You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: inst/help/PLSSEM.md
+43-19Lines changed: 43 additions & 19 deletions
Original file line number
Diff line number
Diff line change
@@ -4,39 +4,61 @@ This document explains how to perform Partial Least Squares Structural Equation
4
4
5
5
## 1. Model Setup
6
6
---
7
-
In the **Model** section, you can specify the structural model by selecting the appropriate grouping variable and setting the syntax for the model.
7
+
In the **Model** section, you can specify the structural equation model using lavaan syntax. The following operators can be used: =~ to specify a latent variable
8
+
measured by a set of indicators; <~ to specify a composite/emergent variable that is made up of a set of indicators; and ~ to specify the structural model, i.e., the relationships
9
+
between the latent variables and the composites. In specifying the relationships between the latent variables and the composites,
10
+
they must not be isolated in the structural model. In addition, no indicator may be connected to more than one latent variable/composite.
11
+
Furthermore, the structural model may not include any observed variables, i.e., to include observed variables in the structural model they must be specified as
12
+
a single-indicator construct. Finally, a grouping variable can be selected. In this case, the model is estimated separately for each group.
8
13
9
14
-**Grouping Variable**: You can select the grouping variable for multi-group analysis. The grouping variable is optional and can be left empty if not required.
10
15
11
16
## 2. Estimation Options
12
17
---
13
18
In the **Estimation** section, the following options are available:
14
19
15
-
-**Consistent Partial Least Squares**: Enables the option to use consistent PLS-SEM, which provides consistency in estimations for reflective constructs.
20
+
-**Consistent Partial Least Squares**: Enables the option to use consistent partial least squares (PLSc), which, in contrast to traditional PLS, produces consistent estimates for latent variable models (=~). In this case, Mode A weights are transformed to obtain consistent factor loadings.
21
+
In addition, the correlations between latent variables and other variables of the structural model are corrected for attenuation before they are used to estimate the parameters of the structural model.
16
22
17
-
-**Inner Weighting Scheme**: Choose from the following options to calculate inner weights:
18
-
- Path
19
-
- Centroid
20
-
- Factorial
23
+
-**Inner Weighting Scheme**: Choose from the following options to calculate inner weights used in the PLS algorithm:
24
+
- Path weighting scheme
25
+
- Centroid weighting scheme
26
+
- Factorial weighting scheme
21
27
22
-
-**Bias-Corrected Bootstrap**: Activate this option for bias-corrected bootstrapping, which refines the confidence intervals for the estimates.
28
+
In case of centroid and factorial inner weighting schemes, the structural model can be ignored in the calculation of the inner weights. In this case not only the adjacent variables are considered but also all other variables of the structural model.
23
29
24
-
-**Bootstrap Resampling**: You can adjust the number of bootstrap samples for more precise interval estimations. The default value is set to 5,000.
30
+
-**Convergence criterion**: Choose from the following options to determine the convergence criterion in the PLS algorithm:
31
+
- Absolute difference between the weights from the current and previous iteration
32
+
- Squared difference between the weights from the current and previous iteration
33
+
- Relative difference between the weights from the current and previous iteration
25
34
26
-
-**Missing Data Handling**: Options for managing missing data, including pairwise or listwise deletion, are available.
35
+
-**Tolerance**: Specify the tolerance level for the convergence criterion.
36
+
37
+
-**Error calculation method**: Choose from the following options to calculate the standard errors and confidence intervals of the parameter estimates:
38
+
- None
39
+
- Robust: Use one of the following resample techniques:
40
+
- Bootstrap
41
+
- Jackknife
42
+
43
+
**Samples**: The number of bootstrap runs can be specified.
44
+
45
+
**Repeatabilty**: A seed can be set, to make the analysis reproducible.
46
+
27
47
28
48
## 3. Output Options
29
49
---
30
-
The **Output** section allows you to customize the types of output you want to generate:
50
+
The **Output** section includes options to customize the output you want to generate:
31
51
32
-
-**Path Coefficients**: Display the estimated path coefficients.
33
-
-**Weights and Loadings**: Shows both the indicator weights and loadings, offering insights into how well the indicators measure their corresponding latent variables.
34
-
-**Goodness-of-Fit Measures**: Presents different goodness-of-fit measures like SRMR or NFI.
35
-
-**Reliability Measures**: Enables output of reliability measures such as Cronbach's alpha or composite reliability for the constructs.
52
+
-**R-squared**: Enables output of the coefficients of determination for the dependent constructs.
53
+
-**Additional fit measures**: Enables output of fit measures known from classical SEM are reported such as the SRMR and NFI. Note, these fit measures are calculated based on the PLS estimates (Schuberth et al., 2023)
54
+
-**Mardia's coefficient**:
55
+
-**Reliability measures**: Enables output of reliability measures (Cronbach's alpha, composite reliability, and Dijkstra-Henseler's rho_A) for the latent variables.
56
+
-**Add construct scores to data**: Enable adding the PLS construct scores to the dataset.
57
+
-**Observed indicator correlations**: Enable output of the indicator correlation matrix.
58
+
-**Implied indicator correlations**: Enable output of the model-implied indicator correlation matrix
59
+
-**Observed construct correlations**: Enable output of the construct correlation matrix.
60
+
-**Implied construct correlations**: Enable output of the model-implied construct correlation matrix.
36
61
37
-
Additional correlation measures include:
38
-
-**Observed and Implied Indicator Correlations**
39
-
-**Observed and Implied Construct Correlations**
40
62
41
63
You can also add **construct scores** to the dataset for further analysis.
42
64
@@ -99,11 +121,13 @@ These benchmarks help in evaluating how well your PLS-SEM model predicts the end
- Benitez, J. Henseler, J., Castillo, A., & Schuberth, F. (2020). How to perform and report an impactful analysis using partial least squares: Guidelines for confirmatory and explanatory IS research. *Information & Management, 2*(57), 103-168. doi: 10.1016/j.im.2019.05.003.
104
-
- Henseler, J. (2021). *Composite-Based Structural Equation Modeling: Analyzing Latent and Emergent Variables.* New York, Guilford Press.
125
+
-Dijkstra, T. K., & Henseler, J. (2015). Consistent and asymptotically normal PLS estimators for linear structural equations. *Computational Statistics & Data Analysis 81*, 10–23. doi: 10.1016/j.csda.2014.07.008
105
126
- Evermann, J., & Rönkkö, M. (2021). Recent developments in PLS. *Communications of the Association for Information Systems, 44.* doi: 10.17705/1CAIS.044XX
127
+
- Henseler, J. (2021). *Composite-Based Structural Equation Modeling: Analyzing Latent and Emergent Variables.* New York, Guilford Press.
106
128
- Hair, J.F., Sarstedt, M., Ringle, C.M., & Mena, J.A. (2012). An assessment of the use of partial least squares structural equation modeling in marketing research. *Journal of the Academy of Marketing Science 40*, 414–433. doi: 10.1007/s11747-011-0261-6
- Schuberth, F., Rademaker, M. E., & Henseler, J. (2023). Assessing the overall fit of composite models estimated by partial least squares path modeling. *European Journal of Marketing 57*(6), 1678–1702. doi: 10.1108/EJM-08-2020-0586
0 commit comments