Table 1
An Overview of Confirmatory Factor Analysis and Measurement Invariance Examination in the Current SCM Literature.
| REFERENCE | MODELLED FACTORS | METHOD OF ANALYSIS | RESULTS CFA(ACCEPTED/TESTED) | RESULTS MI |
|---|---|---|---|---|
| Grigoryan et al. (2020) | warmth, competence, status, competition | MGCFA1 | / | full configural and metric, partial scalar MI |
| Hackbart et al. (2020) | warmth, competence | CFA | 1/1 target | / |
| Halkias & Diamantopoulos (2020) | warmth, competence | CFA and MGCFA | Study 6: 1/1 target Study 7: 1/1 target | Study 7: full scalar MI |
| Janssens et al. (2015) | warmth, competence | CFA1 | Study 1: reasonable Study 2: acceptable after deleting an item | Study 1: no acceptable fit Study 2: partial MI2 |
| Kotzur et al. (2019) | warmth, competence | CFA and alignment optimization1 | 10/16 targets | full metric and partial scalar MI |
| Kotzur et al. (2020) | warmth, competence | CFA and MGCFA across two conditions | Study 1: 1/6 targets Study 2: 5/18 targets after item exclusion Study 3: 4/13 before + 4/13 after item exclusion | Study 1: scalar MI Study 2: (partial) scalar MI for 4 targets Study 3: (partial) scalar MI for 6 targets |
| Stanciu (2015) | warmth and competence (two factor model) vs. trustworthiness, friendliness, efficacy, conscientiousness (four factor model) | CFA and MGCFA1 | Two factor model: 1/25 Four factor model: 13/25 | MI for two targets applying the four factor-model. |
| Stanciu et al. (2017) | warmth, competence | CFA1 | Study 1: 2/2 Study 2: 22/22 | / |
| Vauclair et al. (2016) | warmth, competence, four BIAS map behaviours | CFA1 | 1/1 targets in both samples | partial scalar MI |
[i] Note: MGCFA = Multiple-group confirmatory factor analysis; MI = Measurement Invariance 1 The applied methods and/or model fit criteria deviated from the ones chosen in this paper. 2 MI level not specified.
Table 2
Confirmatory Factor Analysis and Measurement Invariance Results for all Datasets in Study 1.
| DATASET | TOTAL # TARGETS | CFA | CONFIGURAL MI | METRIC MI | SCALAR MI | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| # ACCEPTABLE TARGETS | % OF TOTAL TARGETS | # TARGETS | # TARGETS (MI LEVEL) | # TARGETS (MI LEVEL) | % OF ACCEPTABLE TARGETS | % OF TOTAL TARGETS | |||||
| 1 | 3 | 0 | 00.0 | / | / | / | / | / | |||
| 2 | 20 | 9 | 45.0 | 9 | Full (6) | Full (4) | 44.4 | 20.0 | |||
| 3 | 12 | 1 | 8.3 | / | / | / | / | / | |||
| 4 | 4 | 1 | 25.0 | / | / | / | / | / | |||
| 5 | 12 | 3 | 25.0 | 3 | / | / | / | / | |||
| 6 | 2 | 2 | 100.0 | 2 | Partial (2) | Partial (2) | 100.0 | 100.0 | |||
| 7 | 4 | 1 | 25.0 | / | / | / | / | / | |||
| 8 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 9 | 5 | 0 | 00.0 | / | / | / | / | / | |||
| 10 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 11 | 8 | 0 | 00.0 | / | / | / | / | / | |||
| 12 | 8 | 0 | 00.0 | / | / | / | / | / | |||
| 13 | 16 | 0 | 00.0 | / | / | / | / | / | |||
| 14 | 3 | 3 | 100.0 | 3 | Full (3) | Full (3) | 100.00 | 100.0 | |||
| 15 | 5 | 4 | 80.0 | 4 | Full (2) | Full (2) | 50.00 | 40.00 | |||
| 16 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 17 | 30 | 20 | 66.7 | 20 | Full (8) | Full (2) | 10.0 | 6.7 | |||
| 18 | 30 | 23 | 76.7 | 23 | Full (10) | Full (2) | 8.6 | 6.7 | |||
| 19 | 22 | 14 | 63.6 | 14 | Full (6) | / | / | / | |||
| 20 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 21 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 22 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 23 | 2 | 1 | 50.0 | / | / | / | / | / | |||
| 24 | 61 | 13 | 21.3 | 13 | Partial (13) | Partial (8) | 61.5 | 21.3 | |||
| 25 | 10 | 10 | 100.0 | 10 | Full (10) | Full (10) | 100.0 | 100.0 | |||
| 26 | 20 | 9 | 45.0 | Full | Full (2) | / | / | / | |||
