A new WarpPLS YouTube video is available:

http://www.youtube.com/watch?v=G49aIm-14kU

This video shows how problems with indicators that load poorly on their latent variables, and that have high cross-loadings, can be solved in a structural equation modeling (SEM) analysis using the software WarpPLS.

Enjoy!

## Tuesday, December 29, 2009

## Thursday, December 24, 2009

### Warped paths become significant in WarpPLS: YouTube video

Yet another new YouTube video is available for WarpPLS:

This video shows how path coefficients sometimes go up, and P values become significant, when warping takes place in a structural equation modeling (SEM) analysis using the software WarpPLS.

Since path coefficients are typically associated with hypotheses, which are supported if the paths are found to be significant, this will likely be music to many researchers' ears.

However, it is important to make two important points regarding this effect:

1. Path coefficients are not artificially inflated. They increase simply because the software is taking the nonlinear associations between latent variables into account when estimating path coefficients. Much like a researcher would apply a log(X) transformation to a predictor, before an ordinary regression analysis, if he or she knew that the predictor's relationship with a criterion variable Y was of the type Y=log(X).

2. Path coefficients do not always increase. Due to the nature of standardized partial regression coefficient calculation (the path coefficients, or betas, are standardized partial regression coefficients), when several predictor latent variables (LVs) point a one criterion LV, if one of the predictor LVs increases, some of the others predictor LVs may decrease as a result. In a sense, the predictor LVs "compete" for pieces of the space of variance explained for the criterion LV; if the predictor LVs are correlated, they tend "steal" variance space from each other (so to speak).

Labels:
APC,
ARS,
AVIF,
nonlinear relationship,
YouTube video

### View nonlinear relationships in WarpPLS: YouTube video

A new Youtube video is available for WarpPLS:

http://www.youtube.com/watch?v=lHrTxWmM43A

This video shows how one can view nonlinear and linear relationships estimated through a structural equation modeling (SEM) analysis using the software WarpPLS.

The video also highlights one fact that makes software like WarpPLS particularly useful - most relationships in nature are nonlinear. This includes relationships in biology, business, sociology, physics etc.

As you will see in this video, the software shows a table with the types of relationships, warped or linear, between latent variables that are linked in the model. The term “warped” is used for relationships that are clearly nonlinear, and the term “linear” for linear or quasi-linear relationships. Quasi-linear relationships are slightly nonlinear relationships, which look linear upon visual inspection on plots of the regression curves that best approximate the relationships.

Plots with the points as well as the regression curves that best approximate the relationships can be viewed by clicking on a cell containing a relationship type description. These cells are the same as those that contain path coefficients, in the path coefficients table.

The plots of relationships between pairs of latent variables provide a much more nuanced view of how each pair of latent variables is related. However, caution must be taken in the interpretation of these plots, especially when the distribution of data points is very uneven.

An extreme example would be a warped plot in which all of the data points would be concentrated on the right part of the plot, with only one data point on the far left part of the plot. That single data point, called an outlier, would influence the shape of the nonlinear relationship. In these cases, the researcher must decide whether the outlier is “good” data that should be allowed to shape the relationship, or is simply “bad” data resulting from a data collection error.

http://www.youtube.com/watch?v=lHrTxWmM43A

This video shows how one can view nonlinear and linear relationships estimated through a structural equation modeling (SEM) analysis using the software WarpPLS.

The video also highlights one fact that makes software like WarpPLS particularly useful - most relationships in nature are nonlinear. This includes relationships in biology, business, sociology, physics etc.

As you will see in this video, the software shows a table with the types of relationships, warped or linear, between latent variables that are linked in the model. The term “warped” is used for relationships that are clearly nonlinear, and the term “linear” for linear or quasi-linear relationships. Quasi-linear relationships are slightly nonlinear relationships, which look linear upon visual inspection on plots of the regression curves that best approximate the relationships.

Plots with the points as well as the regression curves that best approximate the relationships can be viewed by clicking on a cell containing a relationship type description. These cells are the same as those that contain path coefficients, in the path coefficients table.

The plots of relationships between pairs of latent variables provide a much more nuanced view of how each pair of latent variables is related. However, caution must be taken in the interpretation of these plots, especially when the distribution of data points is very uneven.

An extreme example would be a warped plot in which all of the data points would be concentrated on the right part of the plot, with only one data point on the far left part of the plot. That single data point, called an outlier, would influence the shape of the nonlinear relationship. In these cases, the researcher must decide whether the outlier is “good” data that should be allowed to shape the relationship, or is simply “bad” data resulting from a data collection error.

