[{"data":1,"prerenderedAt":456},["ShallowReactive",2],{"content-query-df33JLNDXH":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":9,"layout":10,"body":11,"_type":450,"_id":451,"_source":452,"_file":453,"_extension":454,"sitemap":455},"/documentation/algorithms-and-techniques/resampling-and-inference/permutation","resampling-and-inference",false,"","Permutation Testing for PLS-SEM Multigroup Analysis","Permutation tests whether pre-defined groups differ significantly in their PLS-SEM parameter estimates and supports MICOM measurement invariance testing. Learn how to run it in SmartPLS.","algorithm-description",{"type":12,"children":13,"toc":435},"root",[14,23,29,36,41,56,61,67,69,206,212,219,224,230,235,241,246,252,257,263,274,280,330,336],{"type":15,"tag":16,"props":17,"children":19},"element","h1",{"id":18},"permutation",[20],{"type":21,"value":22},"text","Permutation",{"type":15,"tag":24,"props":25,"children":26},"p",{},[27],{"type":21,"value":28},"Permutation is a nonparametric test that lets researchers check whether pre-defined data groups (e.g., customers from different countries) have statistically significant differences in their group-specific PLS-SEM parameter estimates, such as outer weights, outer loadings, and path coefficients. It also supports the MICOM procedure for assessing measurement invariance, which is a prerequisite for meaningful group comparisons. Researchers use permutation when they want to conduct a multigroup analysis (MGA) or test whether a construct is measured equivalently across groups.",{"type":15,"tag":30,"props":31,"children":33},"h2",{"id":32},"what-permutation-is-used-for",[34],{"type":21,"value":35},"What Permutation Is Used For",{"type":15,"tag":24,"props":37,"children":38},{},[39],{"type":21,"value":40},"The purpose of the permutation routine in SmartPLS is twofold:",{"type":15,"tag":42,"props":43,"children":44},"ol",{},[45,51],{"type":15,"tag":46,"props":47,"children":48},"li",{},[49],{"type":21,"value":50},"It allows conducting a PLS-SEM multigroup analysis (Hair et al., 2024; Sarstedt, Henseler, & Ringle, 2011) as suggested by Dibbern and Chin (2005) and Chin and Dibbern (2010). This lets you decide if group-specific PLS-SEM results have statistically significant differences.",{"type":15,"tag":46,"props":52,"children":53},{},[54],{"type":21,"value":55},"It allows conducting the PLS-SEM measurement invariance assessment as suggested by Henseler, Ringle, and Sarstedt's (2015) MICOM routine. This lets you substantiate that significant differences in group-specific PLS-SEM results do not stem from differences in how constructs (e.g., customer loyalty) are measured across groups.",{"type":15,"tag":24,"props":57,"children":58},{},[59],{"type":21,"value":60},"The permutation results report in SmartPLS includes both the outcomes of the PLS-SEM multigroup analysis (using the permutation test) and the MICOM results for assessing measurement invariance.",{"type":15,"tag":30,"props":62,"children":64},{"id":63},"permutation-settings-in-smartpls",[65],{"type":21,"value":66},"Permutation Settings in SmartPLS",{"type":21,"value":68},"\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\n\n\n\n\n\n\n\n\n\n",{"type":15,"tag":70,"props":71,"children":72},"table",{},[73,97],{"type":15,"tag":74,"props":75,"children":76},"thead",{},[77],{"type":15,"tag":78,"props":79,"children":80},"tr",{},[81,87,92],{"type":15,"tag":82,"props":83,"children":84},"th",{},[85],{"type":21,"value":86},"Setting",{"type":15,"tag":82,"props":88,"children":89},{},[90],{"type":21,"value":91},"Default",{"type":15,"tag":82,"props":93,"children":94},{},[95],{"type":21,"value":96},"Description",{"type":15,"tag":98,"props":99,"children":100},"tbody",{},[101,120,152,170,188],{"type":15,"tag":78,"props":102,"children":103},{},[104,110,115],{"type":15,"tag":105,"props":106,"children":107},"td",{},[108],{"type":21,"value":109},"Select groups",{"type":15,"tag":105,"props":111,"children":112},{},[113],{"type":21,"value":114},"—",{"type":15,"tag":105,"props":116,"children":117},{},[118],{"type":21,"value":119},"The data group selected under Group A is compared against the data group selected under Group B; both are assessed for significant differences in parameter estimates and for measurement invariance (MICOM). If the group selection combo box is empty, double-click the data set in the SmartPLS project window and use the available options to generate data groups for the multigroup analysis.",{"type":15,"tag":78,"props":121,"children":122},{},[123,128,133],{"type":15,"tag":105,"props":124,"children":125},{},[126],{"type":21,"value":127},"Permutations",{"type":15,"tag":105,"props":129,"children":130},{},[131],{"type":21,"value":132},"1,000",{"type":15,"tag":105,"props":134,"children":135},{},[136,138,144,146,150],{"type":21,"value":137},"Number of permutation runs, each created by randomly drawing (without