski9

Model families

The catalogue uses four registered model families. The family name tells readers which syntax template is being used; the analytic purpose — measurement validation, construct representation, structural prediction, scale reduction — is read off the purpose crosswalk above.

  1. First-Order Block Models — test individual construct domains separately (ideology, abandonment, Russia/China admiration) to establish baseline first-order measurement properties before larger measurement or prediction models are interpreted.
  2. Full First-Order SEM — integrate all first-order constructs simultaneously and estimate their paths to the named FIMI criterion. This is a structural prediction model using first-order predictors.
  3. Higher-Order Models — organise first-order factors into broader DisInforMeter dimensions (THREAT, FEAR, ABAND, RULE/SUPF). Three distinct lavaan representations are compared where the data support them: reflective second-order (THREAT =~ EXPL + GAY + MIGR), pure formative composite (THREAT <~ EXPL + GAY + MIGR), and hybrid formative–reflective / MIMIC-style (THREAT =~ th9 + th4 + th6; THREAT ~ EXPL + GAY + MIGR). Legacy aliases retained as documentation: S1 used USE for EXPL and LEFT for the abandonment composite (ABAND); S2–S4 used PRAG for FEAR. When these models also include FIMI ~ ..., the prediction paths are interpreted as a separate stage after FIMI operationalisation has been defined.
  4. Brief Models — operationalise each construct with 2–3 highly diagnostic items to create a reduced instrument for survey deployment. Their FIMI paths evaluate whether predictive utility is retained after reduction.
Model families implemented across studies
Study Family N Models Model IDs
S1 Abbreviated 1 S1_brief
S1 First-order blocks 4 S1_block_ideology, S1_block_abandon, S1_block_abandon_free, S1_block_russia
S1 Full SEM 1 S1_full
S1 Higher-order (hybrid MIMIC) 1 S1_second_hybrid
S1 Higher-order (pure formative composite) 1 S1_second_formative
S1 Higher-order (reflective) 1 S1_second_reflective
S1 Two-step measurement CFA 1 S1_second_twostep_measurement
S1 Two-step structural 1 S1_second_twostep_struct
S2 Abbreviated 1 S2_brief
S2 Higher-order (hybrid MIMIC) 1 S2_main
S2 Higher-order (pure formative composite) 1 S2_main_formative
S3 Abbreviated 1 S3_brief
S3 Higher-order (hybrid MIMIC) 1 S3_main
S3 Higher-order (pure formative composite) 1 S3_main_formative
S4 Abbreviated 1 S4_deploy_cfa
S4 Full SEM 4 S4_pred_full, S4_pred_russian, S4_pred_chinese, S4_pred_short
S5 Abbreviated 1 S5_brief_cfa
S5 Higher-order (hybrid MIMIC) 1 S5_long_mimic
S5 Invariance 1 S5_S2_long_invariance_meta
S5 Measurement 1 S5_long_cfa

Item-level mapping across studies

The tables below show how items align across all five ingested waves. Each per-wave column carries the canonical variable name used in the wrangled item-level parquet exports (data/wrangled_data/study{1..5}_items.parquet), so the entries are directly addressable from the per-study modelling pages. The hand-built master mapping with both Qualtrics-recorded and harmonised names lives at data/item_mapping_mini.csv (mirrored to outputs/item_mapping_mini.csv); a flattened machine-readable copy of the rendered tables is exported below to outputs/item_mapping_overview.csv and outputs/item_mapping_overview.xlsx.

