[{"data":1,"prerenderedAt":319},["ShallowReactive",2],{"content-query-qCpppBsqjn":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":9,"layout":10,"body":11,"_type":313,"_id":314,"_source":315,"_file":316,"_extension":317,"sitemap":318},"/documentation/algorithms-and-techniques/validity-and-model-fit/goodness-of-fit","validity-and-model-fit",false,"","Goodness of Fit (GoF) Index in PLS-SEM: Why It's Limited","The goodness of fit (GoF) index was proposed as an overall PLS-SEM model fit measure but cannot reliably distinguish valid from invalid models. Learn its limitations in SmartPLS.","algorithm-description",{"type":12,"children":13,"toc":298},"root",[14,23,38,45,50,56,61,67,72,78,85,90,96,101,107,112,118,129,135,185,191],{"type":15,"tag":16,"props":17,"children":19},"element","h1",{"id":18},"goodness-of-fit-gof",[20],{"type":21,"value":22},"text","Goodness of Fit (GoF)",{"type":15,"tag":24,"props":25,"children":26},"p",{},[27,29,36],{"type":21,"value":28},"The goodness of fit (GoF) index was developed as an overall measure of model fit for PLS-SEM. However, as the GoF cannot reliably distinguish valid from invalid models, and since its applicability is limited to certain model setups, researchers should avoid using it as a general goodness-of-fit measure. The GoF may still be useful within a PLS multigroup analysis (PLS-MGA). Also see the information on ",{"type":15,"tag":30,"props":31,"children":33},"a",{"href":32},"/documentation/algorithms-and-techniques/validity-and-model-fit/model-fit",[34],{"type":21,"value":35},"model fit",{"type":21,"value":37},".",{"type":15,"tag":39,"props":40,"children":42},"h2",{"id":41},"why-pls-sem-does-not-rely-on-a-single-global-fit-measure",[43],{"type":21,"value":44},"Why PLS-SEM Does Not Rely on a Single Global Fit Measure",{"type":15,"tag":24,"props":46,"children":47},{},[48],{"type":21,"value":49},"Unlike CB-SEM, PLS-SEM does not optimize a unique global scalar function. Some scholars have traditionally considered the lack of a global scalar function and the consequent lack of global goodness-of-fit measures drawbacks of PLS-SEM, but we do not take this position. When using PLS-SEM, it is important to recognize that the term fit has different meanings in the contexts of CB-SEM and PLS-SEM (Hair, Hollingsworth, Randolph, & Chong, 2017; Rigdon, Sarstedt, & Ringle, 2017). Fit statistics for CB-SEM are derived from the discrepancy between the empirical and the model-implied (theoretical) covariance matrix, whereas PLS-SEM focuses on the discrepancy between the observed (in the case of manifest variables) or approximated (in the case of latent variables) values of the dependent variables and the values predicted by the model in question (Hair, Sarstedt, & Ringle, 2019; Henseler et al., 2014). While researchers have proposed various model fit measures for PLS-SEM (Schuberth, Henseler, & Dijkstra, 2018; Tenenhaus et al., 2005), their efficacy for identifying misspecified models is highly limited (see Exhibit 6.2 for a discussion of the measures and their limitations). As a consequence, to judge the model’s quality researchers using PLS-SEM rely on alternative measures that assess the model’s predictive capabilities (Shmueli, Ray, Velasquez Estrada, & Chatla, 2016; Shmueli et al., 2019), both in-sample and out-of-sample (Hair, 2020). (Hair et al., 2027).",{"type":15,"tag":39,"props":51,"children":53},{"id":52},"the-gof-index-and-its-limitations",[54],{"type":21,"value":55},"The GoF Index and Its Limitations",{"type":15,"tag":24,"props":57,"children":58},{},[59],{"type":21,"value":60},"Henseler and Sarstedt (2013) explain in detail that the global goodness of fit (GoF) for PLS by Tenenhaus et al. (2004) does not represent a fit measure and should not be used as such (see also Hair et al., 2022). However, Henseler and Sarstedt (2012) also show that the GoF may be useful for a PLS multi-group analysis (PLS-MGA) when researchers compare the PLS-SEM results of different data groups for the same PLS path model.",{"type":15,"tag":39,"props":62,"children":64},{"id":63},"fit-indexes-in-generalized-structured-component-analysis-gsca",[65],{"type":21,"value":66},"Fit Indexes in Generalized Structured Component Analysis (GSCA)",{"type":15,"tag":24,"props":68,"children":69},{},[70],{"type":21,"value":71},"The study by Cho et al. (2020) investigates structural equation modeling (SEM) based on components or composites using the Generalized Structured Component Analysis (GSCA) approach. While GSCA employs fit indexes such as the Goodness-of-Fit Index (GFI) and the Standardized Root Mean Square Residual (SRMR), their performance in this specific context had not been systematically examined. Through a simulation study, Cho et al. (2020) demonstrated that both GFI and SRMR effectively distinguish between correctly specified and misspecified models. Based on their findings, the authors propose practical cutoff criteria for these fit indexes across various sample sizes, providing guidance for model evaluation in applied research. These insights are also relevant for assessing model fit in composite-based approaches such as PLS-SEM (see also Schuberth et al., 2023).",{"type":15,"tag":39,"props":73,"children":75},{"id":74},"frequently-asked-questions",[76],{"type":21,"value":77},"Frequently Asked Questions",{"type":15,"tag":79,"props":80,"children":82},"h3",{"id":81},"what-is-the-goodness-of-fit-gof-index-in-pls-sem",[83],{"type":21,"value":84},"What is the goodness of fit (GoF) index in PLS-SEM?",{"type":15,"tag":24,"props":86,"children":87},{},[88],{"type":21,"value":89},"The GoF index was developed as an overall measure of model fit for PLS-SEM, combining information from the measurement and structural model into a single value.",{"type":15,"tag":79,"props":91,"children":93},{"id":92},"should-i-report-the-gof-index-for-my-pls-sem-model",[94],{"type":21,"value":95},"Should I report the GoF index for my PLS-SEM model?",{"type":15,"tag":24,"props":97,"children":98},{},[99],{"type":21,"value":100},"No. The GoF cannot reliably distinguish valid from invalid models, and its applicability is limited to certain model setups. It should not be used as a general goodness-of-fit measure.",{"type":15,"tag":79,"props":102,"children":104},{"id":103},"is-the-gof-index-ever-useful-in-pls-sem",[105],{"type":21,"value":106},"Is the GoF index ever useful in PLS-SEM?",{"type":15,"tag":24,"props":108,"children":109},{},[110],{"type":21,"value":111},"Yes, in one specific situation: Henseler and Sarstedt (2012) show that the GoF can be useful for a PLS multigroup analysis (PLS-MGA), when comparing PLS-SEM results across different data groups for the same PLS path model.",{"type":15,"tag":79,"props":113,"children":115},{"id":114},"are-there-fit-indexes-for-composite-based-sem-at-all",[116],{"type":21,"value":117},"Are there fit indexes for composite-based SEM at all?",{"type":15,"tag":24,"props":119,"children":120},{},[121,123,127],{"type":21,"value":122},"Cho et al. (2020) show, in the context of generalized structured component analysis (GSCA), that the GFI and SRMR fit indexes can effectively distinguish correctly specified from misspecified models, and propose cutoff criteria across sample sizes. These insights are also relevant for composite-based approaches such as PLS-SEM. See also the SmartPLS documentation on ",{"type":15,"tag":30,"props":124,"children":125},{"href":32},[126],{"type":21,"value":35},{"type":21,"value":128}," for the SRMR and other fit criteria implemented in SmartPLS.",{"type":15,"tag":39,"props":130,"children":132},{"id":131},"related-smartpls-methods",[133],{"type":21,"value":134},"Related SmartPLS Methods",{"type":15,"tag":136,"props":137,"children":138},"ul",{},[139,149,158,167,176],{"type":15,"tag":140,"props":141,"children":142},"li",{},[143],{"type":15,"tag":30,"props":144,"children":146},{"href":145},"/documentation/algorithms-and-techniques/validity-and-model-fit/model-fit/",[147],{"type":21,"value":148},"Model fit (SRMR, d_ULS, d_G, NFI)",{"type":15,"tag":140,"props":150,"children":151},{},[152],{"type":15,"tag":30,"props":153,"children":155},{"href":154},"/documentation/algorithms-and-techniques/validity-and-model-fit/confirmatory-composite-analysis/",[156],{"type":21,"value":157},"Confirmatory composite analysis (CCA)",{"type":15,"tag":140,"props":159,"children":160},{},[161],{"type":15,"tag":30,"props":162,"children":164},{"href":163},"/documentation/algorithms-and-techniques/validity-and-model-fit/discriminant-validity-assessment/",[165],{"type":21,"value":166},"Discriminant