## Wednesday, December 23, 2009

### Change resampling method in WarpPLS: YouTube video

A new Youtube video is available for WarpPLS:

http://www.youtube.com/watch?v=Hf-t70r7NKo

This video shows how one can conduct an SEM analysis using WarpPLS, save that analysis with a different project name, change the resampling method (from bootstrapping to jackknifing), and then redo the analysis.

At the end, the user has two project files, one with all of the P values calculated through bootstrapping, and the other with all of the P values calculated through jackknifing.

As noted in the WarpPLS User Manual, bootstrapping and jackknifing provide a good complement to each other in the context of warped PLS-based SEM.

Thus, some users may want to run two analyses of the same model, one with each resampling method, and use the results that are associated with the most stable resample path coefficients. These will typically be the ones with the lowest P values, since P values go up as the standard errors in the resample set go up. High resample standard errors are associated with instability. The instability itself often comes from outliers, which may drastically change the shape of a warped relationship in each resample.

Well, moving from statspeach to plain English, there are good theoretical reasons to recommend that users choose the most stable results (i.e., with the lowest P values) as the results that they will use in research reports, whether they are obtained with bootstrapping or jackknifing. The choice may be made individually, for each path coefficient. This should be disclosed to the readers of the report; a sentence like this would probably be enough: "Both bootstrapping or jackknifing were used in the analyses. The results reported here are those associated with the most stable resample estimates."

http://www.youtube.com/watch?v=Hf-t70r7NKo

This video shows how one can conduct an SEM analysis using WarpPLS, save that analysis with a different project name, change the resampling method (from bootstrapping to jackknifing), and then redo the analysis.

At the end, the user has two project files, one with all of the P values calculated through bootstrapping, and the other with all of the P values calculated through jackknifing.

As noted in the WarpPLS User Manual, bootstrapping and jackknifing provide a good complement to each other in the context of warped PLS-based SEM.

Thus, some users may want to run two analyses of the same model, one with each resampling method, and use the results that are associated with the most stable resample path coefficients. These will typically be the ones with the lowest P values, since P values go up as the standard errors in the resample set go up. High resample standard errors are associated with instability. The instability itself often comes from outliers, which may drastically change the shape of a warped relationship in each resample.

Well, moving from statspeach to plain English, there are good theoretical reasons to recommend that users choose the most stable results (i.e., with the lowest P values) as the results that they will use in research reports, whether they are obtained with bootstrapping or jackknifing. The choice may be made individually, for each path coefficient. This should be disclosed to the readers of the report; a sentence like this would probably be enough: "Both bootstrapping or jackknifing were used in the analyses. The results reported here are those associated with the most stable resample estimates."

Labels:
bootstrapping,
jackknifing,
resampling,
YouTube video

### Windows Vista issue with WarpPLS 1.0: mclmcrrt710.dll was not found

(Note: This post refers to version 1.0 of WarpPLS only.)

Some Windows Vista users have reported a problem installing and running WarpPLS 1.0. The error message looks like this:

"WarpPLS_1_0.exe - Unable To Locate Component: This application has failed to start because mclmcrrt710.dll was not found. Re-installing the application may fix this problem."

This seems to be a problem of incompatibility between the MATLAB Compiler Runtime and Windows Vista. The problem appears to occur in some computer configurations, but not all of them.

The solution below has worked so far for all users that contacted me with this problem:

- Check your "Program Files" directory, and make sure that you have this folder there: C:\Program Files\MATLAB\MATLAB Compiler Runtime\v710\runtime\win32.

- If yes (usually the case when this problem occurs), go to the Windows command prompt, and enter this:

set PATH=C:\Program Files\MATLAB\MATLAB Compiler Runtime\v710\runtime\win32;%PATH%

(See screen snapshot below).

- Then restart the computer, and try to run WarpPLS again.

- If only restarting the computer does not work; reinstall WarpPLS, and then try to run WarpPLS again.

Some Windows Vista users have reported a problem installing and running WarpPLS 1.0. The error message looks like this:

"WarpPLS_1_0.exe - Unable To Locate Component: This application has failed to start because mclmcrrt710.dll was not found. Re-installing the application may fix this problem."

This seems to be a problem of incompatibility between the MATLAB Compiler Runtime and Windows Vista. The problem appears to occur in some computer configurations, but not all of them.

The solution below has worked so far for all users that contacted me with this problem:

- Check your "Program Files" directory, and make sure that you have this folder there: C:\Program Files\MATLAB\MATLAB Compiler Runtime\v710\runtime\win32.