<b>First-order construct items</b>
First-order construct items across studies. Cell entries are the canonical variable names used in the wrangled item-level exports for each wave; dashes mark items not administered.
Item Text (abbreviated) S1 S2 S3 S4 S5
Exploitation
We are unable to use our nation’s greatest potential beca... poi3 exp1 exp1 — exp1
Foreign countries are exploiting our nation’s resources. exp2 exp2 exp2 — exp2
Western civilization is characterized by materialism and ... exp3 exp3 exp3 — exp3
Globalization poses a big threat to our statehood and nat... exp4 exp4 exp4 — exp4
Over the past decades, moral values have declined due to ... dec1 exp5 exp5 — exp5
We have become puppets of Brussels. exp1 — — — —
LGBT+ Opposition
We should protect and enforce traditional gender roles. lgbt1 lgb1 lgb1 — lgb1
The LGBT+ movement is a threat to our values. lgbt2 lgb2 lgb2 — lgb2
LGBT+ rights promotion is a disguised form of colonization. lgbt3 lgb3 lgb3 — lgb3
We should ban LGBT+ propaganda like countries as Russia o... lgbt4 lgb4 lgb4 — lgb4
We should immediately stop promoting leftist, woke gender... — lgb5 lgb5 — lgb5
We should acknowledge biological reality that only two ge... — lgb6 lgb6 — lgb6
Immigration
The EU is unable to handle immigration. unp3 mi1 mi1 — mi1
Immigrants are changing Europe for the worse. unp4 mi2 mi2 — mi2
We should adopt a much harder line against immigration. — mi3 mi3 — mi3
Immigrants take advantage of our country. — mi4 mi4 — mi4
We should deport all immigrants to where they came from. — mi5 mi5 — mi5
Immigrants are responsible for many of my country's bigge... — mi6 mi6 — mi6
Foreigners do not belong in Lithuania. — mi7 mi7 — mi7
Unprotected by international allies
EU is weak and has no power. unp1 unp1 unp1 — unp1
NATO will not be brave enough to defend our nation in cas... unp5 unp2 unp2 — unp2
NATO will betray us like Ukraine has been betrayed. unp6 unp3 unp3 — unp3
NATO has expanded too much and will be torn apart by inte... unp8 unp4 unp4 — unp4
The influence of the USA in the world is getting weaker a... unp2 — — — —
We should quit NATO as NATO membership poses a great thre... unp7 — — — —
Abandoned by own state
My state has abandoned its citizens. aban1 aban1 aban1 — aban1
My state is exploiting its citizens. aban2 aban2 aban2 — aban2
My state is a failed state. aban3 aban3 aban3 — aban3
I don't feel that my state takes good care of me. aban4 aban4 aban4 — aban4
My state is not able to ensure jobs and fair income for e... aban5 aban5 aban5 — aban5
I feel anger towards specific politicians who made our da... aban6 — — — —
I feel outraged with specific politicians who have failed... aban7 — — — —
I possess information on how specific politicians worked ... aban8 — — — —
Abandoned by media (censorship)
My state is censoring access to truthful information. — cen1 cen1 — cen1
My state is supporting media you cannot trust. — cen2 cen2 — cen2
My state actively restricts my freedom of opinion. — cen3 cen3 — cen3
All mainstream media are lying to us. cens1 cen4 cen4 — cen4
Mainstream media are trying to brainwash citizens of my c... — cen5 cen5 — cen5
Mainstream media are useless in providing truthful and ac... — cen6 cen6 — cen6
Pragmatism — Russia
It is a mistake that we are not allowed to collaborate wi... prag_ru1 pru1 pru1 — pru1
Countries like Ukraine should finally start building good... prag_ru2 pru2 pru2 — pru2
We should not become enemies with countries like Russia. prag_ru3 pru3 pru3 — pru3
The West should not behave aggressively towards countries... prag_ru4 pru4 pru4 — pru4
Countries like Russia never attack without being provoked. prag_ru5 pru5 pru5 — pru5
Russia is like a sleeping bear that we should not wake up. prag_ru6 pru6 pru6 — pru6
Pragmatism — China
It is a mistake that we are not allowed to collaborate wi... prag_kin1 pch1 pch1 — pkin1
Taiwan should finally stop provoking China. prag_kin2 pch2 pch2 — pkin2
We should not become enemies with countries like China. prag_kin3 pch3 pch3 — pkin3
The West should not behave aggressively towards countries... prag_kin4 pch4 pch4 — pkin4
Countries like China never attack without being provoked. prag_kin5 pch5 pch5 — pkin5
China is like a sleeping dragon that we should not wake up. prag_kin6 pch6 pch6 — pkin6
Superiority — Russia (beliefs)
Russia has an important historic mission. sup_ru1 sru1 sru1 — sru1
Russia will reemerge as the most powerful nation in the w... sup_ru2 sru2 sru2 — sru2
Russia is technologically advanced. sup_ru3 sru3 sru3 — sru3
Russia has innovative military technologies. sup_ru4 sru4 sru4 — sru4
Russia represents a unique Slavic civilization. sup_ru6 sru5 sru5 — sru5
Russian culture is a superior culture. sup_ru7 sru6 sru6 — sru6
Russia is the last bastion of anti-systemic and anti-glob... sup_ru8 sru7 sru7 — sru7
Russia is able to defend its core values. sup_ru9 sru8 sru8 — sru8
Russia is able to take good care of its citizens. sup_ru10 sru9 sru9 — sru9
Russia has a unique spiritual potential. sup_ru11 sru10 sru10 — sru10
Russia draws its strength from its places of spiritual im... sup_ru13 sru11 sru11 — sru11
Russia will protect us if needed. — sru12 sru12 — sru12
Russian hackers are able to hack any institution in the w... sup_ru5 — — — —
Siberian cedar is a tree of exceptional spiritual importa... sup_ru12 — — — —
Putin's strong and masculine personality resonates well w... sup_ru14 — — — —
Putin is a strong leader standing up against the West. sup_ru15 — — — —
Superiority — China (beliefs)
China has an important historic mission. sup_kin1 ski1 ski1 — ski1
China will reemerge as the most powerful nation in the wo... sup_kin2 ski2 ski2 — ski2
China will soon have full control over the world economy. sup_kin3 ski3 ski3 — ski3
China is technologically advanced. sup_kin4 ski4 ski4 — ski4
China has innovative military technologies. sup_kin5 ski5 ski5 — ski5
China represents a unique civilization. sup_kin7 ski6 ski6 — ski6
Chinese culture is a superior culture. sup_kin8 ski7 ski7 — ski7
China is successfully reshaping the global system for its... sup_kin9 ski8 ski8 — ski8
China is able to defend its core values. sup_kin10 ski9 ski9 — ski9
China is able to take good care of its citizens.. sup_kin11 ski10 ski10 — ski10
China will protect us if needed. — ski11 ski11 — ski11
Chinese agents are able to infiltrate into any institutio... sup_kin6 — — — —
Poisonous ethnocentrism
Our national interests are more important than other coun... — cet1 cet1 — cet1
We should protect our nation's interests by any means nec... — cet2 cet2 — cet2
Preserving our culture, language, and identity as the pre... — cet3 cet3 — cet3
Everything that is non-Lithuanian may threaten the surviv... — cet4 cet4 — cet4
Our enemies are constantly threatening our national inter... — cet5 cet5 — cet5
We should protect our culture, language and identity from... — cet6 cet6 — cet6
By joining unions like the EU or NATO, we are losing our ... poi6 cet7 cet7 — cet7
We have sold our national identity to unions like the EU ... poi7 cet8 cet8 — cet8
We should not easily adopt values and lifestyles that are... poi1 — — — —
Outsiders from abroad are constantly threatening our nati... poi2 — — — —
We should keep the land where our ancestors lived for our... poi4 — — — —
We should protect our traditions from outsiders. poi5 — — — — 


