Joe F. Hair, Jr. Founder & Senior Scholar, DBA Program Joe F. Hair, Jr. Founder & Senior Scholar, DBA Program PLS-SEM: Introduction Continued (Part 2)

Joe F. Hair, Jr.Joe F. Hair, Jr.Founder & Senior Scholar, DBA Founder & Senior Scholar, DBA

ProgramProgram

Joe F. Hair, Jr.Joe F. Hair, Jr.Founder & Senior Scholar, DBA Founder & Senior Scholar, DBA

ProgramProgram

PLS-SEM: Introduction Continued PLS-SEM: Introduction Continued (Part 2)(Part 2)

Specifying the Structural Model

Specifying the Measurement Models

Data Collection and Examination

PLS-SEM Model Estimation

Assessing PLS-SEM Results for ReflectiveMeasurement Models

Assessing PLS-SEM Results for Formative Measurement Models

Assessing PLS-SEM Results for the StructuralModel

Interpretation of Results and Drawing Conclusions

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5a

Stage 5b

Stage 6

Stage 7

Systematic Process for applying PLS-SEM Systematic Process for applying PLS-SEM

Significance of PLS-SEM Parameters = BootstrappingSignificance of PLS-SEM Parameters = Bootstrapping

PLS-SEM does not assume the data is normally distributed, which PLS-SEM does not assume the data is normally distributed, which implies that parametric significance tests used in regression analyses implies that parametric significance tests used in regression analyses cannot be applied to test whether coefficients such as outer weights cannot be applied to test whether coefficients such as outer weights and loadings are significant. Instead, PLS-SEM relies on a and loadings are significant. Instead, PLS-SEM relies on a nonparametric bootstrap procedure to test coefficients for their nonparametric bootstrap procedure to test coefficients for their significance.significance.

In bootstrapping, a large number of subsamples (i.e., bootstrap In bootstrapping, a large number of subsamples (i.e., bootstrap samples) is drawn from the original sample with replacement. samples) is drawn from the original sample with replacement. Replacement means that each time an observation is drawn at Replacement means that each time an observation is drawn at random from the sampling population, it is returned to the sampling random from the sampling population, it is returned to the sampling population before the next observation is drawn (i.e., the population population before the next observation is drawn (i.e., the population from which the observations are drawn always contains all the same from which the observations are drawn always contains all the same elements). Therefore, an observation for a certain subsample can be elements). Therefore, an observation for a certain subsample can be selected more than once, or may not be selected at all for another selected more than once, or may not be selected at all for another subsample. The number of bootstrap samples should be high but subsample. The number of bootstrap samples should be high but must be at least equal to the number of valid observations in the must be at least equal to the number of valid observations in the dataset. The recommended number of bootstrap samples is 5,000.dataset. The recommended number of bootstrap samples is 5,000.

SmartPLS Bootstrapping SmartPLS Bootstrapping

• Bootstrapping estimates a PLS path model for each subsample:Bootstrapping estimates a PLS path model for each subsample: Samples: Number of random samples drawn from the original sample Samples: Number of random samples drawn from the original sample

(at minimum should equal the number of observations in the original (at minimum should equal the number of observations in the original sample, but 5,000 is recommended).sample, but 5,000 is recommended).

Cases:Cases: Number of cases drawn in each sample run Number of cases drawn in each sample run (should be at least (should be at least as large as the number of valid observations in the original sample).as large as the number of valid observations in the original sample).

• Bootstrapping provides mean values and standard errors for:Bootstrapping provides mean values and standard errors for: inner model path coefficients.inner model path coefficients. weights and loadings in the measurement models.weights and loadings in the measurement models.

Use bootstrappingUse bootstrapping

If you have missing data do not use mean If you have missing data do not use mean replacement because bootstrapping draws replacement because bootstrapping draws samples with replacement. Use Casewise samples with replacement. Use Casewise Replacement.Replacement.

Use individual (sign) changes optionUse individual (sign) changes option

• Make sure the number of cases are Make sure the number of cases are equal to the number of equal to the number of validvalid observations in your dataset.observations in your dataset.

• Set Set casescases = = samplessamples size (or higher) size (or higher)

Caution!!! Caution!!! It is a common mistake to set It is a common mistake to set samples equal to the overall number of samples equal to the overall number of observations.observations.



• Make sure the number of cases are Make sure the number of cases are equal to (or more than) the number of equal to (or more than) the number of validvalid observations in your dataset. Set observations in your dataset. Set casescases = = sample sizesample size (or higher). Note (or higher). Note that the number is now 344.that the number is now 344.

• We have also set the number of We have also set the number of samples as 5,000.samples as 5,000.

