[{"data":1,"prerenderedAt":357},["ShallowReactive",2],{"content-query-NqGc2NtjW3":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":9,"layout":10,"body":11,"_type":351,"_id":352,"_source":353,"_file":354,"_extension":355,"sitemap":356},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/micom","heterogeneity-and-multigroup",false,"","Measurement Invariance Assessment (MICOM) in PLS-SEM","MICOM is the three-step procedure for testing measurement invariance before a PLS-SEM multigroup analysis. Learn its steps and how SmartPLS reports them.","algorithm-description",{"type":12,"children":13,"toc":335},"root",[14,23,29,36,41,48,50,137,142,173,179,185,190,196,201,207,212,218,223,229,234,240,273,279],{"type":15,"tag":16,"props":17,"children":19},"element","h1",{"id":18},"measurement-invariance-assessment-micom",[20],{"type":21,"value":22},"text","Measurement Invariance Assessment (MICOM)",{"type":15,"tag":24,"props":25,"children":26},"p",{},[27],{"type":21,"value":28},"When using PLS-SEM, group comparisons can be misleading unless researchers first establish that their measures are invariant across groups. Measurement invariance of composite models (MICOM) is a three-step procedure that should be run before undertaking a multigroup analysis in PLS-SEM, so that observed differences reflect genuine group differences rather than measurement artifacts.",{"type":15,"tag":30,"props":31,"children":33},"h2",{"id":32},"understanding-micom",[34],{"type":21,"value":35},"Understanding MICOM",{"type":15,"tag":24,"props":37,"children":38},{},[39],{"type":21,"value":40},"Measurement invariance is an important issue when conducting PLS-SEM multigroup analyses. The research by Henseler et al. (2016) introduces a procedure to assess measurement invariance of composite models (MICOM) when using PLS-SEM. The article explains each step in detail, shows simulation study results, and reports the outcomes of an empirical example (also see Hair et al., 2024).",{"type":15,"tag":42,"props":43,"children":45},"h3",{"id":44},"the-three-steps-of-micom",[46],{"type":21,"value":47},"The Three Steps of MICOM",{"type":21,"value":49},"\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":51,"props":52,"children":53},"table",{},[54,78],{"type":15,"tag":55,"props":56,"children":57},"thead",{},[58],{"type":15,"tag":59,"props":60,"children":61},"tr",{},[62,68,73],{"type":15,"tag":63,"props":64,"children":65},"th",{},[66],{"type":21,"value":67},"Step",{"type":15,"tag":63,"props":69,"children":70},{},[71],{"type":21,"value":72},"What it assesses",{"type":15,"tag":63,"props":74,"children":75},{},[76],{"type":21,"value":77},"In SmartPLS",{"type":15,"tag":79,"props":80,"children":81},"tbody",{},[82,101,119],{"type":15,"tag":59,"props":83,"children":84},{},[85,91,96],{"type":15,"tag":86,"props":87,"children":88},"td",{},[89],{"type":21,"value":90},"1. Configural invariance",{"type":15,"tag":86,"props":92,"children":93},{},[94],{"type":21,"value":95},"Whether the composite is specified identically (same indicators, same measurement model) across groups.",{"type":15,"tag":86,"props":97,"children":98},{},[99],{"type":21,"value":100},"Not a statistical test. It requires inspecting the model set-up and settings. Running MICOM in SmartPLS usually automatically establishes configural invariance, so Step 1 is not included in the results report.",{"type":15,"tag":59,"props":102,"children":103},{},[104,109,114],{"type":15,"tag":86,"props":105,"children":106},{},[107],{"type":21,"value":108},"2. Compositional invariance",{"type":15,"tag":86,"props":110,"children":111},{},[112],{"type":21,"value":113},"Whether composite scores are formed identically across groups.",{"type":15,"tag":86,"props":115,"children":116},{},[117],{"type":21,"value":118},"The permutation algorithm returns permutation-based confidence intervals that show whether the correlation between a composite in Group A and Group B is significantly lower than one. If it is not, the composite does not differ much between the groups and compositional invariance is established.",{"type":15,"tag":59,"props":120,"children":121},{},[122,127,132],{"type":15,"tag":86,"props":123,"children":124},{},[125],{"type":21,"value":126},"3. Equality