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Learn the MGA methods SmartPLS offers.","algorithm-description",{"type":12,"children":13,"toc":384},"root",[14,23,29,36,50,68,75,80,82,162,168,173,179,185,190,196,201,207,212,218,223,229,234,240,271,277],{"type":15,"tag":16,"props":17,"children":19},"element","h1",{"id":18},"multigroup-analysis-mga",[20],{"type":21,"value":22},"text","Multigroup Analysis (MGA)",{"type":15,"tag":24,"props":25,"children":26},"p",{},[27],{"type":21,"value":28},"Multigroup analysis (MGA) tests whether predefined data groups differ significantly in their group-specific parameter estimates, such as outer weights, outer loadings, and path coefficients. Researchers use it to check whether a PLS-SEM model's relationships hold equally across groups, for example different countries, customer segments, or demographic categories, or whether they differ in a statistically meaningful way. SmartPLS provides outcomes from three different approaches, all based on bootstrapping results computed separately for every group.",{"type":15,"tag":30,"props":31,"children":33},"h2",{"id":32},"how-multigroup-analysis-works",[34],{"type":21,"value":35},"How Multigroup Analysis Works",{"type":15,"tag":24,"props":37,"children":38},{},[39,41,48],{"type":21,"value":40},"SmartPLS offers the ",{"type":15,"tag":42,"props":43,"children":45},"a",{"href":44},"/documentation/algorithms-and-techniques/resampling-and-inference/permutation",[46],{"type":21,"value":47},"permutation MGA",{"type":21,"value":49}," (Chin & Dibbern, 2010) and the bootstrap MGA (Sarstedt et al., 2011). Hair et al. (2024) and Matthews (2017) describe these MGA methods for PLS-SEM (i.e., the PLS-MGA) in detail.",{"type":15,"tag":24,"props":51,"children":52},{},[53,55,60,62,66],{"type":21,"value":54},"Based on the ",{"type":15,"tag":42,"props":56,"children":57},{"href":44},[58],{"type":21,"value":59},"permutation procedure",{"type":21,"value":61},", SmartPLS provides MGA results that allow you to test whether predefined data groups have statistically significant differences in their group-specific parameter estimates (e.g., outer weights, outer loadings, and path coefficients). The ",{"type":15,"tag":42,"props":63,"children":64},{"href":44},[65],{"type":21,"value":59},{"type":21,"value":67}," also supports the MICOM procedure for analyzing measurement invariance.",{"type":15,"tag":69,"props":70,"children":72},"h3",{"id":71},"bootstrap-mga-results",[73],{"type":21,"value":74},"Bootstrap MGA Results",{"type":15,"tag":24,"props":76,"children":77},{},[78],{"type":21,"value":79},"The bootstrap MGA provides the following results:",{"type":21,"value":81},"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n",{"type":15,"tag":83,"props":84,"children":85},"table",{},[86,105],{"type":15,"tag":87,"props":88,"children":89},"thead",{},[90],{"type":15,"tag":91,"props":92,"children":93},"tr",{},[94,100],{"type":15,"tag":95,"props":96,"children":97},"th",{},[98],{"type":21,"value":99},"Method",{"type":15,"tag":95,"props":101,"children":102},{},[103],{"type":21,"value":104},"What it tests",{"type":15,"tag":106,"props":107,"children":108},"tbody",{},[109,123,136,149],{"type":15,"tag":91,"props":110,"children":111},{},[112,118],{"type":15,"tag":113,"props":114,"children":115},"td",{},[116],{"type":21,"value":117},"(1) Confidence intervals (bias corrected)",{"type":15,"tag":113,"props":119,"children":120},{},[121],{"type":21,"value":122},"Computes bias-corrected confidence intervals for the group-specific parameter estimates in the PLS path model. The group-specific results of a path coefficient are significantly different if the bias-corrected confidence intervals do not overlap.",{"type":15,"tag":91,"props":124,"children":125},{},[126,131],{"type":15,"tag":113,"props":127,"children":128},{},[129],{"type":21,"value":130},"(2) Partial least squares multigroup analysis (PLS-MGA)",{"type":15,"tag":113,"props":132,"children":133},{},[134],{"type":21,"value":135},"A