Bootstrapping HTML Report – Table of ContentsBootstrapping HTML Report – Table of Contents

Click on to access HTML reportClick on to access HTML report

Significant t-valuesSignificant t-values•1.65 for 10%1.65 for 10%•1.96 for 5%1.96 for 5%•2.58 for 1%2.58 for 1%

(all two-tailed)(all two-tailed)

Results based on Cases = 344 and Samples = 5,000Results based on Cases = 344 and Samples = 5,000

Bootstrapping Option (Total Effects tables) – Bootstrapping Option (Total Effects tables) – Significance of Structural Path CoefficientsSignificance of Structural Path Coefficients

Results based on Cases = 344 and Samples = 5,000Results based on Cases = 344 and Samples = 5,000

Bootstrapping Option – Significance of Bootstrapping Option – Significance of Indicator LoadingsIndicator Loadings

SmartPLS Predictive Relevance – SmartPLS Predictive Relevance – BlindfoldingBlindfolding

o QQ² is a criterion to evaluate how well the model predicts the data of ² is a criterion to evaluate how well the model predicts the data of omitted cases. It is referred to as predictive relevance.omitted cases. It is referred to as predictive relevance.

o The process involves omitting (removing) or “blindfolding” one case The process involves omitting (removing) or “blindfolding” one case at a time and re-estimating the model parameters based on the at a time and re-estimating the model parameters based on the remaining cases. The omitted case values are then predicted on the remaining cases. The omitted case values are then predicted on the basis of the newly estimated parameters of the remaining cases.basis of the newly estimated parameters of the remaining cases.

o Procedure:Procedure:• Set an omission distance D. Note: The number of cases in your Set an omission distance D. Note: The number of cases in your

data must not be a multiple integer number of the omission data must not be a multiple integer number of the omission distance (otherwise the blindfolding procedure yields erroneous distance (otherwise the blindfolding procedure yields erroneous results). Experience has shown that d values between 5 and 10 results). Experience has shown that d values between 5 and 10 typically work well.typically work well.

• Interpret the cross-validated redundancy, because it uses the Interpret the cross-validated redundancy, because it uses the PLS-SEM estimates of both the structural model and the PLS-SEM estimates of both the structural model and the measurement models for data prediction. Also, in most instances measurement models for data prediction. Also, in most instances the focus is on predicting the data of the target endogenous the focus is on predicting the data of the target endogenous constructs.constructs.

11

LV3

MV 1

MV 2

MV 3

LV1

LV2

LV3

MV 1

MV 2

MV 3

LV1

LV2

Step 1:The scores of the endogenous LV(s) are estimated using the scores of the

exogenous LVs

Step 2:Newly estimated LV scores are used

to estimate the missing MV data

Cross-validated redundancy

Cross-validated redundancy

Cross-validated communalityCross-validated communality Only step 2.Only step 2.

SmartPLS Predictive Relevance – SmartPLS Predictive Relevance – BlindfoldingBlindfolding

Redundancy vs. Communality?Redundancy vs. Communality?

SmartPLS Results – BlindfoldingSmartPLS Results – Blindfolding

Use blindfoldingUse blindfolding


Make sure that Make sure that n / Omission n / Omission distance distance is not an integeris not an integer (here: (here: n = 344n = 344).).

Check all boxesCheck all boxes

Click on to access HTML reportClick on to access HTML report


Click on Construct Crossvalidated RedundancyClick on Construct Crossvalidated Redundancy

Predictive relevance is demonstrated for both Predictive relevance is demonstrated for both endogenous constructs.endogenous constructs.


Q² > 0: model has predictive relevance.Q² > 0: model has predictive relevance.Q² ≈ 0 or Q² < 0: model is lacking predictive relevance.Q² ≈ 0 or Q² < 0: model is lacking predictive relevance.

1980-

1984

1985-

1989

1990-

1994

1995-

1999

2000-

2004

* Ranking based on Hult et al. (2009)

2005 2006 2007 2008 2009 2010

PLS-SEM and Research in MarketingPLS-SEM and Research in Marketing

• Top 30 marketing journals* – 204 articles / 311 models Top 30 marketing journals* – 204 articles / 311 models

• 80% of articles published since 2000, 35% in JM, IMM & EJM80% of articles published since 2000, 35% in JM, IMM & EJM

2010 = 25%

Totals for 5 year periods

Individual years

An Assessment of the Use of Partial Least Squares Structural Equation Modeling in Marketing Research, JAMS, Vol. 40 (3), May 2012.

