Partial Least Squares. Regression and Structural Equation by G. David Garson

By G. David Garson

It is a graduate-level advent and illustrated educational on partial least squares (PLS). PLS can be used within the context of variance-based structural equation modeling, not like the standard covariance-based structural equation modeling, or within the context of enforcing regression types. PLS is essentially a nonparametric method of modeling, now not assuming general distributions within the info, usually prompt whilst the focal point of study is prediction instead of speculation checking out, whilst pattern dimension isn't huge, or within the presence of noisy data.

Why we predict the hot variation is important:
* Covers the much-enhanced model three of SmartPLS
* Now publication size at 262 pages (was 139)
* Covers the normal PLS set of rules and constant PLS
* Covers bootstrapped PLS, constant bootstrapped PLS, and PLS with blindfolding
* Covers confirmatory tetrad analysis
* Covers importance-performance map research (IPMA)
* Covers finite-mixture segmentation (FIMIX) and prediction-oriented segmentation (POS)
* Covers multi-group research (MGA)
* Covers importance trying out with the permutation set of rules (MICOM)

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Additional resources for Partial Least Squares. Regression and Structural Equation Models

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1. Go to the “the “Path coefficients hyperlink view” discussed above. 2. Select the hyperlink “Stop Criterion Changes” 3. Note the matrix output in the upper portion of the display. If the number of listed iterations is below the maximum (default = 300), the solution converged. In the figure below, convergence was reached in six iterations. Copyright @c 2016 by G. David Garson and Statistical Associates Publishing Page 57 OUTPUT Path coefficients for the inner model At the top of the HTML output are the path coefficients for the inner model (the arrows connecting latent variables).

In the context of PLS-SEM, factors are the latent variables which are extracted as linear (usually equally weighted) combinations of the measured (indicator) variables. For PLS-regression, which uses a factor rather than path weighting scheme, the researcher may specify how many factors to extract from the measured indicator variables. For PLS-regression, ordinarily the first 3 - 7 factors will account for 99% of the variance (five factors is the default in PLS-regression in SPSS, for example).

Both predictor and response variables will have the same number of factors. There is no one criterion for deciding how many latent variables to employ. Common alternatives are: Cross-validating the model with increasing numbers of factors, then choosing the number with minimum prediction error on the validation set. This is the most common method, where cross-validation is "leave-one-out cross-validation" discussed below, prediction error may be measured by the PRESS statistic discussed below, and models are computed for 1, 2, 3, ....

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