1. PLS-SEM: Introduction and Overview
Joe F. Hair, Jr.
Founder & Senior Scholar

2. The greatest interest in any factor solution centers on the correlations between the original variables and the factors. The matrix of such test-factor correlations is called the factor structure, and it is the primary interpretative device in principal components analysis. In the factor structure the element rjk gives the correlation of the jth test with the kth factor. Assuming that the content of the observation variables is well known, the correlations in the kth column of the structure help in interpreting, and perhaps naming, the kth factor. Also, the coefficients in the jth row give the best view of the factor composition of the jth test.
MV Analysis - The Past?!
Another set of coefficients of interest in factor analysis is the weights that compound predicted observations z from factor scores f. These regression coefficients for the multiple regression of each element of the observation vector z on the factor f are called factor loadings and the matrix A that contains them as its rows is
Source: Cooley, William W., and Paul R. Lohnes, Multivariate Data Analysis, John Wiley & Sons, Inc., New York, 1971, page 106.

3. SEM Model:
Predicting the Birth Weight of Guinea Pigs
X & Y = different outcomes
B, C & D = common causes
A & E = independent causes
Sewall Wright, Correlation and Causation, Journal of Agricultural Research, Vol. XX, No. 7, 1921.

4. Structural Equations Modeling
What comes to mind?
CB-SEM
LISREL AMOS ?
PLS-SEM

5. Structural Equations Modeling
Wireless Phone Service
Brand
Attitudes
Advertising
Budget
Information Search
Purchase
Likelihood
Experience
Risk

6. Structural Equations Modeling (SEM)
Two Steps:
Confirm measurement model (CFA) = CFA assesses reliability and validity of the model’s constructs. CB-SEM – must achieve fit to move to 2nd step. PLS-SEM – confirm measurement before examining structural model (2nd step).
Evaluate structural model (SEM) = SEM determines whether hypothesized relationships exist between the constructs.
In developing models to test using CFA/SEM, researchers draw upon theory, prior experience, expert judgment, and research objectives to identify and develop hypotheses about relationships between multiple independent and dependent variables.

7. CB-SEM (Covariance-based SEM) – statistical objective = to reproduce the theoretical covariance matrix, without focusing on explained variance.
PLS-SEM (Partial Least Squares SEM) – statistical objective = to maximize the explained variance of the endogenous latent constructs (dependent variables).

8. CB-SEM – statistical objective (goodness of fit) = minimize the differences between the observed covariance matrix and the estimated covariance matrix.
Research objective: testing and confirmation where prior theory is strong.
Assumes normality of data distribution, homoscedasticity, large sample size, etc.
A “full information approach” which means small changes in model specification can result in substantial changes in model fit.

9. PLS-SEM – statistical objective = maximize the explained (predicted) variance of the dependent variables.
Research objective: theory development and prediction.
Normality of data distribution not assumed.
Good solutions with smaller sample sizes.
Measurement models:
Can be used with fewer indicator variables (1 or 2) per construct.
OK to have ordinal scaled questions.
Can include a larger number of indicator variables (CB-SEM = solution unlikely with 50+ items).
Preferred alternative with formative constructs.

10. PLS Path Model
Steps 1 & 2 are combined, but still look at measurement theory first before moving to structural model assessment.

11. Rules of Thumb: PLS-SEM or CB-SEM
Which SEM Approach Should Be Used?
Rules of Thumb: PLS-SEM or CB-SEM
Use CB-SEM when:
The goal is theory testing, theory confirmation, or the comparison of alternative theories.
Structural model has non-recursive relationships.
Research requires a global goodness of fit criterion.

12. Rules of Thumb: PLS-SEM or CB-SEM?
Use PLS-SEM when:
The goal is predicting key target constructs.
Formative constructs are included in the structural model. Note that formative measures can also be used with CB-SEM, but doing so requires construct specification modifications (e.g., the construct must include both formative and reflective indicators to meet identification requirements = MIMIC measurement model).
The structural model is complex (many constructs and many indicators).
The sample size is small and/or the data is not-normally distributed.
The plan is to use latent variable scores in subsequent analyses.