validity assessment (HTMT)",{"type":15,"tag":140,"props":168,"children":169},{},[170],{"type":15,"tag":30,"props":171,"children":173},{"href":172},"/documentation/algorithms-and-techniques/core-algorithm/pls/",[174],{"type":21,"value":175},"PLS-SEM algorithm",{"type":15,"tag":140,"props":177,"children":178},{},[179],{"type":15,"tag":30,"props":180,"children":182},{"href":181},"/documentation/algorithms-and-techniques/cbsem/",[183],{"type":21,"value":184},"CB-SEM",{"type":15,"tag":39,"props":186,"children":188},{"id":187},"references",[189],{"type":21,"value":190},"References",{"type":15,"tag":136,"props":192,"children":193},{},[194,224,241,259,277,289],{"type":15,"tag":140,"props":195,"children":196},{},[197,199,207,209,215,217,222],{"type":21,"value":198},"Cho, G., Hwang, H., Sarstedt, M., & Ringle, C. M. (2020). ",{"type":15,"tag":30,"props":200,"children":204},{"href":201,"rel":202},"https://doi.org/10.1057/s41270-020-00089-1",[203],"nofollow",[205],{"type":21,"value":206},"Cutoff criteria for overall model fit indexes in generalized structured component analysis.",{"type":21,"value":208}," ",{"type":15,"tag":210,"props":211,"children":212},"em",{},[213],{"type":21,"value":214},"Journal of Marketing Analytics",{"type":21,"value":216},", ",{"type":15,"tag":210,"props":218,"children":219},{},[220],{"type":21,"value":221},"8",{"type":21,"value":223},", 189–202.",{"type":15,"tag":140,"props":225,"children":226},{},[227,229,239],{"type":21,"value":228},"Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2027). ",{"type":15,"tag":30,"props":230,"children":232},{"href":231},"/documentation/must-reads/pls-sem-book",[233],{"type":15,"tag":234,"props":235,"children":236},"strong",{},[237],{"type":21,"value":238},"A primer on partial least squares structural equation modeling (PLS-SEM).",{"type":21,"value":240}," (4rd ed.). Sage.",{"type":15,"tag":140,"props":242,"children":243},{},[244,246,251,252,257],{"type":21,"value":245},"Henseler, J., & Sarstedt, M. (2013). Goodness-of-fit indices for partial least squares path modeling. ",{"type":15,"tag":210,"props":247,"children":248},{},[249],{"type":21,"value":250},"Computational Statistics",{"type":21,"value":216},{"type":15,"tag":210,"props":253,"children":254},{},[255],{"type":21,"value":256},"28",{"type":21,"value":258},"(2), 565–580.",{"type":15,"tag":140,"props":260,"children":261},{},[262,264,269,270,275],{"type":21,"value":263},"Schuberth, F., Rademaker, M. E., & Henseler, J. (2023). Assessing the overall fit of composite models estimated by partial least squares path modeling. ",{"type":15,"tag":210,"props":265,"children":266},{},[267],{"type":21,"value":268},"European Journal of Marketing",{"type":21,"value":216},{"type":15,"tag":210,"props":271,"children":272},{},[273],{"type":21,"value":274},"57",{"type":21,"value":276},"(6), 1678–1702.",{"type":15,"tag":140,"props":278,"children":279},{},[280,282,287],{"type":21,"value":281},"Tenenhaus, M., Amato, S., & Esposito Vinzi, V. (2004). A global goodness-of-fit index for PLS structural equation modeling. In ",{"type":15,"tag":210,"props":283,"children":284},{},[285],{"type":21,"value":286},"Proceedings of the XLII SIS Scientific Meeting",{"type":21,"value":288}," (pp. 739–742). CLEUP.",{"type":15,"tag":140,"props":290,"children":291},{},[292],{"type":15,"tag":30,"props":293,"children":295},{"href":294},"/documentation",[296],{"type":21,"value":297},"More literature ...",{"title":7,"searchDepth":299,"depth":299,"links":300},2,[301,302,303,304,311,312],{"id":41,"depth":299,"text":44},{"id":52,"depth":299,"text":55},{"id":63,"depth":299,"text":66},{"id":74,"depth":299,"text":77,"children":305},[306,308,309,310],{"id":81,"depth":307,"text":84},3,{"id":92,"depth":307,"text":95},{"id":103,"depth":307,"text":106},{"id":114,"depth":307,"text":117},{"id":131,"depth":299,"text":134},{"id":187,"depth":299,"text":190},"markdown","content:documentation:algorithms-and-techniques:validity-and-model-fit:goodness-of-fit:index.md","content","documentation/algorithms-and-techniques/validity-and-model-fit/goodness-of-fit/index.md","md",{"loc":4},1784805369795]