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Garson, G. D. (2016). Partial Least Squares: Regression and Structural Equation Models. Asheboro, NC: Statistical Associates Publishers.

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ISBN-13: 978-1-62638-039-4
@c 2016 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.



This is a graduate-level introduction and illustrated tutorial on partial least squares (PLS). PLS may be used in the context of variance-based structural equation modeling, in contrast to the usual covariance-based structural equation modeling, or in the context of implementing regression models. PLS is largely a nonparametric approach to modeling, not assuming normal distributions in the data, often recommended when the focus of research is prediction rather than hypothesis testing, when sample size is not large, or in the presence of noisy data.

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Below is the unformatted table of contents.

Overview	8
Data	9
Key Concepts and Terms	10
Background	10
Models	13
Overview	13
PLS-regression vs. PLS-SEM models	13
Components vs. common factors	14
Components vs. summation scales	16
PLS-DA models	16
Mixed methods	16
Bootstrap estimates of significance	17
Reflective vs. formative models	17
Confirmatory vs. exploratory models	20
Inner (structural) model vs. outer (measurement) model	21
Endogenous vs. exogenous latent variables	21
Mediating variables	22
Moderating variables	23
Interaction terms	25
Partitioning direct, indirect, and total  effects	28
Variables	29
Case identifier variable	30
Measured factors and covariates	30
Modeled factors and response variables	30
Single-item measures	31
Measurement level of variables	32
Parameter estimates	33
Cross-validation and goodness-of-fit	33
PRESS and optimal number of dimensions	34
PLS-SEM in SPSS, SAS, and Stata	35
Overview	35
PLS-SEM in SmartPLS	35
Overview	35
Estimation options in SmartPLS	36
Running the PLS algorithm	37
Options	37
Data input and standardization	40
Setting the default workspace	41
Creating a PLS project and importing data	41
Validating the data settings	43
Drawing the path model	44
Reflective vs. formative models	47
Displaying/hiding the measurement model	48
Saving the model	49
Model report output	52
Checking for convergence	57
Path coefficients for the inner model	58
Direct, indirect, and total path coefficients	59
Outer model measurement loadings and weights	60
Bootstrapped significance output	62
Assessing model fit: Overview	62
Measurement fit for reflective models	63
Measurement fit for formative models	73
Goodness of fit for structural models	79
Latent variable correlations output	85
Analyzing residuals	86
Estimation with the consistent PLS (PLSc) algorithm	88
Overview	88
PLSc output	90
Estimation with PLS bootstrapping	91
Overview	91
Running the PLS bootstrapping algorithm	92
PLS bootstrap output	97
Dropping indicators	103
Estimation with consistent PLS bootstrapping	104
Overview	104
Running the PLSc bootstrapping algorithm	104
Consistent PLS bootstrap output	109
Dropping indicators	115
Estimation with blindfolding	115
Overview	115
Running the blindfolding algorithm	116
Output unique to blindfolding estimation	117
Confirmatory tetrad analysis (CTA)	122
Overview	122
The example model	123
Running confirmatory tetrad analysis	124
PLS-CTA output	125
PLS-CTA and sample size	128
Importance-performance map analysis (IPMA)	128
Overview	128
The example model	129
Running IPMA	131
Overview	133
IPMA Output	134
Finite-mixture segmentation analysis (FIMIX)	137
Unobserved heterogeneity	137
Comparing models with differing numbers of segments	139
Fit Indices	143
Entropy	147
Path coefficients	149
T-tests of differences in path coefficients	152
Labeling the segments	152
Prediction-oriented segmentation (POS)	154
Overview	154
The example model	156
Running POS	156
POS output	158
Labeling the segments	166
Multi- group Analysis (MGA)	166
Overview	166
Measurement invariance	166
The example model	167
Defining groups	168
Running MGA	172
Multi-group output	175
Testing for segment difference	180
Permutation algorithm (MICOM)	182
Overview	182
The example model	183
Running the permutation algorithm	183
Permutation algorithm output	184
Measurement invariance (MICOM) tests	185
Type I and Type II error	187
PLS regression modeling with SmartPLS	189
PLS regression: SmartPLS vs SPSS or SAS	189
PLS regression: SPSS vs. SAS	189
Example	190
Creating a simple regression model in SmartPLS	190
SmartPLS output for PLS-regression	192
Path coefficient	192
Outer loadings and weights	193
Model fit/quality criteria	194
Other output	196
PLS regression modeling with SPSS	197
Overview	197
SPSS example	197
SPSS input	199
SPSS output	202
Proportion of variance explained by latent factors	202
PRESS (predicted error sum of squares)	202
Latent component weights and loadings	203
Variable importance in the projection (VIP) for the independent variables	205
Regression parameter estimates by dependent variable	206
Charts/plots	207
Plots of latent factor weights	210
Residual and normal quantile plots	211
Saving variables	211
PLS regression modeling using SAS	212
Overview	212
SAS example	213
SAS syntax	213
SAS output	214
R-square analysis	214
Correlation loading plot	215
Variable Importance Plot	216
Response scores by predictor scores plots	217
Residuals plots	218
Parameter estimates	220
Summary	221
PLS regression modeling using Stata	221
Overview	221
Assumptions	222
Robustness	222
Parametric v. non-parametric	223
Independent observations	224
Data level	225
Unobserved homogeneity	225
Linearity	226
Outliers	226
Residuals	226
Appropriate sample size	226
Missing values	228
Model specification	229
Appropriate model fit assessment	229
Recursivity	230
Multicollinearity	230
Proper use of dummy variables	231
Standardized variables	231
Frequently Asked Questions	231
How does PLS-SEM compare to SEM using analysis of covariance structures?	231
What are higher order/hierarchical component models in PLS-SEM?	235
How does norming work?	236
What other software packages support PLS-regression?	237
How is PLS installed for SPSS?	238
What other software packages support PLS-SEM apart from SmartPLS?	239
What are the SIMPLS and PCR methods in PROC PLS in SAS?	240
Why is PLS sometimes described as a 'soft modeling' technique?	241
You said PLS could handle large numbers of independent variables, but can't OLS regression do this too?	241
Is PLS always a linear technique?	241
How is PLS related to principal components regression (PCR) and maximum redundancy analysis (MRA)?	241
What are the NIPALS and SVD algorithms?	243
How does PLS relate to two-stage least squares (2SLS)?	243
How does PLS relate to neural network analysis (NNA)?	243
Acknowledgments	244
Bibliography	245
Pagecount:	262