13. Should You Use SEM In Your Research?
Journal reviewers rate SEM papers more favorably on key manuscript attributes
Mean Score
Attributes SEM No SEM p-value
Topic Relevance
Research Methods
Data Analysis
Conceptualization
Writing Quality
Contribution
Note: scores based on 5-point scale, with 5 = more favorable
Source: Babin, Hair & Boles, Publishing Research in Marketing Journals Using Structural Equation Modeling, Journal of Marketing Theory and Practice, Vol. 16, No. 4, 2008, pp

14. The use of PLS-SEM is increasing in different fields
Marketing (Hair et al. 2012a)
Cumulative number of articles
MISQ (Ringle et al. 2012)
Strategic Mgmt. (Ringle et al. 2012b)
Mgmt. Accounting (Nitzl 2012)
1980
1990
2000
2010
Year
Hair, J. F., M. Sarstedt, C. M. Ringle, and J. A. Mena (2012a). An Assessment of the Use of Partial Least Squares Structural Equation Modeling in Marketing Research, Journal of the Academy of Marketing Science, 40 (3),
Hair, J. F., M. Sarstedt, T. Pieper, and C. M. Ringle (2012b). The Use of Partial Least Squares Structural Equation Modeling in Strategic Management Research: A Review of Past Practices and Recommendations for Future Applications, Long Range Planning, 45(5/6),
Nitzl, C. (2012). The Use of Partial Least Squares Path Modeling in Management Accounting, White Paper.
Ringle, C. M., M. Sarstedt, and D. Straub (2012). A Critical Look at the Application of PLS-SEM in MIS Quarterly, MIS Quarterly, 36(1), iii-xiv.

15. Corporate Reputation SEM Model
All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.

16. Corporate Reputation Simple Model. .
COMP = Competence
Like = Likable
CUSA = Satisfaction
CUSL = Loyalty
All rights reserved ©. Cannot be reproduced or distributed without express written permission from Prentice-Hall, McGraw-Hill, Sage, SmartPLS, and session presenters.

17. Inner Model – Outer Model ??.

18. A PLS path model consists of two elements:
First, there is a structural model (also referred to as the inner model in the context of PLS-SEM) that represents the constructs (circles or ovals). The structural model also displays the relationships (paths) between the constructs.
Second, there are the measurement models (also referred to as the outer models in PLS-SEM) of the constructs that display the relationships between the constructs and the indicator variables (rectangles).
There are two types of constructs in a SEM: the exogenous latent variables (i.e., those constructs that explain other constructs in the model) and the endogenous latent variables (i.e., those constructs that are being explained in the model).
All rights reserved ©. Cannot be reproduced or distributed without express written permission from Prentice-Hall, McGraw-Hill, Sage, SmartPLS, and session presenters.

19. Path models = diagrams used to visually display the hypotheses and variable relationships that are examined when SEM is applied.
Constructs = variables that are not directly measured) are represented in path models as circles or ovals (Y1 to Y4).
Indicators = also referred to as items or manifest variables, are the directly measured proxy variables that contain the raw data. They are represented in path models as rectangles (x1 to x10).
Paths = relationships between constructs, and between constructs and their assigned indicators, shown as arrows. In PLS-SEM, the arrows are always single-headed, thus representing directional relationships. Single-headed arrows are considered a predictive relationship, and with strong theoretical support, can be interpreted as causal relationships.
All rights reserved ©. Cannot be reproduced or distributed without express written permission from Prentice-Hall, McGraw-Hill, Sage, SmartPLS, and session presenters.