| 27 | 23 | 11 | 47.8 | Full | Full (7) | / | / | / | |||
| 28 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 29 | 2 | 2 | 100.0 | 2 | Full (2) | Full (2) | 100.0 | 100.0 | |||
| 30 | 2 | 1 | 50.0 | / | / | / | / | / | |||
| 31 | 10 | 1 | 10.0 | / | / | / | / | / | |||
| 32 | 10 | 0 | 00.0 | / | / | / | / | / | |||
| 33 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 34 | 4 | 1 | 25.0 | / | / | / | / | / | |||
| 35 | 16 | 3 | 18.7 | 3 | / | / | / | / | |||
| 36 | 6 | 3 | 50.0 | 3 | Partial (3) | Partial (3) | 100.0 | 50.0 | |||
| 37 | 8 | 2 | 25.0 | 2 | Full (2) | Full (2) | 100.0 | 25.0 | |||
| 38 | 8 | 1 | 12.5 | / | / | / | / | / | |||
| 39 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 40 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 41 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 42 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 43 | 3 | 0 | 00.0 | / | / | / | / | / | |||
| 44 | 6 | 0 | 00.0 | / | / | / | / | / | |||
| 45 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 46 | 6 | 1 | 16.7 | / | / | / | / | / | |||
| 47 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 48 | 10 | 8 | 80.0 | 8 | Partial (8) | Partial (2) | 25.0 | 20.0 | |||
| 49 | 3 | 3 | 100.0 | 3 | Full (2) | Partial (2) | 66.7 | 66.7 | |||
| 50 | 6 | 3 | 50.0 | 3 | Partial (2) | / | / | / | |||
| 51 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 52 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 53 | 2 | 2 | 100.0 | 2 | Full (2) | / | / | / | |||
| 54 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 55 | 4 | 0 | 00.0 | / | / | / | / | / | |||
| 56 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 57 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 58 | 2 | 2 | 100.0 | 2 | Full (2) | Partial (2) | 100.0 | 100.0 | |||
| 59 | 2 | 1 | 50.0 | / | / | / | / | / | |||
| 60 | 2 | 1 | 50.0 | / | / | / | / | / | |||
| 61 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 62 | 35 | 8 | 22.8 | 8 | Partial (6) | Partial (2) | 25.0 | 5.7 | |||
| 63 | 4 | 1 | 25.0 | / | / | / | / | / | |||
| 64 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 65 | 2 | 0 | 00.0 | / | / | / | / | / | |||
| 66 | 25 | 15 | 60.0 | 15 | Partial (13) | Partial (4) | 26.7 | 16.0 | |||
| 67 | 3 | 1 | 33.3 | / | / | / | / | / | |||
| 68 | 3 | 0 | 00.0 | / | / | / | / | / | |||
| 69 | 4 | 2 | 50.0 | 2 | Full (2) | Partial (2) | 100.0 | 100.0 | |||
| 70 | 5 | 0 | 00.0 | / | / | / | / | / | |||
| 71 | 3 | 0 | 00.0 | / | / | / | / | / | |||
| 72 | 6 | 4 | 66.7 | 4 | Partial (4) | Full (2) | 50.0 | 33.3 | |||
| 73 | 6 | 1 | 16.7 | / | / | / | / | / | |||
| 74 | 6 | 0 | 00.0 | / | / | / | / | / | |||
| 75 | 6 | 1 | 16.7 | / | / | / | / | / | |||
| 76 | 4 | 4 | 50.0 | 4 | Full (4) | Partial (4) | 100.0 | 100.0 | |||
| 77 | 4 | 3 | 75.0 | 3 | Full (3) | Partial (3) | 100.0 | 75.0 | |||
| 78 | 4 | 4 | 100.0 | 4 | Full (4) | Partial (4) | 100.0 | 100.0 | |||
| Total | 586 | 204 | 34.8 | 189 | 77 Full/51 Partial | 29 Full/38 Partial | 69.9 | 56.5 | |||
[i] Note: CFA = Confirmatory Factor Analysis. / = The testing of this level of MI was not possible due to the number of target groups with acceptable model fit being below 2. 1 Of accepted CFA models (column Total CFA Fit). The dataset number refers to the numbering system in OSM-6; for full references, see OSM-6.
Figure 1
Highest Level of Established Measurement Invariance Based on CFA Models in Study 1.
Note: The figure shows the highest level of measurement equivalence in which the target dropped out from analyses, thus the numbers may vary compared to the descriptions in the text, which describes the results on the level of datasets. MI = Measurement invariance. The total number of CFA models K = 586.
