Using the SmartPLS Software

“

Structural Model Assessment

”

Joe F. Hair, Jr.

Founder & Senior Scholar

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1

Step 3: Assess the Level of R

2

The R² values of the endogenous latent variables are available in the PLS Algorithm default report (

PLS

→

Quality Criteria

→

Overview

), as shown below. The R 2 values of COMP (0.6309), CUSL (0.5620), and LIKE (0.5576) can be considered moderate. In contrast, the R² value of CUSA (0.2919) is rather weak. All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, SmartPLS, and session presenters.

2 2

Note: calculation of Q

2

value is shown in a later slide.

3

Step 4: Assessing Effect Size –

ƒ

2 The ƒ² effect size is a measure of the impact of a specific predictor construct on an endogenous construct. In addition to evaluating the size of the R² values of all endogenous constructs, the ƒ² effect size can be calculated (it is not available from the SmartPLS software output). The ƒ² effect size measures the change in the R² value when a specified exogenous construct is omitted from the model. It is used to evaluate whether the omitted predictor construct has a substantive impact on the R² values of the endogenous construct(s).

The formula for calculating the ƒ² effect size is shown on the next slide. Guidelines for assessing ƒ 2 values for the exogenous latent constructs in predicting the endogenous constructs are: Value 0.02

0.15

0.35

= = = Effect Size small medium large (Cohen, 1988) All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, SmartPLS, and session presenters.

4

Calculating the Effect Size – ƒ

2 The f 2 effect size can be calculated as shown below. In the formula R 2 included and R 2 excluded are the R² values of the endogenous latent variable when a selected exogenous latent variable is included or excluded from the model. The change in the R² values is calculated by estimating the PLS path model twice. It is estimated the first time with the exogenous latent variable included (yielding R the second time with the exogenous latent variable excluded (yielding R 2 excluded).

The results of calculating the f 2 for the reputation model example endogenous variables are shown in a later slide.

2 included) and All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, SmartPLS, and session presenters.

5

Example: Calculation of f

2

Effect Size

As indicated in the previous slide, to compute the f 2 selected endogenous latent construct, we need the R and R R R 2 2 2 excluded values. The R has an original R 2 2 included results from the overall model estimation were previously shown (Exhibit 6.15). The excluded value is obtained from a model re-estimation after deleting a specific predecessor of that endogenous latent variable. For example, the endogenous latent variable CUSL value of 0.562 (R 2 included). If CUSA is deleted from the path model and the model is re-estimated, the of CUSL has a value of only 0.385 (R 2 excluded). These two values are the inputs for computing the f CUSL. The formula is shown below: 2 value of a 2 included effect size of CUSA on 6

Example: Calculation of f

2

for other endogenous constructs

To get the f 2 values you need to run the full model first and determine the R 2 for the endogenous construct you want to evaluate. Next, eliminate one path pointing at the construct you are looking at (simply right click on a construct and delete the predictor construct), and re-run the model. The R 2 with the construct/path will be lower since the predictor construct was removed. Now enter the R 2 included for the selected construct (based on the full model) and the R 2 excluded (based on the reduced model where one path/construct has been deleted) into the formula on the previous slide.

The same procedure is followed for the q 2 but instead of entering the R 2 to get the Q 2 (excluded and included), you use blindfolding values for the full model (included) and the reduced model (construct/path deleted). All rights reserved ©. Cannot be reproduced or distributed without express written permission from Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.

7

Summary of Results – Path Coefficients, f

2

and q

2

ATTR COMP CSOR CUSA LIKE PERF QUAL Path Coefficient COMP f 2 effect size

0.0861

0.011

0.0589

0.2955

0.4297

0.005

0.076

0.144

q 2 effect size Path Coefficient

0.028

0.0057

0.004

0.5050

0.3440

0.042

0.062

CUSL f 2 effect size q 2 effect size

0.000

0.404

0.139

0.101

0.229

0.081

Example interpretation of f the 0.404 is the f 2 2 : Look under the f 2 column for CUSL. Note effect size for the predictive value of CUSA on CUSL. The 0.404 indicates that CUSA has a large effect in producing the R 2 for CUSL. In contrast, the 0.139 is the f CUSL. The 0.139 indicates that LIKE has close to a medium effect in producing the R 2 for CUSL.

2 effect size for the predictive value of LIKE on 8

Reputation Model Results – Path Coefficients –

from Sage, Prentice-Hall, SmartPLS, and session presenters.

Guidelines for assessing

ƒ

2 values: Value Effect Size 0.02

0.35

= small = medium = large 9

ATTR COMP CSOR CUSA LIKE PERF QUAL

Summary of Results – Path Coefficients, f

2

and q

2 Path Coefficient

CUSA LIKE

f 2 effect size q 2 effect size Path Coefficient f 2 effect size q 2 effect size 0.1455

0.4357

0.018

0.161

0.001

0.140

0.1671

0.1784

0.1170

0.3800

0.029

0.036

0.011

0.095

0.019

0.029

0.007

0.053

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Step 5: Blindfolding and Predictive Relevance –

Q

2 In addition to evaluating the magnitude of the R² values as a criterion of predictive accuracy, researchers should also examine the

Q² value

is an indicator of the model ’ s

predictive relevance.

