## Tuesday, November 24, 2015

### Nonlinear analyses versus data segmentation in PLS-SEM

Those who conduct PLS-SEM analyses employing software other than WarpPLS and data segmentation approaches such as FIMIX-PLS may want to also conduct their analyses with WarpPLS, using a nonlinear algorithm, and compare the results against those obtained with data segmentation.

Data segmentation assumes the presence of underlying heterogeneity, which is also assumed (and accounted for) in a nonlinear analysis. The differences are that a nonlinear analysis assumes that the heterogeneity is somewhat uniform (a more reasonable assumption than that of “fragmented” heterogeneity), and that the heterogeneity can be described by nonlinear functions.

In WarpPLS users can define a main general type of nonlinear function for each structural link in their models.

Additionally, the “View focused relationship graphs with segments” options of WarpPLS allow users to view graphs that focus on the best-fitting line or curve, that exclude data points to provide the effect of zooming in on the best-fitting line or curve area, and that show curves as linear segments. The segments are shown with their respective beta coefficients and with or without P values (see figure below).

The options available are: “View focused multivariate relationship graph with segments (standardized scales)”, “View focused multivariate relationship graph with segments (standardized scales, P values)”, “View focused multivariate relationship graph with segments (unstandardized scales)”, “View focused bivariate relationship graph with segments (standardized scales)”, “View focused bivariate relationship graph with segments (standardized scales, P values)”, and “View focused bivariate relationship graph with segments (unstandardized scales)”.

The number of segments shown in the graphs above depends on the absolute effect segmentation delta chosen by the user using the “Settings” menu option. This absolute effect segmentation delta is the change (or delta) threshold in the first derivative of the nonlinear function depicting the relationship before a new segment is started.

For example, a delta of 0.1 means that in each segment the first derivative of the nonlinear function depicting the relationship does not vary more than 0.1. Since the first derivative does not change in linear relationships, segmentation only occurs in nonlinear relationships.

This graph segmentation option allows for the identification of unobserved heterogeneity without a corresponding reduction in sample size, providing a convenient alternative in this respect to data segmentation approaches such as FIMIX-PLS.

See the latest version of the User Manual for more details. The User Manual is available from the web site below.

http://warppls.com/

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