<b>Higher-order composite indicators</b>
Direct higher-order composite / affective indicators (introduced from Study 2 onward). The GENERAL block carries forward to S4 (5-item subset) and S5 (full 8 items).
Item Text (abbreviated) S1 S2 S3 S4 S5
Threat (affective)
I’m worried that our ways of life are sought to be destro... — th1 th1 th1 th1
I am sad because our culture, language, and identity are ... — th2 th2 — th2
I feel a threat to the survival of our nation-state. — th3 th3 — th3
I hate Western liberalism. — th4 th4 — th4
I’m worried that my country is being exploited by foreign... — th5 th5 th5 th5
I am angry when I think about how my country is being use... — th6 th6 th6 th6
I am angry because immigration is changing our way of lif... — th7 th7 th7 th7
I feel worried because of uncontrolled immigration. — th8 th8 th8 th8
I am worried about the spread of LGBT+ propaganda. — th9 th9 th9 th9
I’m outraged when thinking about the promotion LGBT+ ideas. — th10 th10 th10 th10
I’m disgusted by the LGBT+ propaganda. — th11 th11 — th11
I feel nostalgic for the days when moral values truly mat... — th12 th12 — th12
Distrust / betrayal / abandonment
In general, I distrust our international allies. — ab1 ab1 ab1 ab1
I feel disappointed by the actions of the international a... — ab2 ab2 ab2 ab2
I feel frustrated by how my state addresses citizens' needs. — ab3 ab3 ab3 ab3
I’m angry at my state for failing to protect the interest... — ab4 ab4 ab4 ab4
I feel sad when I think about how my country takes care o... — ab5 ab5 — ab5
I hate my state because it fails to take care of its citi... — ab6 ab6 — ab6
I feel angry because the knowledge I want to access is be... cens4 ab7 ab7 ab7 ab7
I'm frustrated because my state bans the media I want to ... — ab8 ab8 ab8 ab8
Fear / pragmatic-accommodation affect
I feel tense when thinking about potential conflicts with... — pa1 pa1 pa1 pa1
I would feel safer if peace with countries like Russia is... — pa2 pa2 — pa2
I would feel safer if peace with countries like China is ... — pa3 pa3 — pa3
I’m anxious about the consequences of a conflict with cou... — pa4 pa4 — pa4
I’m anxious about the consequences of a conflict with cou... — pa5 pa5 — pa5
I am angry that we are risking the safety of its citizens... — pa6 pa6 — pa6
I would feel safer if peace with countries like Russia or... — — — pa2 —
I’m anxious about the consequences of a conflict with cou... — — — pa4 —
Superiority (affective admiration)
To a certain extent, I admire China. — fch1 fch1 fch1 sup5
Sometimes, I feel inspired by the actions of China. — fch2 fch2 fch2 sup6
China gives me hope. — fch3 fch3 fch3 sup7
I respect China. — fch4 fch4 — sup8
To a certain extent, I admire Russia. — fru1 fru1 fru1 sup1
Sometimes, I feel inspired by the actions of Russia. — fru2 fru2 fru2 sup2
Russia gives me hope. — fru3 fru3 fru3 sup3
I respect Russia. — fru4 fru4 — sup4
General / global DisInformeter items
I have a very negative feeling about how my state handles... — gen1 gen1 gen1 gen1
I dislike the actions of our international allies in ensu... — gen2 gen2 gen2 gen2
I fear the consequences of provoking countries like Russia. — gen3 gen3 — gen3
I fear the consequences of provoking countries like China. — gen4 gen4 — gen4
I like Russia. — gen5 gen5 gen5 gen5
I trust Russia. — gen6 gen6 — gen6
I like China. — gen7 gen7 gen7 gen7
I trust China. — gen8 gen8 — gen8
I fear the consequences of provoking countries like Russi... — — — gen3 — 


