# Partial Least Squares – Structural Equation Modeling (PLS-SEM)

What the?!?

PLS-SEM provides the researcher an ability to analyze cause and effect relationships with latent variables.  Latent variables are variables that are ‘inferred’ and not directly measured.  More simply, if you measure a bunch of variables (e.g. “how much do you like chocolate”, or “on a scale of 1 to 5, 5 being the mostest, how much do you like chocolate over creamed corn?”), the results of those variables can be combined to form a latent variable.  Just so this post doesn’t get too stupid, let’s use an example from my dissertation, which measured the latent variables of perceived ease of use (PEOU)  and perceive use (PU), both independent variables, that were derived from observable (indicator) variables that came from a survey.  Note that predicted use (USE) is also a latent variable, and is the dependent variable that is influenced, or effected by the independent variables of PU and PEOU.

From a previous post, you know that my PhD dissertation committee informed me that PLS-SEM was the ‘traditional’ method of analyzing data derived using the technology acceptance model (TAM) as the theoretical lens.  Having used PLS-SEM, I agree it is appropriate to use with TAM (and I discovered today that the multiequation econometric model used to link customer satisfaction to customer expectations, perceived quality, etc. is perfectly suited to PLS-SEM analysis), but I find it hard to believe that PLS-SEM is a traditional method.  It hasn’t been around that long, as far as I can tell.  The beauty of PLS-SEM is that there is software that takes your raw data and with a few clicks, etc. you can create your model and analyze the data.  I used SmartPLS (available here: https://www.pls-sem.net/smartpls/) to conduct data analysis.  If you are interested in what PLS-SEM does and how it works, I recommend you first search for PLS-SEM and read about it.  I used the PLS-SEM primer (Hair Jr., J. F., Hult, G. T. M., Ringle, C., & Sarstedt, M. (2014). A primer on partial least squares structural equation modeling (pls-sem): SAGE Publications, Incorporated.) as my primer on the subject (mission accomplished!), guideline for data analysis, etc.  Following the processes from start to finish, as detailed in this book, I was able to not only write about my data analysis processes, but also describe if that data was valid (or was in conformance, etc.).

Note in the figure above that there is a structural model, a formative measurement model, and a reflective measurement model.  The structural model is depicted showing hypothesized relationships of the latent variables, and the formative and reflective measurement models are shown along with their associated indicator variables.  In my meager mind, I figured that anything that was formative came before the final results, and anything that was reflective came afterwards.  From my dissertation, I noted the following:

Within PLS-SEM, the measurement models represent the relationships between the latent variables and the observed data, or the indicator variables. The reflective measurement model depicts how the dependent variable USE is derived from the reflective measures. Similarly, the formative measurement model depicts how the independent variables of PU and PEOU are derived from their associated formative measures.