Table 3
Confirmatory Factor Analysis and Measurement Invariance Results for all Datasets in Study 2.
| DATASET | TOTAL # TARGETS | CFA | CONFIGURAL MI | METRIC MI | SCALAR MI | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| # ACCEPTABLE TARGETS | % OF TOTAL TARGETS | # TARGETS | # TARGETS (MI LEVEL) | # TARGETS (MI LEVEL) | % OF ACCEPTABLE TARGETS | % OF TOTAL TARGETS | ||||
| 1 | 29 | 7 | 24.14 | 7 | 7 (Partial) | 4 (Partial) | 57.14 | 13.79 | ||
| 2 | 15 | 5 | 33.33 | 5 | 4 (Partial) | 3 (Partial) | 60.00 | 20.00 | ||
| 3 | 2 | 0 | 00.00 | / | / | / | / | / | ||
| 4 | 16 | 7 | 43.75 | 7 | 7 (Partial) | 5 (Partial) | 71.43 | 31.25 | ||
| 5 | 4 | 1 | 25.00 | / | / | / | / | / | ||
| 6 | 4 | 1 | 25.00 | / | / | / | / | / | ||
| 7 | 4 | 2 | 50.00 | 2 | 2 (Full) | 0 | 00.00 | 00.00 | ||
| 8 | 6 | 2 | 33.33 | 2 | 0 | 0 | 00.00 | 00.00 | ||
| 9 | 6 | 3 | 50.00 | 3 | 0 | 0 | 00.00 | 00.00 | ||
| 10 | 3 | 1 | 33.33 | / | / | / | / | / | ||
| 11 | 4 | 1 | 25.00 | / | / | / | / | / | ||
| 12 | 32 | 19 | 59.38 | 19 | 14 (Partial) | 2 (Full) | 10.53 | 6.25 | ||
| 13 | 2 | 1 | 50.00 | / | / | / | / | / | ||
| 14 | 3 | 0 | 00.00 | / | / | / | / | / | ||
| 15 | 2 | 1 | 50.00 | / | / | / | / | / | ||
| 16 | 4 | 1 | 25.00 | / | / | / | / | / | ||
| 17 | 16 | 10 | 62.50 | 10 | 10 (Full) | 8 (Partial) | 80.00 | 50.00 | ||
| 18 | 12 | 4 | 33.33 | 2 | 2 (Full) | 2 (Full) | 50.00 | 16.67 | ||
| 19 | 18 | 12 | 66.67 | 8 | 6 (2 Full/ 4 Partial) | 4 (2 Full/ 2 Partial) | 33.33 | 22.22 | ||
| 20 | 20 | 15 | 75.00 | 12 | 2 (Partial) | 2 (Full) | 13.33 | 10.00 | ||
| 21 | 2 | 2 | 100.00 | 2 | 2 (Full) | 2 (Full) | 100.00 | 100.00 | ||
| 22 | 204 | 50 | 24.51 | 50 | 8 (Full) | 5 (Full) | 10.00 | 2.45 | ||
| 23 | 4 | 4 | 100.00 | 4 | 4 (Full) | 4 (Full) | 100.00 | 100.00 | ||
| 24 | 4 | 1 | 25.00 | / | / | / | / | / | ||
| 25 | 64 | 22 | 34.38 | 22 | 12 (Partial) | 12 (Partial) | 54.55 | 18.75 | ||
| 26 | 16 | 3 | 18.75 | 3 | 3 (Full) | 3 (Partial) | 100.00 | 18.75 | ||
| 27 | 5 | 1 | 20.00 | / | / | / | / | / | ||
| 28 | 3 | 0 | 00.00 | / | / | / | / | / | ||
| 29 | 3 | 2 | 66.67 | 2 | 2 (Full) | 2 (Partial) | 100.00 | 66.67 | ||
| Total | 507 | 178 | 35.10 | 160 | 85 | 58 | 32.58 | 11.44 | ||
[i] Note: CFA = Confirmatory Factor Analysis, MI = Measurement Invariance. # = Number. / = The testing of this level of MI was not possible due to the number of target groups with acceptable model fit being below 2. Note that for Samples 18–20, measurement equivalence was tested for each target group separately across experimental conditions if prerequisites were met (see OSM-9 for details). The dataset number refers to the numbering system in OSM-9; for full references, see OSM-9.
Figure 2
Highest Level of Established Measurement Invariance Based on CFA Models in Study 2.
Note: The figure shows the highest level of measurement equivalence in which the target dropped out from analyses, thus the numbers may vary compared to the descriptions in the text, which describes the results on the level of datasets. MI = Measurement invariance. The total number of CFA models K = 507.
| MTF: | Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Supervision, Validation, Visualization, Writing – Original draft |
| PFK: | Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Supervision, Writing – Review & editing |
| JB: | Data Curation, Formal analysis, Investigation, Validation, Visualization, Writing – Original draft |
| AKCZ: | Data curation, Formal analysis, Investigation, Methodology, Writing – Review & editing |
| TL: | Data Curation, Formal analysis, Investigation, Validation, Writing – Review & editing |
| UW: | Conceptualization, Resources, Supervision, Writing – Review & editing |
| FA: | Conceptualization, Resources, Supervision, Writing – Review & editing |
| MHWVZ: | Resources, Writing – Review & editing |