3Significance of PLS-SEM Parameters = Bootstrapping PLS-SEM does not assume the data is normally distributed, which implies that parametric significance tests used in regression analyses cannot be applied to test whether coefficients such as outer weights and loadings are significant. Instead, PLS-SEM relies on a nonparametric bootstrap procedure to test coefficients for their significance.In bootstrapping, a large number of subsamples (i.e., bootstrap samples) is drawn from the original sample with replacement. Replacement means that each time an observation is drawn at random from the sampling population, it is returned to the sampling population before the next observation is drawn (i.e., the population from which the observations are drawn always contains all the same elements). Therefore, an observation for a certain subsample can be selected more than once, or may not be selected at all for another subsample. The number of bootstrap samples should be high but must be at least equal to the number of valid observations in the dataset. The recommended number of bootstrap samples is 5,000.
4SmartPLS Bootstrapping Bootstrapping estimates a PLS path model for each subsample:Samples: Number of random samples drawn from the original sample (at minimum should equal the number of observations in the original sample, but 5,000 is recommended).Cases: Number of cases drawn in each sample run (should be at least as large as the number of valid observations in the original sample).Bootstrapping provides mean values and standard errors for:inner model path coefficients.weights and loadings in the measurement models.Use bootstrapping
5SmartPLS Bootstrapping If you have missing data do not use mean replacement because bootstrapping draws samples with replacement. Use Casewise Replacement.Use individual (sign) changes optionMake sure the number of cases are equal to the number of valid observations in your dataset.Set cases = samples size (or higher)Caution!!! It is a common mistake to set samples equal to the overall number of observations.
6SmartPLS Bootstrapping Make sure the number of cases are equal to (or more than) the number of valid observations in your dataset. Set cases = sample size (or higher). Note that the number is now 344.We have also set the number of samples as 5,000.
7Bootstrapping HTML Report – Table of Contents Click on to access HTML report
8Results based on Cases = 344 and Samples = 5,000 Bootstrapping Option (Total Effects tables) – Significance of Structural Path CoefficientsResults based on Cases = 344 and Samples = 5,000Significant t-values1.65 for 10%1.96 for 5%2.58 for 1%(all two-tailed)
9Bootstrapping Option – Significance of Indicator Loadings Results based on Cases = 344 and Samples = 5,000
10SmartPLS Predictive Relevance – Blindfolding Q² is a criterion to evaluate how well the model predicts the data of omitted cases. It is referred to as predictive relevance.The process involves omitting (removing) or “blindfolding” one case at a time and re-estimating the model parameters based on the remaining cases. The omitted case values are then predicted on the basis of the newly estimated parameters of the remaining cases.Procedure:Set an omission distance D. Note: The number of cases in your data must not be a multiple integer number of the omission distance (otherwise the blindfolding procedure yields erroneous results). Experience has shown that d values between 5 and 10 typically work well.Interpret the cross-validated redundancy, because it uses the PLS-SEM estimates of both the structural model and the measurement models for data prediction. Also, in most instances the focus is on predicting the data of the target endogenous constructs.
11SmartPLS Predictive Relevance – Blindfolding Redundancy vs. Communality? Cross-validated redundancyLV1Step 1:The scores of the endogenous LV(s)are estimated using the scores of theexogenous LVsMV 1LV3MV 2LV2MV 3LV1LV3MV 1Step 2:Newly estimated LV scores are usedto estimate the missing MV dataMV 2LV2MV 3Cross-validated communalityOnly step 2.
12SmartPLS Results – Blindfolding Use blindfolding
13SmartPLS Results – Blindfolding Make sure that n / Omission distance is not an integer(here: n = 344).Check all boxes
14SmartPLS Results – Blindfolding Click on to access HTML report
15SmartPLS Results – Blindfolding Click on Construct Crossvalidated RedundancyQ² > 0: model has predictive relevance.Q² ≈ 0 or Q² < 0: model is lacking predictive relevance.Predictive relevance is demonstrated for both endogenous constructs.
16Totals for 5 year periods * Ranking based on Hult et al. (2009) PLS-SEM and Research in MarketingTop 30 marketing journals* – 204 articles / 311 models80% of articles published since 2000, 35% in JM, IMM & EJM2010 = 25%1980-19841985-19891990-19941995-19992000-2004200520062007200820092010Individual yearsTotals for 5 year periodsAn Assessment of the Use of Partial Least Squares Structural Equation Modeling in Marketing Research, JAMS, Vol. 40 (3), May 2012.* Ranking based on Hult et al. (2009)
17PLS-SEM and Research in Marketing Reasons for using PLS – non-normal data (50%), small sample size (46%), formative measures (33%), prediction = research objective (28%), complex models (13%), categorical variables (13%).Average PLS sample size is 211 compared to 246 for CB-SEM. But 25% had less than 100 observations, and 9% did not meet recommended sample size criteria.No studies report skewness or kurtosis.42% reflective only; 6% formative only; 40% mixed; 12% no indication.
