Partial Least Squares (PLS) is a structural equation technique, which is an iterative numerical causal modeling technique for multivariate analysis. Causal or structural modeling is a technique to simultaneously assess the reliability and validity of the measures of theoretical constructs and to estimate the relationships among these constructs. There are two different approaches to causal modeling that were considered in this research effort: covariance structure analysis as implemented in LISTREL, and as implemented in PLS. Both of these methodologies
belong to the “second generation” of multivariate analysis. These second generation techniques possess the advantages of incorporating multiple dependent constructs, explicitly recognizing error terms and integrating theory with empirical data.
PLS was chosen for the suicide bomber data analysis because the other option, LISTREL, is poorly suited to deal with small data samples and can yield non-unique or otherwise improper solutions in some cases. The main purpose of the PLS analysis is to build a linear model, Y=f(X) + Error, where Y= Question, and X=Explanations. Multiple explanations can be organized into vector-matrix relationships to identify root causes that have the strongest coupling to the identified problem of interest.
PLS is a distribution-free approach to parameter estimation that can accommodate small sample sizes by use of cross-validation. Cross validation, also known as jackknifing, is a statistical technique for estimating a model’s prediction error when the available data set is too small to divide into a training and a test set. The key feature of PLS soft modeling is the explicit estimation of each latent variable by a weighted aggregate of indicators. This method of weighted aggregation makes interpretation of the theories (latent variables) and their relation to the measurements (manifest variables) very straightforward
The conceptual core of PLS is an iterative combination of relating measures and constructs. Theory and experience on the part of the experimenter guides the original relationships between both the measures and constructs, and also between multiple constructs. PLS analysis then modifies these original relationships to estimate the weighted relationship between the constructs.