replacement) ",{"type":15,"tag":139,"props":140,"children":141},"em",{},[142],{"type":21,"value":143},"n",{"type":21,"value":145}," observations for Group A, where ",{"type":15,"tag":139,"props":147,"children":148},{},[149],{"type":21,"value":143},{"type":21,"value":151}," equals Group A's size in the original data set; all remaining observations are assigned to Group B. Group-specific sample sizes therefore stay constant across runs. For a quick initial assessment, a smaller number (e.g., 500–1,000) may suffice; for final results, use a large number (e.g., 5,000). Larger numbers increase computation time.",{"type":15,"tag":78,"props":153,"children":154},{},[155,160,165],{"type":15,"tag":105,"props":156,"children":157},{},[158],{"type":21,"value":159},"Test type",{"type":15,"tag":105,"props":161,"children":162},{},[163],{"type":21,"value":164},"Two-tailed",{"type":15,"tag":105,"props":166,"children":167},{},[168],{"type":21,"value":169},"Specifies whether a one-tailed (one-sided) or two-tailed (two-sided) significance test is conducted; this also affects the p value computation.",{"type":15,"tag":78,"props":171,"children":172},{},[173,178,183],{"type":15,"tag":105,"props":174,"children":175},{},[176],{"type":21,"value":177},"Significance level",{"type":15,"tag":105,"props":179,"children":180},{},[181],{"type":21,"value":182},"0.05",{"type":15,"tag":105,"props":184,"children":185},{},[186],{"type":21,"value":187},"Specifies the significance level used for the confidence interval computations.",{"type":15,"tag":78,"props":189,"children":190},{},[191,196,201],{"type":15,"tag":105,"props":192,"children":193},{},[194],{"type":21,"value":195},"Do parallel processing",{"type":15,"tag":105,"props":197,"children":198},{},[199],{"type":21,"value":200},"Enabled",{"type":15,"tag":105,"props":202,"children":203},{},[204],{"type":21,"value":205},"Runs the permutation procedure on multiple processors, if available, considerably reducing computation time.",{"type":15,"tag":30,"props":207,"children":209},{"id":208},"frequently-asked-questions",[210],{"type":21,"value":211},"Frequently Asked Questions",{"type":15,"tag":213,"props":214,"children":216},"h3",{"id":215},"what-does-the-permutation-procedure-test-in-pls-sem",[217],{"type":21,"value":218},"What does the permutation procedure test in PLS-SEM?",{"type":15,"tag":24,"props":220,"children":221},{},[222],{"type":21,"value":223},"It tests whether pre-defined data groups have statistically significant differences in their group-specific parameter estimates, such as outer weights, outer loadings, and path coefficients (a multigroup analysis), and it supports the MICOM procedure for assessing measurement invariance across groups.",{"type":15,"tag":213,"props":225,"children":227},{"id":226},"why-do-i-need-micom-before-comparing-groups",[228],{"type":21,"value":229},"Why do I need MICOM before comparing groups?",{"type":15,"tag":24,"props":231,"children":232},{},[233],{"type":21,"value":234},"MICOM substantiates that significant differences in group-specific PLS-SEM results stem from genuine differences between groups rather than from the constructs being measured differently across groups. It is a prerequisite for meaningful multigroup comparisons.",{"type":15,"tag":213,"props":236,"children":238},{"id":237},"how-many-permutations-should-i-use",[239],{"type":21,"value":240},"How many permutations should I use?",{"type":15,"tag":24,"props":242,"children":243},{},[244],{"type":21,"value":245},"For a quick initial assessment, a smaller number such as 500 or 1,000 permutations may be sufficient. For final results preparation, use a larger number, such as 5,000, since more permutations increase the stability of the results at the cost of additional computation time. SmartPLS defaults to 1,000.",{"type":15,"tag":213,"props":247,"children":249},{"id":248},"should-i-use-a-one-tailed-or-two-tailed-test",[250],{"type":21,"value":251},"Should I use a one-tailed or two-tailed test?",{"type":15,"tag":24,"props":253,"children":254},{},[255],{"type":21,"value":256},"SmartPLS defaults to a two-tailed test. The choice between a one-tailed and two-tailed test depends on whether your hypothesis predicts the direction of the group difference, and it affects how the p value is computed.",{"type":15,"tag":213,"props":258,"children":260},{"id":259},"why-is-group-a-always-compared-against-group-b-with-fixed-sample-sizes",[261],{"type":21,"value":262},"Why is Group A always compared against Group B with fixed sample sizes?",{"type":15,"tag":24,"props":264,"children":265},{},[266,268,272],{"type":21,"value":267},"In each permutation run, ",{"type":15,"tag":139,"props":269,"children":270},{},[271],{"type":21,"value":143},{"type":21,"value":273}," observations equal to Group A's original size are drawn without replacement and assigned to Group A, and the rest are assigned to Group B. This keeps the group-specific sample sizes constant across all runs and equal to the sizes observed in the original data