of composite mean values and variances",{"type":15,"tag":86,"props":128,"children":129},{},[130],{"type":21,"value":131},"Whether a composite's mean value and variance differ across groups.",{"type":15,"tag":86,"props":133,"children":134},{},[135],{"type":21,"value":136},"The permutation algorithm returns permutation-based confidence intervals for the mean values and variances, which reveal whether partial or full measurement invariance has been established.",{"type":15,"tag":24,"props":138,"children":139},{},[140],{"type":21,"value":141},"The article by Henseler et al. (2016) explains in detail how to interpret the results tables provided by SmartPLS in accordance with the three-step MICOM procedure (also see Hair et al., 2018).",{"type":15,"tag":24,"props":143,"children":144},{},[145,151,153,159,161,166,168],{"type":15,"tag":146,"props":147,"children":148},"strong",{},[149],{"type":21,"value":150},"Please note",{"type":21,"value":152}," that MICOM builds on permutation-based confidence intervals. For this reason, the sentence on page 416 in the article by Henseler et al. (2016), ",{"type":15,"tag":154,"props":155,"children":156},"em",{},[157],{"type":21,"value":158},"\"If the confidence intervals of differences in mean values and logarithms of variances between the construct scores of the first and second group include zero, the researcher can assume that the composite mean values and variances are equal.\"",{"type":21,"value":160},", ",{"type":15,"tag":146,"props":162,"children":163},{},[164],{"type":21,"value":165},"needs to be changed",{"type":21,"value":167},". The more precise and corrected version of this sentence is as follows: ",{"type":15,"tag":154,"props":169,"children":170},{},[171],{"type":21,"value":172},"“If the permutation-based confidence intervals of differences in mean values and logarithms of variances between the construct scores of the first and second group include the obtained difference, the researcher can assume that the composite mean values and variances are equal.”",{"type":15,"tag":30,"props":174,"children":176},{"id":175},"frequently-asked-questions",[177],{"type":21,"value":178},"Frequently Asked Questions",{"type":15,"tag":42,"props":180,"children":182},{"id":181},"what-is-micom-and-why-is-it-needed-before-a-multigroup-analysis",[183],{"type":21,"value":184},"What is MICOM and why is it needed before a multigroup analysis?",{"type":15,"tag":24,"props":186,"children":187},{},[188],{"type":21,"value":189},"MICOM (measurement invariance of composite models) is a three-step procedure that checks whether composites are measured equivalently across groups before running a PLS-SEM multigroup analysis. Without establishing measurement invariance, group differences in path coefficients or other parameters could reflect differences in measurement rather than genuine differences in the underlying relationships.",{"type":15,"tag":42,"props":191,"children":193},{"id":192},"what-are-the-three-steps-of-micom",[194],{"type":21,"value":195},"What are the three steps of MICOM?",{"type":15,"tag":24,"props":197,"children":198},{},[199],{"type":21,"value":200},"The three steps are (1) configural invariance, which checks that the composite is specified identically across groups, (2) compositional invariance, which checks that composite scores are formed identically across groups, and (3) equality of composite mean values and variances, which checks whether a composite's mean and variance differ across groups.",{"type":15,"tag":42,"props":202,"children":204},{"id":203},"can-smartpls-test-configural-invariance-step-1",[205],{"type":21,"value":206},"Can SmartPLS test configural invariance (Step 1)?",{"type":15,"tag":24,"props":208,"children":209},{},[210],{"type":21,"value":211},"No. Configural invariance requires inspecting the model set-up and selected settings rather than running a statistical test, so it is not included in the SmartPLS results report. Running MICOM in SmartPLS usually automatically establishes configural invariance.",{"type":15,"tag":42,"props":213,"children":215},{"id":214},"how-do-i-interpret-step-2-compositional-invariance-in-smartpls",[216],{"type":21,"value":217},"How