(Note: This post refers to version 1.0 - 2.0 of WarpPLS. See this YouTube video on how to view and change settings for version 3.0.)

The view or change settings window (see figure below, click on it to enlarge) allows you to select an algorithm for the SEM analysis, select a resampling method, and select the number of resamples used, if the resampling method selected was bootstrapping. The analysis algorithms available are Warp3 PLS Regression, Warp2 PLS Regression, PLS Regression, and Robust Path Analysis.

The view or change settings window (see figure below, click on it to enlarge) allows you to select an algorithm for the SEM analysis, select a resampling method, and select the number of resamples used, if the resampling method selected was bootstrapping. The analysis algorithms available are Warp3 PLS Regression, Warp2 PLS Regression, PLS Regression, and Robust Path Analysis.

Many relationships in nature, including relationships involving behavioral variables, are nonlinear and follow a pattern known as U-curve (or inverted U-curve). In this pattern a variable affects another in a way that leads to a maximum or minimum value, where the effect is either maximized or minimized, respectively. This type of relationship is also referred to as a J-curve pattern; a term that is more commonly used in economics and the health sciences.

The Warp2 PLS Regression algorithm tries to identify a U-curve relationship between latent variables, and, if that relationship exists, the algorithm transforms (or “warps”) the scores of the predictor latent variables so as to better reflect the U-curve relationship in the estimated path coefficients in the model. The Warp3 PLS Regression algorithm, the default algorithm used by the software, tries to identify a relationship defined by a function whose first derivative is a U-curve. This type of relationship follows a pattern that is more similar to an S-curve (or a somewhat distorted S-curve), and can be seen as a combination of two connected U-curves, one of which is inverted.

The PLS Regression algorithm does not perform any warping of relationships. It is essentially a standard PLS regression algorithm, whereby indicators’ weights, loadings and factor scores (a.k.a. latent variable scores) are calculated based on a least squares minimization sub-algorithm, after which path coefficients are estimated using a robust path analysis algorithm. A key criterion for the calculation of the weights, observed in virtually all PLS-based algorithms, is that the regression equation expressing the relationship between the indicators and the factor scores has an error term that equals zero. In other words, the factor scores are calculated as exact linear combinations of their indicators. PLS regression is the underlying weight calculation algorithm used in both Warp3 and Warp2 PLS Regression. The warping takes place during the estimation of path coefficients, and after the estimation of all weights and loadings in the model. The weights and loadings of a model with latent variables make up what is often referred to as outer model, whereas the path coefficients among latent variables make up what is often called the inner model.

Finally, the Robust Path Analysis algorithm is a simplified algorithm in which factor scores are calculated by averaging all of the indicators associated with a latent variable; that is, in this algorithm weights are not estimated through PLS regression. This algorithm is called “Robust” Path Analysis, because, as with most robust statistics methods, the P values are calculated through resampling. If all latent variables are measured with single indicators, the Robust Path Analysis and the PLS Regression algorithms will yield identical results.

One of two resampling methods may be selected: bootstrapping or jackknifing. Bootstrapping, the software’s default, is a resampling algorithm that creates a number of resamples (a number that can be selected by the user), by a method known as “resampling with replacement”. This means that each resample contains a random arrangement of the rows of the original dataset, where some rows may be repeated. (The commonly used analogy of a deck of cards being reshuffled, leading to many resample decks, is a good one, but not entirely correct because in bootstrapping the same card may appear more than once in each of the resample decks.) Jacknifing, on the other hand, creates a number of resamples that equals the original sample size, and each resample has one row removed. That is, the sample size of each resample is the original sample size minus 1. Thus, the choice of number of resamples has no effect on jackknifing, and is only relevant in the context of bootstrapping.

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