18PLS-SEM and Research in Marketing Outer Model EvaluationReliability70% reported (56% composite reliability)46% included formative constructs, but 23% used reflective criteria on formative constructsConvergent Validity (AVE) – 57%Discriminant ValidityFornell-Larcker – 44%Cross-loadings – 5%Both – 12%Significance of formative indicator weights – 17%Inner Model EvaluationR2 – 88%Predictive relevance (Q2) – 16% (for endogenous variables)Path coefficient sizes – 96%Path coefficient significance – 92%
19Observations and Conclusions PLS-SEM = rapidly emerging tool in marketing literature becauseFlexible data distribution and scaling requirements.Achieves high levels of statistical power with smaller sample sizes and complex models.With complex models produces superior results to CB-SEM.Easily handles both reflective and formative measured constructs.PLS-SEM’s methodological properties are widely misunderstood (CB-SEM bias).Marketing scholars need to become familiar with advantages and limitations.
20Special Issue, PLS in Marketing, March 2011 Hair, Joseph F., Christian M. Ringle, and Marko Sarstedt. PLS-SEM: Indeed a Silver Bullet.Haenlein, Michael and Andreas M. Kaplan. The Influence of Observed Heterogeneity on Path Coefficient Significance: Technology Acceptance within the Marketing Discipline.Eggert, Andreas and Murat Serdaroglu. Exploring the Impact of Sales Technology on Salesperson Performance: A Task-Based Approach.Navarro, Antonio, Francisco J. Acedo, Fernando Losada, and Emilio Ruzo. Integrated Model of Export Activity: Analysis of Heterogeneity in Managers’ Orientations and Perceptions on Strategic Marketing Management in Foreign Markets.Wiedmann, Klaus-Peter, Nadine Hennigs, Steffen Schmidt, and Thomas Wuestefeld. Drivers and Outcomes of Brand Heritage: Consumers’ Perception of Heritage Brands in the Automotive Industry.Anderson, Rolph, and Srinivasan Swaminathan. Customer Satisfaction and Loyalty in e-Markets: A PLS Path Modeling Approach.Hoffmann, Stefan, Robert Mai, and Maria Smirnova. Development and Validation of a Cross-Nationally Stable Scale of Consumer Animosity.
21Other Sources: An Assessment of the Use of Partial Least Squares Structural Equation ModelingIn Marketing Research, JAMS, Vol 40 (3), May2012;Special Issue, LRP, forthcoming 2013,PLS in Long Range Planning.Book: A Primer on Partial Least Squares,Sage, forthcoming 2013.
22Variance-Based Modeling Covariance-Based Modeling Summary Comparison: PLS-SEM vs. CB-SEMCriteriaVariance-Based Modeling(e.g. SmartPLS, PLS Graph)Covariance-Based Modeling(e.g. LISREL, AMOS, Mplus)ObjectivePrediction orientedParameter orientedDistribution AssumptionsNon-parametricNormal distribution (parametric)Required sample sizeSmall (min. 30 – 100)High (min. 100 – 800)Model complexityLarge models OKLarge models problematic(50+ indicator variables)Parameter EstimatesPotential BiasStable, if assumptions metIndicators perconstructOne – two OKLarge number OKTypically 3 – 4 minimum to meet identification requirementsStatistical tests for parameter estimatesInference requires Jackknifing or BootstrappingAssumptions must be metMeasurement ModelFormative and Reflective indicators OKTypically only Reflective indicatorsGoodness-of-fit measuresNoneMany
23Sample Size Determination – PLS-SEM Sample size should be equal to the larger of:ten times the largest number of formative indicators used to measure a single construct, orten times the largest number of structural paths directed at a particular latent construct in the structural model.
24Sample Size Guidelines – PLS-SEM The overall complexity of a structural model has little influence on the sample size requirements for PLS-SEM. The reason is the algorithm does not compute all relationships in the structural model at the same time. Instead, it uses OLS to estimate the SEM model’s partial regression relationships. Two early studies systematically evaluated the performance of PLS-SEM with small sample sizes and concluded it performed well (e.g., Chin & Newsted, 1999; Hui & Wold, 1982). More recently a simulation study by Reinartz et al. (2009) indicated that PLS-SEM is a good choice when the sample size is small. Moreover, compared to its covariance-based counterpart, PLS-SEM has higher levels of statistical power in situations with complex model structures or smaller sample sizes.
25Path Model and Data for PLS-SEM Hypothetical Example HBAT