PLS-SEM and Research in MarketingPLS-SEM and Research in Marketing

• Reasons for using PLS – non-normal data (50%), small Reasons for using PLS – non-normal data (50%), small sample size (46%), formative measures (33%), sample size (46%), formative measures (33%), prediction = research objective (28%), complex models prediction = research objective (28%), complex models (13%), categorical variables (13%).(13%), categorical variables (13%).

• Average PLS sample size is 211 compared to 246 for Average PLS sample size is 211 compared to 246 for CB-SEM. But 25% had less than 100 observations, CB-SEM. But 25% had less than 100 observations, and 9% did not meet recommended sample size and 9% did not meet recommended sample size criteria.criteria.

• No studies report skewness or kurtosis.No studies report skewness or kurtosis.• 42% reflective only; 6% formative only; 40% mixed; 42% reflective only; 6% formative only; 40% mixed;

12% no indication.12% no indication.

Observations and ConclusionsObservations and Conclusions

PLS-SEM = rapidly emerging tool in marketing literature PLS-SEM = rapidly emerging tool in marketing literature because . . . because . . . Flexible data distribution and scaling requirements.Flexible data distribution and scaling requirements. Achieves high levels of statistical power with smaller sample Achieves high levels of statistical power with smaller sample

sizes and complex models.sizes and complex models. With complex models produces superior results to CB-SEM.With complex models produces superior results to CB-SEM. Easily handles both reflective and formative measured Easily handles both reflective and formative measured

constructs.constructs.

PLS-SEM’s methodological properties are widely PLS-SEM’s methodological properties are widely misunderstood (CB-SEM bias).misunderstood (CB-SEM bias).

Marketing scholars need to become familiar with Marketing scholars need to become familiar with advantages and limitations.advantages and limitations.

Special Issue, PLS in Marketing, March 2011Special Issue, PLS in Marketing, March 2011

Hair, Joseph F., Christian M. Ringle, and Marko Sarstedt. PLS-SEM: Hair, Joseph F., Christian M. Ringle, and Marko Sarstedt. PLS-SEM: Indeed a Silver Bullet.Indeed a Silver Bullet.

Haenlein, Michael and Andreas M. Kaplan. The Influence of Observed Haenlein, Michael and Andreas M. Kaplan. The Influence of Observed Heterogeneity on Path Coefficient Significance: Technology Acceptance within Heterogeneity on Path Coefficient Significance: Technology Acceptance within the Marketing Discipline.the Marketing Discipline.

Eggert, Andreas and Murat Serdaroglu. Exploring the Impact of Sales Eggert, Andreas and Murat Serdaroglu. Exploring the Impact of Sales Technology on Salesperson Performance: A Task-Based Approach.Technology on Salesperson Performance: A Task-Based Approach.

Navarro, Antonio, Francisco J. Acedo, Fernando Losada, and Emilio Ruzo. Navarro, Antonio, Francisco J. Acedo, Fernando Losada, and Emilio Ruzo. Integrated Model of Export Activity: Analysis of Heterogeneity in Managers’ Integrated Model of Export Activity: Analysis of Heterogeneity in Managers’ Orientations and Perceptions on Strategic Marketing Management in Foreign Orientations and Perceptions on Strategic Marketing Management in Foreign Markets.Markets.

Wiedmann, Klaus-Peter, Nadine Hennigs, Steffen Schmidt, and Thomas Wiedmann, Klaus-Peter, Nadine Hennigs, Steffen Schmidt, and Thomas Wuestefeld. Drivers and Outcomes of Brand Heritage: Consumers’ Wuestefeld. Drivers and Outcomes of Brand Heritage: Consumers’ Perception of Heritage Brands in the Automotive Industry.Perception of Heritage Brands in the Automotive Industry.

Anderson, Rolph, and Srinivasan Swaminathan. Customer Satisfaction and Anderson, Rolph, and Srinivasan Swaminathan. Customer Satisfaction and Loyalty in e-Markets: A PLS Path Modeling Approach.Loyalty in e-Markets: A PLS Path Modeling Approach.

Hoffmann, Stefan, Robert Mai, and Maria Smirnova. Development and Hoffmann, Stefan, Robert Mai, and Maria Smirnova. Development and Validation of a Cross-Nationally Stable Scale of Consumer Animosity.Validation of a Cross-Nationally Stable Scale of Consumer Animosity.

Other Sources:Other Sources:

An Assessment of the Use of Partial Least An Assessment of the Use of Partial Least Squares Structural Equation Modeling Squares Structural Equation Modeling In Marketing Research, In Marketing Research, JAMSJAMS, Vol 40 (3), May , Vol 40 (3), May 2012; 414-433.2012; 414-433.

Special Issue, Special Issue, LRPLRP, forthcoming 2013, , forthcoming 2013, PLS in Long Range Planning.PLS in Long Range Planning.