non-parametric significance test for the difference of group-specific results that builds on PLS-SEM bootstrapping results. A result is significant at the 5% probability of error level if the p-value is smaller than 0.05 or larger than 0.95 for a given difference of group-specific path coefficients. The PLS-MGA method (Henseler et al., 2009), as implemented in SmartPLS, is an extension of the bootstrap-based MGA approach originally proposed for PLS-SEM (as described, for example, by Sarstedt et al., 2011).",{"type":15,"tag":91,"props":137,"children":138},{},[139,144],{"type":15,"tag":113,"props":140,"children":141},{},[142],{"type":21,"value":143},"(3) Parametric test",{"type":15,"tag":113,"props":145,"children":146},{},[147],{"type":21,"value":148},"A parametric significance test for the difference of group-specific PLS-SEM results that assumes equal variances across groups.",{"type":15,"tag":91,"props":150,"children":151},{},[152,157],{"type":15,"tag":113,"props":153,"children":154},{},[155],{"type":21,"value":156},"(4) Welch-Satterthwaite test",{"type":15,"tag":113,"props":158,"children":159},{},[160],{"type":21,"value":161},"A parametric significance test for the difference of group-specific PLS-SEM results that assumes unequal variances across groups.",{"type":15,"tag":30,"props":163,"children":165},{"id":164},"mga-settings-in-smartpls",[166],{"type":21,"value":167},"MGA Settings in SmartPLS",{"type":15,"tag":24,"props":169,"children":170},{},[171],{"type":21,"value":172},"Select Groups: The selected groups will be assessed for significant differences in the parameter estimates (e.g., outer weights, outer loadings, and path coefficients). All data groups selected under Group A will be compared against all data groups selected under Group B.",{"type":15,"tag":30,"props":174,"children":176},{"id":175},"frequently-asked-questions",[177],{"type":21,"value":178},"Frequently Asked Questions",{"type":15,"tag":69,"props":180,"children":182},{"id":181},"what-is-multigroup-analysis-mga-in-pls-sem",[183],{"type":21,"value":184},"What is multigroup analysis (MGA) in PLS-SEM?",{"type":15,"tag":24,"props":186,"children":187},{},[188],{"type":21,"value":189},"MGA tests whether predefined data groups, such as different countries or customer segments, have statistically significant differences in group-specific parameter estimates like outer weights, outer loadings, or path coefficients.",{"type":15,"tag":69,"props":191,"children":193},{"id":192},"which-mga-methods-does-smartpls-provide",[194],{"type":21,"value":195},"Which MGA methods does SmartPLS provide?",{"type":15,"tag":24,"props":197,"children":198},{},[199],{"type":21,"value":200},"SmartPLS provides the permutation MGA and the bootstrap MGA. The bootstrap MGA in turn reports four sets of results: bias-corrected confidence intervals, the non-parametric PLS-MGA significance test, a parametric test assuming equal variances, and a Welch-Satterthwaite test assuming unequal variances.",{"type":15,"tag":69,"props":202,"children":204},{"id":203},"how-do-i-know-if-a-path-coefficient-differs-significantly-between-two-groups",[205],{"type":21,"value":206},"How do I know if a path coefficient differs significantly between two groups?",{"type":15,"tag":24,"props":208,"children":209},{},[210],{"type":21,"value":211},"Using bias-corrected confidence intervals, the group-specific results for a path coefficient are significantly different if the confidence intervals of the two groups do not overlap. Alternatively, the PLS-MGA test flags a significant difference at the 5% probability of error level when the p-value is smaller than 0.05 or larger than 0.95.",{"type":15,"tag":69,"props":213,"children":215},{"id":214},"should-i-use-the-parametric-test-or-the-welch-satterthwaite-test",[216],{"type":21,"value":217},"Should I use the parametric test or the Welch-Satterthwaite test?",{"type":15,"tag":24,"props":219,"children":220},{},[221],{"type":21,"value":222},"That depends on whether the variances of the parameter estimates are equal across groups. The parametric test assumes equal variances across groups, while the Welch-Satterthwaite test assumes unequal variances.",{"type":15,"tag":69,"props":224,"children":226},{"id":225},"do-i-need-to-check-measurement-invariance-before-running-an-mga",[227],{"type":21,"value":228},"Do I need to check measurement invariance before running an MGA?",{"type":15,"tag":24,"props":230,"children":231},{},[232],{"type":21,"value":233},"Yes. 