do I interpret Step 2 (compositional invariance) in SmartPLS?",{"type":15,"tag":24,"props":219,"children":220},{},[221],{"type":21,"value":222},"SmartPLS reports permutation-based confidence intervals for the correlation between a composite's scores in Group A and Group B. If this correlation is not significantly lower than one, the composite does not differ much between the groups and compositional invariance is supported.",{"type":15,"tag":42,"props":224,"children":226},{"id":225},"what-does-step-3-tell-me-about-partial-or-full-measurement-invariance",[227],{"type":21,"value":228},"What does Step 3 tell me about partial or full measurement invariance?",{"type":15,"tag":24,"props":230,"children":231},{},[232],{"type":21,"value":233},"Step 3 uses permutation-based confidence intervals for the composite's mean values and variances across groups. Depending on whether these are equal, you can conclude that partial or full measurement invariance has been established, which determines whether a meaningful multigroup comparison is possible.",{"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",{},[244,255,264],{"type":15,"tag":245,"props":246,"children":247},"li",{},[248],{"type":15,"tag":249,"props":250,"children":252},"a",{"href":251},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/multigroup-analysis",[253],{"type":21,"value":254},"Multigroup analysis (MGA)",{"type":15,"tag":245,"props":256,"children":257},{},[258],{"type":15,"tag":249,"props":259,"children":261},{"href":260},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/consistent-multigroup-analysis",[262],{"type":21,"value":263},"Consistent multigroup analysis (MGA)",{"type":15,"tag":245,"props":265,"children":266},{},[267],{"type":15,"tag":249,"props":268,"children":270},{"href":269},"/documentation/algorithms-and-techniques/resampling-and-inference/permutation",[271],{"type":21,"value":272},"Permutation test",{"type":15,"tag":30,"props":274,"children":276},{"id":275},"references",[277],{"type":21,"value":278},"References",{"type":15,"tag":241,"props":280,"children":281},{},[282,298,326],{"type":15,"tag":245,"props":283,"children":284},{},[285,287,296],{"type":21,"value":286},"Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024). ",{"type":15,"tag":154,"props":288,"children":289},{},[290],{"type":15,"tag":249,"props":291,"children":293},{"href":292},"/documentation/must-reads/book-on-advanced-pls-sem-issues",[294],{"type":21,"value":295},"Advanced issues in partial least squares structural equation modeling (PLS-SEM)",{"type":21,"value":297}," (2nd ed.). Sage.",{"type":15,"tag":245,"props":299,"children":300},{},[301,303,311,313,318,319,324],{"type":21,"value":302},"Henseler, J., Ringle, C. M., & Sarstedt, M. (2016). ",{"type":15,"tag":249,"props":304,"children":308},{"href":305,"rel":306},"http://www.emeraldinsight.com/doi/abs/10.1108/IMR-09-2014-0304",[307],"nofollow",[309],{"type":21,"value":310},"Testing measurement invariance of composites using partial least squares.",{"type":21,"value":312}," ",{"type":15,"tag":154,"props":314,"children":315},{},[316],{"type":21,"value":317},"International Marketing Review",{"type":21,"value":160},{"type":15,"tag":154,"props":320,"children":321},{},[322],{"type":21,"value":323},"33",{"type":21,"value":325},"(3), 405–431.",{"type":15,"tag":245,"props":327,"children":328},{},[329],{"type":15,"tag":249,"props":330,"children":332},{"href":331},"/documentation",[333],{"type":21,"value":334},"More literature ...",{"title":7,"searchDepth":336,"depth":336,"links":337},2,[338,342,349,350],{"id":32,"depth":336,"text":35,"children":339},[340],{"id":44,"depth":341,"text":47},3,{"id":175,"depth":336,"text":178,"children":343},[344,345,346,347,348],{"id":181,"depth":341,"text":184},{"id":192,"depth":341,"text":195},{"id":203,"depth":341,"text":206},{"id":214,"depth":341,"text":217},{"id":225,"depth":341,"text":228},{"id":236,"depth":336,"text":239},{"id":275,"depth":336,"text":278},"markdown","content:documentation:algorithms-and-techniques:heterogeneity-and-multigroup:micom:index.md","content","documentation/algorithms-and-techniques/heterogeneity-and-multigroup/micom/index.md","md",{"loc":4},1784805339094]