<b>FIMI items</b>
FIMI news-item mapping and model inclusion across S1–S4. Study 5 deliberately omits the FIMI battery and is therefore not represented here.
Item Text (abbreviated) S1 S2 S3 S4 Main Model (S2–S4) Short FIMI (4-item)
Zelensky bought a British mansion from King Charles for 2... news3 news1 news1 news1 S2 + S3 + S4 —
France asked Russia not to touch the French military in U... news4 news2 news2 news2 S2 + S3 + S4 Yes
The 2026 Milan–Cortina d'Ampezzo Olympics and Paralympics... news7 news3 news3 news3 S2 + S3 + S4 —
Ukrainian army is looking for a mentor on tolerance worki... news8 news4 news4 news4 S2 + S3 + S4 —
Gays and transvestites in Kiev are invited to join LGBT b... news9 news5 news5 news5 S2 + S3 + S4 Yes
Li-Meng Yan, a Chinese virologist who alleges that the CO... news12 news6 news6 news6 S2 + S3 + S4 —
CGTN: Closer People-to-People Bonds foster China-Vietnam ... news14 news7 news7 news7 S2 + S3 + S4 Yes
The plague-like rule of extreme right-wing religious lead... news15 news8 news8 news8 S2 + S3 + S4 Yes
Russian hackers hacked the website of the Finnish Parliam... news1 — — — — —
Ukraine and Poland join forces: joint production of war d... news2 — — — — —
Global Times &#124; US the exploiter news5 — — — — —
No Lenin – no electrification. Its logical that “we have ... news6 — — — — —
Russian hackers from KillNet registered NATO employees on... news10 — — — — —
In Bremerhaven, Germany, a young boy is forcefully remove... news11 — — — — —
USA is conducting human experiments on Thai-Myanmar border news13 — — — — —