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The permutation procedure that underlies MGA in SmartPLS also supports the MICOM procedure for analyzing measurement invariance.",{"type":15,"tag":30,"props":235,"children":237},{"id":236},"related-smartpls-methods",[238],{"type":21,"value":239},"Related SmartPLS Methods",{"type":15,"tag":241,"props":242,"children":243},"ul",{},[244,254,263],{"type":15,"tag":245,"props":246,"children":247},"li",{},[248],{"type":15,"tag":42,"props":249,"children":251},{"href":250},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/micom",[252],{"type":21,"value":253},"Measurement invariance assessment (MICOM)",{"type":15,"tag":245,"props":255,"children":256},{},[257],{"type":15,"tag":42,"props":258,"children":260},{"href":259},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/consistent-multigroup-analysis",[261],{"type":21,"value":262},"Consistent multigroup analysis (MGA)",{"type":15,"tag":245,"props":264,"children":265},{},[266],{"type":15,"tag":42,"props":267,"children":268},{"href":44},[269],{"type":21,"value":270},"Permutation test",{"type":15,"tag":30,"props":272,"children":274},{"id":273},"references",[275],{"type":21,"value":276},"References",{"type":15,"tag":241,"props":278,"children":279},{},[280,293,309,338,350,375],{"type":15,"tag":245,"props":281,"children":282},{},[283,285,291],{"type":21,"value":284},"Chin, W. W., & Dibbern, J. (2010). A permutation based procedure for multi-group PLS analysis: Results of tests of differences on simulated data and a cross cultural analysis of the sourcing of information system services between Germany and the USA. In V. Esposito Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), ",{"type":15,"tag":286,"props":287,"children":288},"em",{},[289],{"type":21,"value":290},"Handbook of partial least squares: Concepts, methods and applications",{"type":21,"value":292}," (Springer Handbooks of Computational Statistics Series, Vol. II) (pp. 171–193). Springer.",{"type":15,"tag":245,"props":294,"children":295},{},[296,298,307],{"type":21,"value":297},"Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024). ",{"type":15,"tag":286,"props":299,"children":300},{},[301],{"type":15,"tag":42,"props":302,"children":304},{"href":303},"/documentation/must-reads/book-on-advanced-pls-sem-issues",[305],{"type":21,"value":306},"Advanced issues in partial least squares structural equation modeling (PLS-SEM)",{"type":21,"value":308}," (2nd ed.). Sage.",{"type":15,"tag":245,"props":310,"children":311},{},[312,314,322,324,329,331,336],{"type":21,"value":313},"Henseler, J., Ringle, C. M., & Sinkovics, R. R. (2009). ",{"type":15,"tag":42,"props":315,"children":319},{"href":316,"rel":317},"https://www.escholar.manchester.ac.uk/uk-ac-man-scw:89555",[318],"nofollow",[320],{"type":21,"value":321},"The use of partial least squares path modeling in international marketing.",{"type":21,"value":323}," ",{"type":15,"tag":286,"props":325,"children":326},{},[327],{"type":21,"value":328},"Advances in International Marketing",{"type":21,"value":330},", ",{"type":15,"tag":286,"props":332,"children":333},{},[334],{"type":21,"value":335},"20",{"type":21,"value":337},", 277–320.",{"type":15,"tag":245,"props":339,"children":340},{},[341,343,348],{"type":21,"value":342},"Matthews, L. (2017). Applying multi-group analysis in PLS-SEM: A step-by-step process. In H. Latan & R. 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