- If yes (usually the case when this problem occurs), go to the Windows command prompt, and enter this:

set PATH=C:\Program Files\MATLAB\MATLAB Compiler Runtime\v710\runtime\win32;%PATH%

(See screen snapshot below).

- Then restart the computer, and try to run WarpPLS again.

- If only restarting the computer does not work; reinstall WarpPLS, and then try to run WarpPLS again.

## Sunday, December 6, 2009

### Structural equation modeling made easy with WarpPLS: YouTube video

Conducting a basic structural equation modeling (SEM) analysis using WarpPLS is relatively easy. The software takes the user through 5 steps, from project file creation to model building (using a graphical user interface) and viewing the results of the analysis. Take a look at the Youtube video below.

Choose the high quality (HQ) option for viewing the video clip above, if it is available (usually at the bottom of the video screen), and expand it to the full screen mode.

As you'll see at the end of the video, the project file is quite small, and it contains everything that is needed for the analysis. The file can be copied into a separate file, which the user can then open and change, by modifying the model for example, to conduct a different analysis.

Choose the high quality (HQ) option for viewing the video clip above, if it is available (usually at the bottom of the video screen), and expand it to the full screen mode.

As you'll see at the end of the video, the project file is quite small, and it contains everything that is needed for the analysis. The file can be copied into a separate file, which the user can then open and change, by modifying the model for example, to conduct a different analysis.

## Friday, December 4, 2009

### Welcome to the WarpPLS blog!

Welcome to the WarpPLS blog! WarpPLS is a powerful structural equation modeling (SEM) software. It is commercialized by ScriptWarp Systems: www.scriptwarp.com.

Among other things, WarpPLS identifies nonlinear (or “warped”, hence the name of the software) relationships among latent variables and corrects the values of path coefficients accordingly. WarpPLS is arguably the first SEM software to do this.

Since most relationships between numeric variables are nonlinear, one could argue that WarpPLS finds the "real" relationships between latent variables in an SEM analysis. Typically path coefficients are increased, in some cases going from non-significant to significant at the P lower than 1 percent level.

The underlying algorithm employed by WarpPLS as its outer model default is partial least squares (PLS) regression, whose main characteristic is its ability to minimize multicollinearity among latent variables (even in the presence of overlapping manifest variables, or indicators). Other PLS-based outer model algorithms are also available, including PLS modes A and B.

Additionally, WarpPLS offers the following features, which are largely absent from most, if not all, PLS-based SEM software packages available today:

- It estimates P values for path coefficients automatically, instead of providing only standard errors or T values, and leaving the user to figure out what the corresponding P values are.
- It estimates several model fit indices, which have been designed to be meaningful in the context of PLS-based SEM analyses.
- It automatically builds the indicators’ product structure underlying moderating relationships, and goes a little further. It shows those moderating relationships, related path coefficients, and related P values in a model graph as they should be shown – that is, as links between latent variables and direct links. The latter connect pairs of latent variables, while the former connect latent variables and direct links between pairs of latent variables.
- It allows users to view scatter plots of each of the relationships among latent variables (when they are connected through arrows in the model), together with the curves that best approximate those relationships, and save those plots as .jpg files for inclusion in research reports.
- It provides a variety of graphs from which users can choose, including zoomed 2D graphs and 3D graphs; the latter for moderating effects. Both multivariate and bivariate relationship graphs are provided, for linear and nonlinear relationships, using standardized and unstandardized scales.
- It allows users to segment curves based on increments in the first derivative of the predictor latent variables on each of their criteria latent variables. This provides an alternative to data segmentation approaches such as FIMIX-PLS, without any reduction in sample.
- It calculates variance inflation factor (VIF) coefficients for latent variable predictors associated with each latent variable criterion. This allows users to check whether some predictors should be removed due to multicolinearity (this feature is particularly useful with latent variables that are measured based on only 1 or a few indicators).
- It calculates effect size coefficients analogous to Cohen’s
*f*-squared coefficients for all paths. These are calculated as the absolute values of the individual contributions of the corresponding predictor latent variables to the R-square coefficients of the criterion latent variable in each latent variable block. - It calculates indirect effects for paths with 2, 3 etc. segments; as well as total effects. The corresponding P values, standard errors, and effect sizes are also calculated. Indirect and total effects can be critical in the evaluation of downstream effects of latent variables that are mediated by other latent variables, especially in complex models with multiple mediating effects along concurrent paths.
- It calculates a variety of causality assessment coefficients, all of which are reported. These can be used in the assessment of the plausibility and direction of hypothesized cause-effect relationships.

Labels:
P value,
path coefficient,
variance inflation factor

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