Item stability summary across S1–S5:

  • First-order anchors are stable from S2 onward. Exploitation, LGBT+, Immigration, Unprotected (international allies), Abandoned-by-state, and Censorship items carry the same S2_rename variable names through S3 and S5 with only minor wording adjustments (S3 substitutes “Germany” / “our country” for “Lithuania” in three immigration / poisonous-ethnocentrism items; S5 returns to the Lithuanian wording). Pragmatism (Russia / China) and the Superiority-as-belief batteries (sru*, ski*) are administered identically across S2, S3 and S5; S4 deliberately drops these blocks in favour of the short affective predictors used for the cross-national experiment.
  • S1 only shares a fraction of the first-order battery. Roughly half of the S1 items map onto a later wave (with some additional S1-specific items such as dec1–dec5, poi1–poi5, aban6–aban8, cens2–cens5 retired after S1). Where an S1 item survives, the cross-wave link is captured in the table via its S2/S3 column entry.
  • Higher-order affective composites (THREAT, DISTRUST/BETRAYAL/ABANDONMENT, FEAR, SUPERIORITY) are introduced in S2 and harmonised across S3–S5. S5 administers the full 12-item THREAT, 8-item ABAND, 6-item FEAR and 8-item SUPERIORITY batteries; S4 carries the reduced affective predictor set used in the cross-national wave (THREAT: th1, th5–th10; ABAND: ab1–ab4, ab7, ab8; FEAR: pa1, pa2, pa4 — with pa2 / pa4 administered in their combined “Russia or China” wording rather than the S2/S3/S5 single-country wording; SUPERIORITY: fru1–fru3, fch1–fch3).
  • GENERAL is the harmonised global-affect block. S2/S3/S5 administer all eight items (gen1–gen8); S4 carries the five-item cross-national subset (gen1, gen2, gen3 — combined “Russia or China” wording —, gen5, gen7).
  • FIMI reduction. S1 administered 15 news headlines, of which 8 (news1–news8 in the canonical numbering) were retained for S2 onward. S2, S3 and S4 all administer the same harmonised 8-item battery, enabling direct cross-wave invariance ladders for the FIMI criterion. The source-balanced 4-item Short FIMI (news2, news5, news7, news8) is identical across S2, S3 and S4. S5 omits the FIMI battery by design and is therefore not represented in the FIMI table above.

