PLS-SEM: Introduction Continued (Part 2)

Joe F. Hair, Jr.

Founder & Senior Scholar, DBA Program

Systematic Process for applying PLS-SEM Stage 1 Specifying the Structural Model Stage 2 Specifying the Measurement Models Stage 3 Data Collection and Examination Stage 4 PLS-SEM Model Estimation Stage 5a Stage 5b Stage 6 Assessing PLS-SEM Results for Reflective Measurement Models Assessing PLS-SEM Results for Formative Measurement Models Assessing PLS-SEM Results for the Structural Model Stage 7 Interpretation of Results and Drawing Conclusions

Significance 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.

SmartPLS 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

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

Use individual (sign) changes option • Make 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.

SmartPLS 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.

Bootstrapping HTML Report – Table of Contents

Click on to access HTML report

Bootstrapping Option (Total Effects tables) – Significance of Structural Path Coefficients Results based on Cases = 344 and Samples = 5,000 Significant t-values • 1.65 for 10% • 1.96 for 5% • 2.58 for 1% (all two-tailed)

Bootstrapping Option – Significance of Indicator Loadings Results based on Cases = 344 and Samples = 5,000

SmartPLS Predictive Relevance – Blindfolding

o o o

Q

² 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.

SmartPLS Predictive Relevance – Blindfolding Redundancy vs. Communality?

Cross-validated redundancy Step 1: The scores of the endogenous LV(s) are estimated using the scores of the exogenous LVs LV 1 LV 2 LV 3 MV 1 MV 2 MV 3 Step 2: Newly estimated LV scores are used to estimate the missing MV data LV 1 LV 2 Cross-validated communality

11

Only step 2.

LV 3 MV 1 MV 2 MV 3

SmartPLS Results – Blindfolding

Use blindfolding

SmartPLS Results – Blindfolding

Make sure that

n / Omission distance

is not an integer (here:

n = 344

).

Check all boxes

SmartPLS Results – Blindfolding

 Click on to access HTML report

SmartPLS Results – Blindfolding

Click on Construct Crossvalidated Redundancy Q² > 0: model has predictive relevance.

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

Predictive relevance is demonstrated for both endogenous constructs.



• •

PLS-SEM and Research in Marketing

Top 30 marketing journals* – 204 articles / 311 models 80% of articles published since 2000, 35% in JM, IMM & EJM

2010 = 25%

60 50 40 30 20 17 10 0 3

1980 1984

8 10

1985 1989 1990 1994 1995 1999 Totals for 5 year periods

26

2000 2004

7 15

2005 2006 An Assessment of the Use of Partial Least Squares Structural Equation Modeling in Marketing Research, JAMS, Vol. 40 (3), May 2012.

22 24 17 51

2007 2008 Individual years 2009 2010 * Ranking based on Hult et al. (2009)

• • • •

PLS-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.

PLS-SEM and Research in Marketing

Outer Model Evaluation • Reliability  70% reported (56% composite reliability)  46% included formative constructs, but 23% used reflective • • • criteria on formative constructs Convergent Validity (AVE) – 57% Discriminant Validity  Fornell-Larcker – 44%  Cross-loadings – 5%  Both – 12% Significance of formative indicator weights – 17% Inner Model Evaluation • R 2 – 88% • • • Predictive relevance (Q 2 ) – 16% (for endogenous variables) Path coefficient sizes – 96% Path coefficient significance – 92%

Observations and Conclusions

   PLS-SEM = rapidly emerging tool in marketing literature because . . .   Flexible 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.

Special 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.

Other Sources:

An Assessment of the Use of Partial Least Squares Structural Equation Modeling In Marketing Research,

JAMS

, Vol 40 (3), May 2012; 414-433.

Special Issue,

LRP

, forthcoming 2013, PLS in Long Range Planning.

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

Summary Comparison: PLS-SEM vs. CB-SEM Criteria Variance-Based Modeling

(e.g. SmartPLS, PLS Graph)

Covariance-Based Modeling

(e.g. LISREL, AMOS, Mplus) Objective Distribution Assumptions Required sample size Model complexity Parameter Estimates Indicators per construct Statistical tests for parameter estimates Measurement Model Prediction oriented Non-parametric Parameter oriented Normal distribution (parametric) Small (min. 30 – 100) Large models OK Potential Bias One – two OK Large number OK Inference requires Jackknifing or Bootstrapping Formative and Reflective indicators OK High (min. 100 – 800) Large models problematic (50+ indicator variables) Stable, if assumptions met Typically 3 – 4 minimum to meet identification requirements Assumptions must be met Typically only Reflective indicators Goodness-of-fit measures None Many

Sample 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, or

•

ten times the largest number of structural paths directed at a particular latent construct in the structural model.

Sample 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.

HBAT

Path Model and Data for PLS-SEM Hypothetical Example x 1 x 2 x 3 x 4 w 11 w 12 w 21 w 22 Y Y 1 2 p 13 p 23 Y 3 l 31 l 32 l 33 x 5 x 6 x 7 Measurement Models (Indicators x, latent variables Y, and relationships (i.e., w or l) between indicators and latent variables) x x 1 2 x 3 x 4 x 5 x 6 x 7 Y 1

w 11 w 12

Y 2

w w 21 22

Y 3

l l l 31 32 33

y 1 y 2 y 3 Structural Model (Latent variables Y and relationships between latent variables p) Y 1 Y 2 Y 3

p 13 p 23