20. Error terms = The error terms (e. g. , e7 or e8; Exhibit 1
Error terms = The error terms (e.g., e7 or e8; Exhibit 1.4) are connected to the (endogenous) constructs and (reflectively) measured variables by single-headed arrows. Error terms represent the unexplained variance when path models are estimated.
In Exhibit 1.4, error terms e7 to e10 are on those indicators whose relationships go from the construct to the indicator (i.e., reflectively measured indicators). In contrast, the formatively measured indicators x1 to x6, where the relationship goes from the indicator to the construct, do not have error terms.
The structural model also contains error terms. In Exhibit 1.4, z3 and z4 are associated with the endogenous latent variables Y3 and Y4 (note that error terms on constructs and measured variables are labeled differently). In contrast, the exogenous latent variables that only explain other latent variables in the structural model do not have an error term. .
All rights reserved ©. Cannot be reproduced or distributed without express written permission from Prentice-Hall, McGraw-Hill, Sage, SmartPLS, and session presenters.

21. Reflective (Scale) Versus Formative (Index) Operationalization of Constructs
A central research question in social science research, particularly marketing, management & MIS, focuses on the operationalization of complex constructs:
Are indicators causing or being caused by
the latent variable/construct measured by them?
Construct
Indicator 1
Indicator 2
Indicator 3 ?
Changes in the latent variable directly cause changes in the assigned indicators
Changes in one or more of the indicators causes changes in the latent variable

22. Example: Reflective vs. Formative World View
Can’t walk a straight line
Drunkenness
Smells of alcohol
Slurred speech

23. Example: Reflective vs. Formative World View
Consumption of beer
Drunkenness
Consumption of wine
Consumption of hard liquor

24. Basic Difference Between Reflective and Formative Measurement Approaches
“Whereas reflective indicators are essentially interchangeable (and therefore the removal of an item does not change the essential nature of the underlying construct), with formative indicators ‘omitting an indicator is omitting a part of the construct’.”
(DIAMANTOPOULOS/WINKLHOFER, 2001, p. 271)
The formative measurement approach generally minimizes the overlap between complementary indicators
Construct domain
Construct domain
The reflective measurement approach focuses on maximizing the overlap between interchangeable indicators

25. Exercise: Satisfaction in Hotels as Formative and Reflective Operationalized Constructs
The rooms‘ furnishings are good
The hotel’s recreation offerings are good
The rooms are clean
Taking everything into account, I am satisfied with this hotel
I appreciate this hotel
Satisfaction with Hotels
The hotel‘s personnel are friendly
The hotel is low-priced
The rooms are quiet
I am looking forward to staying overnight in this hotel
I am comfortable with this hotel
The hotel’s service is good
The hotel’s cuisine is good

26. Formative Constructs – Two Types
Composite (formative) constructs – indicators completely determine the “latent” construct. They share similarities because they define a composite variable but may or may not have conceptual unity. In assessing validity, indicators are not interchangeable and should not be eliminated, because removing an indicator will likely change the nature of the latent construct.
Causal constructs – indicators have conceptual unity in that all variables should correspond to the definition of the concept. In assessing validity some of the indicators may be interchangeable, and also can be eliminated.
Bollen, K.A. (2011), Evaluating Effect, Composite, and Causal Indicators in Structural Equations Models, MIS Quarterly, Vol. 35, No. 2, pp

27. Sample Size
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 regressions to estimate the model’s partial regression relationships.
The 10 times rule indicates the sample size should be equal to the larger of:
(1) 10 times the largest number of formative indicators used to measure a single construct, or
(2) 10 times the largest number of structural paths directed at a particular latent construct in the structural model.
This rule of thumb is equivalent to saying that the minimum sample size should be 10 times the maximum number of arrowheads pointing at a latent variable anywhere in the path model. While the 10 times rule offers a rough guideline for minimum sample size requirements, PLS-SEM – like any statistical technique – requires researchers to consider the sample size against the background of the model and data characteristics. Specifically, the required sample size should be determined using power analyses based on the part of the model with the largest number of predictors.

28. Statistical power assumed = 80%.
Statistical power assumed = 80%

29. Indicators for SEM Model Constructs

30. Extended Reputation Model Constructs