In the dynamic landscape of Structural Equation Modeling (SEM), the assessment of measurement invariance plays a key role in granting meaningful comparisons between groups. A popular tool employed in this regard is the Measurement Invariance of Composite Models (MICOM). However, despite its utility, MICOM presents limitations, particularly concerning the correlation method used for comparing recomputed composite scores, and strict assumptions of equal means and variances across groups. Moreover, MICOM is limited to two-sample comparisons. Recognizing these constraints, this thesis presents two alternative methodologies: robustMICOM and multiMICOM. The first, formulated with Wilcoxon Signed-Rank Matched Pairs test, Wilcoxon Rank Sum test, and Levene’s test, is a robust approach which circumvents issues of misleading correlations and the stringent assumption about group means and variances. The second, multiMICOM, employs the Friedman test, Kruskal-Wallis'H test, and Levene’s test to expand the possibilities of robustMICOM and accommodate multigroup comparisons. Both methodologies’ assessment of compositional invariance proves more rigorous, while their assessment of means and variances is similar or a bit more permissive than traditional MICOM depending on the benchmarking scenario. This research delves into an exhaustive exploration of heterogeneity, techniques for heterogeneity discovery in Partial Least Squares Structural Equation Models (PLS-SEM), an analysis of MICOM, and the benchmarking of the proposed methodologies. This seminal work provides a substantial contribution to the extant literature on measurement invariance and creates avenues for future research in the field.

Abstract I
抽象的 II
Acknowledgment III
Table of Contents IV
List of Figures VI
List of Tables VII
1. Introduction 1
2. Heterogeneity and Measurement Invariance in PLS-SEM 5
2.1 Heterogeneity: Definition and Implications 5
2.1.1 Observed and Unobserved Heterogeneity 7
2.1.2 Levels of Heterogeneity 7
2.2 Review of Existing Heterogeneity Detection Methods for PLS-SEM 9
2.2.1 REBUS-PLS 9
2.2.2 Pathmox 11
2.2.3 FIMIX-PLS 13
2.2.4 PLS-POS 17
2.3 Measurement Invariance 23
2.3.1 Measurement Invariance: Definition and Implications 23
2.3.2 Assessing Measurement Invariance 24
3. Understanding MICOM 27
3.1 Measurement Invariance of Composite Models - MICOM 27
3.1.1 MICOM Overview 27
3.1.2 Permutation Algorithms 30
3.1.3 MICOM Algorithm 32
3.2 MICOM Implementation: simpleMICOM 36
3.2.1 A Demo of simpleMICOM 39
3.2.2 Benchmarking simpleMICOM 41
3.3 Limitations of MICOM 45
4. New Approaches to Assessing Measurement Invariance: robustMICOM and multiMICOM 49
4.1 A New Two-sample Measurement Invariance Assessment Tool: robustMICOM 49
4.1.1 Wilcoxon Signed-Rank Matched Pairs Test 51
4.1.2 Wilcoxon Rank Sum (Unpaired) Test 53
4.1.3 Levene’s Test 55
4.1.4 robustMICOM Algorithm 56
4.1.5 Benchmarking robustMICOM 58
4.2 A New Multi-group MI Assessment Tool: multiMICOM 63
4.2.1 Friedman Test 65
4.2.2 Kruskal-Wallis’ H Test 66
4.2.3 Levene’s Test (revisited for multigroup comparisons) 67
4.2.4 multiMICOM Algorithm 67
4.2.5 Benchmarking multiMICOM 70
4.2.6 Demo of multiMICOM on a three-groups scenario 74
5. Discussion 76
6. Future Work and Conclusions 81
References 83
Appendix 89

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