Partial Least Squares-Structural Equation Modeling

 Partial Least Squares-Structural Equation Modeling (PLS-SEM):

Statistical  analysis  has  been  an  essential  tool  for  social  science researchers  for  more  than  a  century.

Researchers initially relied on univariate and bivariate analysis to understand data and relationships. To comprehend more complex relationships associ-ated with current research directions in the social sciences, it is increasingly necessary to apply more sophisticated multivariate data analysis methods.

Multivariate analysis  involves the application of statistical methods that simultaneously analyze multiple variables. The vari-ables typically represent measurements associated with individuals, companies, events, activities, situations, and so forth. The measure-ments are often obtained from surveys or observations that are used to collect primary data, but they may also be obtained from databases consisting of secondary data. Exhibit 1.1 displays some of the major types of statistical methods associated with multivari-ate data analysis.

Why would a researcher want to use Structural Equation Modeling (SEM) and have to deal with its own language and, as you shall soon see, some fairly stringent statistical assumptions?

• SEM has a number of attractive virtues:
• Assumptions underlying the statistical analyses are clear and testable, giving the investigator full control and potentially furthering understanding of the analyses.
• Graphical interface software boosts creativity and facilitates rapid model debugging (a feature limited to selected SEM software packages).
• SEM programs provide overall tests of model fit and individual parameter estimate tests simultaneously.
• Regression coefficients, means, and variances may be compared simultaneously, even across multiple between-subjects groups.
• Measurement and confirmatory factor analysis models can be used to purge errors, making estimated relationships among latent variables less contaminated by measurement error.
• Ability to fit non-standard models, including flexible handling of longitudinal data, databases with autocorrelated error structures (time series analysis), and databases with non-normally distributed variables and incomplete data. This last feature of SEM is its most attractive quality.
• SEM provides a unifying framework under which numerous linear models may be fit using flexible, powerful software.
• SEM users represent relationships among observed and unobserved variables using path diagrams.

SEM users represent relationships among observed and unobserved variables using path diagrams. SEM, as the second-generation of statistical techniques, enables researchers to simultaneously examine a series of interrelated dependence relationships between one or more independent constructs and one or more dependent constructs represented by several variables (eg., scales) to examine a comprehensive model. On the other word, SEM techniques allow the simultaneous examination of both theory (structural model) and measures (measurement model).

Manifest or observed variables are directly measured by researchers, while latent or unobserved variables are not directly measured but are inferred by the relationships or correlations among measured variables in the analysis. This statistical estimation is accomplished in much the same way that an exploratory factor analysis infers the presence of latent factors from shared variance among observed variables.

SEM is a merger of two powerful approaches  for estimating the relationships between variables:

• Covariance-based SEM (CB-SEM)-(J?reskog,1978 & 1982)

• Partial least squares (PLS-SEM)-(L?hmoller; Wold, 1982)

Following figure depicts the most important packages which is used by researchers so far.

Partial least squares (PLS-SEM)

The PLS-SEM method has recently gained increasing attention. The basic PLS design was completed for the first time in 1966 by Herman Wold for the use in multivariate analysis, and subsequently extended for its application in the Structural Equation Modeling (SEM) in 1975 by Wold himself. and later was expanded by Lohmoller (1987, 1989) for the computational aspects (the LVPLS software) and for theoretical developments. Afterward Chin (1998, 2001) as well as Chin and Newsted (1999) were developed software with graphical interface (PLS-Graph) which has  improved validation techniques. In 2005, Professor Christian Ringle developed a new software (SmartPLS) with an easy to use and intuitive graphical user interface. 

A PLS path model consists of two elements:

• Measurement model or outer model (Outer Model), which describe the relationships between the latent variables and their measures (their indicators).

• Structural model or inner model (Inner Model), which describes the relationships between the latent variables.

Therefore, evaluating PLS-SEM results involves completing two stages as it is mentioned.

The measurement models display the relationships between the constructs and the indicator variables (rectangles). The structural model also displays the relationships (paths) between the constructs.

Measurement theory specifies how the latent variables (constructs) are measured. There are two different ways to measure unobservable variables.

• Reflective measurement
• Formative measurement

Formative indicators are assumed to be error free (Diamantopoulos, 2006; Edwards & Bagozzi, 2000).

Reflective measures have an error term associated with each indicator, which is not the case with formative measures.

Reflective measurement approach aims at maximizing the overlap between interchangeable indicators.

Formative measurement approach tries to fully cover the construct domain by the different formative indicators, which should have small overlap.

Evaluating PLS-SEM results involves completing two stages. Stage 1 examines the measurement models, with the analysis varying depending upon whether the model includes reflective measures (Stage 1.1), formative measures (Stage 1.2) or both. If the measurement model evaluation provides satisfactory results, the researcher moves on to Stage 2, which involves evaluating the structural model.

PLS-SEM Justification:

• If the primary objective of applying structural modeling is prediction and explanation of target constructs.

• If PLS-SEM estimates coefficients (i.e., path model relationships) that maximize the R-squared values of the (target) endogenous constructs.

• Small sample sizes

• Complex models

• No assumptions about the underlying data (Normality assumptions)

• Support reflective and formative measurement models as well as single item construct.

PLS can be used to investigate models at a higher level of abstraction (Lohm?ller, 1989). It is often chosen due to its’ ability to estimate complex models (Chin, 1998).

Hierarchical component models are another stream of methodological research on PLS-SEM deals with complex constructs that are operationalized at higher levels of abstraction. This modeling approach leads to more theoretical parsimony, reduces model complexity and may avert confounding effects in multidimensional model structures, such as multicolinearity.