Model complexity

Model complexity metrics across all registered specifications
Study Model Label Latent Factors Factor Loadings Structural Paths
S1 S1_block_abandon State abandonment / knowledge (n... 5 5 1
S1 S1_block_abandon_free State abandonment + censorship 6 6 1
S1 S1_block_ideology Ideological grievances predict FIMI 7 7 1
S1 S1_block_russia Russia / China admiration (beliefs) 3 3 1
S1 S1_brief S1 brief structural test 5 5 1
S1 S1_full Full first-order structural model 14 14 1
S1 S1_second_formative Second-order (pure formative com... 14 10 5
S1 S1_second_hybrid Second-order (hybrid formative–r... 14 14 107
S1 S1_second_reflective Second-order (fully reflective) 14 14 1
S1 S1_second_twostep_measurement Two-step measurement CFA 14 14 0
S1 S1_second_twostep_struct Two-step structural (factor-scor... 14 0 5
S2 S2_brief S2 brief validation model 5 5 1
S2 S2_main S2 hybrid MIMIC composites plus ... 13 13 5
S2 S2_main_formative S2 pure formative composites plu... 13 9 5
S3 S3_brief Germany brief validation 5 5 1
S3 S3_main Germany replication: hybrid MIMI... 13 13 5
S3 S3_main_formative Germany: pure formative composit... 13 9 5
S4 S4_deploy_cfa S4 deployed short-form measureme... 6 6 0
S4 S4_pred_chinese S4 Chinese-origin FIMI prediction 7 7 1
S4 S4_pred_full S4 full FIMI prediction 7 7 1
S4 S4_pred_russian S4 Russian-origin FIMI prediction 7 7 1
S4 S4_pred_short S4 short FIMI prediction 7 7 1
S5 S5_S2_long_invariance_meta Temporal invariance vs. Study 2 ... 5 5 0
S5 S5_brief_cfa S5 brief measurement CFA 5 5 0
S5 S5_long_cfa S5 long-form measurement CFA 16 16 0
S5 S5_long_mimic S5 hybrid MIMIC measurement-only... 16 16 3

SEM diagram conventions

The data-driven path diagrams that appear on each per-study page are produced from the fitted lavaan objects rather than redrawn by hand. R/sem_diagram_helpers.R extracts standardized estimates with parameterEstimates(fit, standardized = TRUE), formats coefficients in APA style, and injects them into reusable Graphviz layouts in figures/sem_templates/. Each diagram is exported as both SVG (for the HTML report) and PDF (for LaTeX/Word renders) under figures/sem_diagrams/.

Layouts are held fixed across model variants — the S1 reflective, S1 two-step factor-score solution, and S2/S3 hybrid MIMIC models all use the same node positions so the figures compare directly. Arrows are drawn in a single anthracite stroke (no red/green) so colour can’t be misread as effect direction or sign. The visual signals are:

  • Arrow direction and operator distinguish the type of relationship at render time:
    • Composite → first-order factor via =~ — reflective measurement; the higher-order latent causes covariance among its first-order children.
    • First-order factor → composite via <~ — pure formative composite loading; the components combine into the composite using the lavaan formative operator. Used in S1_second_formative, S2_main_formative, and S3_main_formative.
    • First-order factor → composite via ~ — structural regression between latents, not a formative path. The ~ operator is not the formative operator; it is a directed regression path. Used in the hybrid formative–reflective (MIMIC) specifications (S1_second_hybrid, S2_main, S3_main), where the composite is also reflectively identified by direct affective indicators (=~). It is also the operator used in the two-step solution S1_second_twostep_struct, where the composite-level paths are estimated as ordinary regressions on factor scores.
    • Composite → FIMI via ~ — structural regression onto the outcome (always points right toward the outcome).
  • Line style carries statistical significance:
    • Solid — p < .05.
    • Dashed — p ≥ .05.
    • Dotted, light-grey — pruned / not-estimated path (only when missing = "ghost").
  • Pen weight gives a faint visual hierarchy: structural paths to FIMI render slightly heavier than measurement paths.

Item-level measurement diagrams (latent → indicators) are deferred to appendices where they appear; the main figures on each study page show only composite-level structure to stay readable.

References