– which The

Q ²

measure applies a sample re-use technique that omits part of the data matrix and uses the model estimates to predict the omitted part. Specifically, when a PLS-SEM model exhibits predictive relevance, it accurately predicts the data points of the indicators in reflective measurement models of multi-item as well as single-item endogenous constructs (the procedure does not apply to formative endogenous constructs).

For SEM models, Q² values larger than zero for a specific reflective endogenous latent variable indicate the path model ’ s predictive relevance for a particular construct. Q² values of zero or below indicate a lack of predictive relevance. As a relative measure of predictive relevance, values of 0.02, 0.15, and 0.35 indicate that an exogenous construct has a small, medium, or large predictive relevance for a selected endogenous construct.

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11

Blindfolding and Predictive Relevance –

Q

2 The

Q

² value can be calculated by using two different approaches. The

cross-validated redundancy

approach uses the path model estimates of both the structural model (scores of the antecedent constructs) and the measurement model (target endogenous constructs).

An alternative method is the

cross-validated communality

approach. This method uses only the construct scores estimated for the target endogenous construct (without including the structural model information) to predict the omitted data points.

of

Q

2 We recommend using the cross-validated redundancy as a measure since it includes the key element of the path model, the structural model, to predict eliminated data points.

When you run the blindfolding option for cross-validated redundancy, all constructs in your SEM model are shown (see next slide). You can select multiple latent variables in the dialog box, but you need to run this routine for one reflective target construct at a time – one after the other until all have been tested. Finally, this option is only used with endogenous constructs that are measured reflectively.

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12

SmartPLS Predictive Relevance – Blindfolding Redundancy vs. Communality?

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

LV 3 MV 1 MV 2 MV 3

.

Running Blindfolding to obtain Q 2 for Endogenous Construct CUSL Note that only CUSL is checked.

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14

Blindfolding Results for Endogenous Construct CUSL

.

Q 2 value for CUSL Full Base Model The result column is at the top right corner (1 – SSE/SSO). For our path model the predictive relevance Q 2 of CUSL has a value of 0.4178, which indicates the model has large predictive relevance for this construct.

When blindfolding is run for all endogenous latent constructs in the model they all have Q 2 values considerably All rights reserved ©. Cannot be reproduced or distributed without express written permission above zero, as shown on the next slide. from Sage, Prentice-Hall, SmartPLS, and session presenters.

15

Reputation Model – R 2 and Q 2 Measures

The table above shows that all Q 2 values are considerably above zero, thus providing support for the reputation model ’ s predictive relevance for the four endogenous constructs.

Computation of

q 2

The final assessment addresses the calculation of the

q

² effect sizes. The calculation of

q

2 for the CUSL construct of the reputation model is shown below. To compute the

q

² value of a selected endogenous latent variable, you need the Q 2 included and Q 2 excluded values. The Q 2 included results for all endogenous constructs from the overall model estimation are available from a previous slide. The Q 2 excluded value is obtained from a model re-estimation after deleting a specific predecessor of that endogenous latent variable. For example, the endogenous latent variable CUSL has an original Q² value of 0.418 ( Q 2 included) . If CUSA is deleted from the path model and the model is re estimated, the Q² of CUSL has a value of only 0.285 ( Q 2 excluded ). These two values are the inputs for computing the q² effect size of CUSA. on CUSL, as shown below: All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, SmartPLS, and session presenters.

17

PLS Algorithm Results Base Model with CUSA Removed

.

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18

Blindfolding Results for CUSL with full Base Model

.

Q 2 value for CUSL with full model All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, SmartPLS, and session presenters.

19

Blindfolding Results for CUSL Reduced Model with CUSA Removed

.

Q 2 value for CUSL with CUSA Removed All rights reserved ©. Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, SmartPLS, and session presenters.

20

Summary of Results – Path Coefficients, f

2

and q

2

ATTR COMP CSOR CUSA LIKE PERF QUAL Path Coefficient COMP f 2 effect size

0.0861

0.011

0.0589

0.2955

0.4297

0.005

0.076

0.144

q 2 effect size Path Coefficient

0.028

0.0057

0.004

0.5050

0.3440

0.042

0.062

CUSL f 2 effect size q 2 effect size

0.000

0.404

0.139

0.101

0.229

0.081

Example interpretation of q the 0.229 is the q 2 effect size for the predictive relevance of CUSA on CUSL. The 0.229 indicates that CUSA has a medium effect in producing the Q (predictive relevance) for CUSL. In contrast, the 0.081 is the q 2 the predictive relevance of LIKE on CUSL. The 0.081 indicates that LIKE has a small effect in producing the Q 2 2 : Look under the q for CUSL.

2 column for CUSL. Note 2 effect size for 21

Reputation Model Results – Path Coefficients –

from Sage, Prentice-Hall, SmartPLS, and session presenters.

Guidelines for assessing

q

2 values: Value Effect Size 0.02

0.35

= small = medium = large

ATTR COMP CSOR CUSA LIKE PERF QUAL

Summary of Results – Path Coefficients, f

2

and q

2 Path Coefficient

CUSA LIKE

f 2 effect size q 2 effect size Path Coefficient f 2 effect size q 2 effect size 0.1455

0.018

0.001

0.4357

0.161

0.140

Guidelines for assessing

q

2 values associated with predictive relevance (Q 2 ): Value 0.02

0.15

0.35

Effect Size = small = medium = large 0.1671

0.1784

0.1170

0.3800

0.029

0.036

0.011

0.095

0.019

0.029

0.007

0.053

23

.

.

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