set.",{"type":15,"tag":30,"props":275,"children":277},{"id":276},"related-smartpls-methods",[278],{"type":21,"value":279},"Related SmartPLS Methods",{"type":15,"tag":281,"props":282,"children":283},"ul",{},[284,294,303,312,321],{"type":15,"tag":46,"props":285,"children":286},{},[287],{"type":15,"tag":288,"props":289,"children":291},"a",{"href":290},"/documentation/algorithms-and-techniques/resampling-and-inference/consistent-permutation/",[292],{"type":21,"value":293},"Consistent permutation",{"type":15,"tag":46,"props":295,"children":296},{},[297],{"type":15,"tag":288,"props":298,"children":300},{"href":299},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/multigroup-analysis/",[301],{"type":21,"value":302},"Multigroup analysis (MGA)",{"type":15,"tag":46,"props":304,"children":305},{},[306],{"type":15,"tag":288,"props":307,"children":309},{"href":308},"/documentation/algorithms-and-techniques/heterogeneity-and-multigroup/micom/",[310],{"type":21,"value":311},"MICOM",{"type":15,"tag":46,"props":313,"children":314},{},[315],{"type":15,"tag":288,"props":316,"children":318},{"href":317},"/documentation/algorithms-and-techniques/resampling-and-inference/bootstrapping/",[319],{"type":21,"value":320},"Bootstrapping",{"type":15,"tag":46,"props":322,"children":323},{},[324],{"type":15,"tag":288,"props":325,"children":327},{"href":326},"/documentation/functionalities/thresholds/",[328],{"type":21,"value":329},"Result color thresholds",{"type":15,"tag":30,"props":331,"children":333},{"id":332},"references",[334],{"type":21,"value":335},"References",{"type":15,"tag":281,"props":337,"children":338},{},[339,351,367,386,414,426],{"type":15,"tag":46,"props":340,"children":341},{},[342,344,349],{"type":21,"value":343},"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":139,"props":345,"children":346},{},[347],{"type":21,"value":348},"Handbook of partial least squares: Concepts, methods and applications",{"type":21,"value":350}," (pp. 171–193). Springer.",{"type":15,"tag":46,"props":352,"children":353},{},[354,356,365],{"type":21,"value":355},"Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024). ",{"type":15,"tag":139,"props":357,"children":358},{},[359],{"type":15,"tag":288,"props":360,"children":362},{"href":361},"/documentation/must-reads/book-on-advanced-pls-sem-issues",[363],{"type":21,"value":364},"Advanced issues in partial least squares structural equation modeling (PLS-SEM)",{"type":21,"value":366}," (2nd ed.). Sage.",{"type":15,"tag":46,"props":368,"children":369},{},[370,372,377,379,384],{"type":21,"value":371},"Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). Testing measurement invariance of composites using partial least squares. ",{"type":15,"tag":139,"props":373,"children":374},{},[375],{"type":21,"value":376},"International Marketing Review",{"type":21,"value":378},", ",{"type":15,"tag":139,"props":380,"children":381},{},[382],{"type":21,"value":383},"33",{"type":21,"value":385},"(3), 405–431.",{"type":15,"tag":46,"props":387,"children":388},{},[389,391,399,401,406,407,412],{"type":21,"value":390},"Sarstedt, M., Henseler, J., & Ringle, C. M. (2011). ",{"type":15,"tag":288,"props":392,"children":396},{"href":393,"rel":394},"https://www.researchgate.net/publication/233408726_Multi-Group_Analysis_in_Partial_Least_Squares_PLS_Path_Modeling_Alternative_Methods_and_Empirical_Results",[395],"nofollow",[397],{"type":21,"value":398},"Multi-group analysis in partial least squares (PLS) path modeling: Alternative methods and empirical results.",{"type":21,"value":400}," ",{"type":15,"tag":139,"props":402,"children":403},{},[404],{"type":21,"value":405},"Advances in International Marketing",{"type":21,"value":378},{"type":15,"tag":139,"props":408,"children":409},{},[410],{"type":21,"value":411},"22",{"type":21,"value":413},", 195–218.",{"type":15,"tag":46,"props":415,"children":416},{},[417,419,424],{"type":21,"value":418},"Edgington, E., & Onghena, P. (2007). ",{"type":15,"tag":139,"props":420,"children":421},{},[422],{"type":21,"value":423},"Randomization tests",{"type":21,"value":425}," (4th ed.). Chapman & Hall.",{"type":15,"tag":46,"props":427,"children":428},{},[429],{"type":15,"tag":288,"props":430,"children":432},{"href":431},"/documentation",[433],{"type":21,"value":434},"More literature ...",{"title":7,"searchDepth":436,"depth":436,"links":437},2,[438,439,440,448,449],{"id":32,"depth":436,"text":35},{"id":63,"depth":436,"text":66},{"id":208,"depth":436,"text":211,"children":441},[442,444,445,446,447],{"id":215,"depth":443,"text":218},3,{"id":226,"depth":443,"text":229},{"id":237,"depth":443,"text":240},{"id":248,"depth":443,"text":251},{"id":259,"depth":443,"text":262},{"id":276,"depth":436,"text":279},{"id":332,"depth":436,"text":335},"markdown","content:documentation:algorithms-and-techniques:resampling-and-inference:permutation:index.md","content","documentation/algorithms-and-techniques/resampling-and-inference/permutation/index.md","md",{"loc":4},1784805333145]