Book: A Primer on Partial Least Squares, Book: A Primer on Partial Least Squares, Sage, forthcoming 2013.Sage, forthcoming 2013.

CriteriaCriteriaVariance-Based ModelingVariance-Based Modeling

(e.g. SmartPLS, PLS Graph)(e.g. SmartPLS, PLS Graph)

Covariance-Based ModelingCovariance-Based Modeling

(e.g. LISREL, AMOS, Mplus)(e.g. LISREL, AMOS, Mplus)

ObjectiveObjective Prediction orientedPrediction oriented Parameter orientedParameter oriented

Distribution Distribution AssumptionsAssumptions Non-parametricNon-parametric Normal distribution (parametric)Normal distribution (parametric)

Required sample sizeRequired sample size Small (min. 30 – 100)Small (min. 30 – 100) High (min. 100 – 800)High (min. 100 – 800)

Model complexityModel complexity Large models OKLarge models OKLarge models problematicLarge models problematic

(50+ indicator variables)(50+ indicator variables)

Parameter EstimatesParameter Estimates Potential BiasPotential Bias Stable, if assumptions metStable, if assumptions met

Indicators per Indicators per

constructconstruct

One – two OKOne – two OK

Large number OKLarge number OKTypically 3 – 4 minimum to meet Typically 3 – 4 minimum to meet

identification requirementsidentification requirements

Statistical tests for Statistical tests for parameter estimatesparameter estimates

Inference requires Inference requires Jackknifing or BootstrappingJackknifing or Bootstrapping Assumptions must be met Assumptions must be met

Measurement ModelMeasurement Model Formative and Reflective Formative and Reflective indicators OKindicators OK

Typically only Reflective Typically only Reflective indicatorsindicators

Goodness-of-fit Goodness-of-fit measuresmeasures NoneNone ManyMany

Summary Comparison: PLS-SEM vs. CB-SEMSummary Comparison: PLS-SEM vs. CB-SEM

Sample Size Determination – PLS-SEMSample Size Determination – PLS-SEM

Sample size should be equal to the larger of:Sample size should be equal to the larger of:

•ten times the largest number of formative ten times the largest number of formative

indicators used to measure a single construct, or indicators used to measure a single construct, or

•ten times the largest number of structural paths ten times the largest number of structural paths

directed at a particular latent construct in the directed at a particular latent construct in the

structural model. structural model.

Sample Size Guidelines – PLS-SEMSample Size Guidelines – PLS-SEM

The overall complexity of a structural model has little The overall complexity of a structural model has little influence on the sample size requirements for PLS-SEM. influence on the sample size requirements for PLS-SEM. The reason is the algorithm does not compute all The reason is the algorithm does not compute all relationships in the structural model at the same time. relationships in the structural model at the same time. Instead, it uses OLS to estimate the SEM model’s partial Instead, it uses OLS to estimate the SEM model’s partial regression relationships. Two early studies regression relationships. Two early studies systematically evaluated the performance of PLS-SEM systematically evaluated the performance of PLS-SEM with small sample sizes and concluded it performed well with small sample sizes and concluded it performed well (e.g., Chin & Newsted, 1999; Hui & Wold, 1982). More (e.g., Chin & Newsted, 1999; Hui & Wold, 1982). More recently a simulation study by Reinartz et al. (2009) recently a simulation study by Reinartz et al. (2009) indicated that PLS-SEM is a good choice when the indicated that PLS-SEM is a good choice when the sample size is small. Moreover, compared to its sample size is small. Moreover, compared to its covariance-based counterpart, PLS-SEM has higher covariance-based counterpart, PLS-SEM has higher levels of statistical power in situations with complex levels of statistical power in situations with complex model structures or smaller sample sizes. model structures or smaller sample sizes.

HBATHBAT

Y1

Y2

Y3x3

x4

x1

x2

x6

x7

w11

w12

w21

w22

l31

l33

l32

p13

p23

Y1 Y2 Y3

x1 w11x2 w12x3 w21x4 w22x5 l31x6 l32x7 l33

Measurement Models(Indicators x, latent variables Y,

and relationships (i.e., w or l) between indicators and latent variables)

Y1 Y2 Y3

y1 p13y2 p23y3

Structural Model(Latent variables Y andrelationships between

latent variables p)

x5

Path Model and Data for PLS-SEM Hypothetical ExamplePath Model and Data for PLS-SEM Hypothetical Example

Documents

Joe F. Hair, Jr. Founder & Senior Scholar, DBA Program Joe F. Hair, Jr. Founder & Senior Scholar, DBA Program PLS-SEM: Introduction Continued (Part 2)