Researchers have long been aware of the mathematics of factor indeterminacy. Yet, while occasionally discussed, the phenomenon is mostly ignored. In metrology, the measurement discipline of the physical sciences, uncertainty—distinct from both random error (but encompassing it) and systematic error—is a crucial characteristic of any measurement. This research argues that factor indeterminacy is uncertainty. Factor indeterminacy fundamentally threatens the validity of psychometric measurement, because it blurs the linkage between a common factor and the conceptual variable that the factor represents. Acknowledging and quantifying factor indeterminacy is important for progress in reducing this component of uncertainty in measurement, and thus improving psychological measurement over time. Based on our elaborations, we offer a range of recommendations toward achieving this goal.

http://jasemjournal.com/journal-of-applied-structural-equation-modeling-volume-2-issue-2-june-2018/jasem_22_becker-et-al-2018/ 

When estimating moderating effects in partial least squares structural equation modeling (PLS-SEM), researchers can choose from a variety of approaches to model the influence of a moderator on a relationship between two constructs by generating different interaction terms. While prior research has evaluated the efficacy of these approaches in the context of PLS-SEM, the impact of different data treatment options on their performance in the context of standard PLS-SEM and consistent PLS-SEM (PLSc-SEM) is as yet unexplored. Our simulation study addresses these limitations and explores if the choice of approach and data treatment option has a pronounced impact on the methods’ parameter recovery. An empirical application substantiates these findings. Based on our results, we offer recommendations for researchers wishing to estimate moderating effects by means of PLS-SEM and PLSc-SEM.

http://dx.doi.org/10.1016/j.emj.2016.06.009

Applications of partial least squares (PLS) path modeling usually focus on survey responses in management, social science, and market research studies, with researchers using their collected samples to estimate population parameters. For this purpose, the sample must represent the population. However, population members are often not equally likely to be included in the sample, which indicates that sampling units have different probabilities of being selected. Hence, sampling (post-stratification) weights should be used to obtain consistent estimates when estimating population parameters. We discuss alterations to the basic PLS path modeling algorithm to consider sampling weights in order to achieve better average population estimates in situations where researchers have a set of appropriate weights. We illustrate the effectiveness and usefulness of the approach with simulations and an empirical example of a job attitude model, using data from Ireland.

doi:10.1016/j.jbusres.2016.04.009

Uncovering unobserved heterogeneity is a requirement to obtain valid results when using structural equation modeling (SEM). Conventional segmentation methods usually fail in an SEM context because they account for the indicator data, but not for the latent variables and their relationships in the structural model. This research introduces a new segmentation approach to variance-based SEM using partial least squares path modeling (PLS). The iterative reweighted regressions segmentation method for PLS (PLS-IRRS) effectively identifies and treats unobserved heterogeneity in data sets. Compared to existing alternatives, PLS-IRRS is multiple times faster while delivering results of the same quality. Researchers should therefore routinely use PLS-IRRS to address the critical issue of unobserved heterogeneity in PLS.

doi:10.​1007/​s11002-014-9299-9

Mixture regression models are an important method for uncovering unobserved heterogeneity. A fundamental challenge in their application relates to the identification of the appropriate number of segments to retain from the data. Prior research has provided several simulation studies that compare the performance of different segment retention criteria. Although collinearity between the predictor variables is a common phenomenon in regression models, its effect on the performance of these criteria has not been analyzed thus far. We address this gap in research by examining the performance of segment retention criteria in mixture regression models characterized by systematically increased collinearity levels. The results have fundamental implications and provide guidance for using mixture regression models in empirical (marketing) studies.

http://search.proquest.com/docview/1650149581

Some retailers use their chain names to identify their private labels. We find that chain labeling increases the likelihood that consumers correctly recognize a private label as belonging to a specific retailer, and that on average, chain labeling improves consumers' attitudes toward private labels. We also identify two boundary conditions for this effect: chain labeling helps for standard, but not for economy private labels, and it improves consumers' attitudes toward private labels in categories with low brand relevance. These results have important implications for managers on whether and when to use chain labeling for their private labels.

doi:10.1287/isre.2014.0543

Aguirre-Urreta and Marakas [Aguirre-Urreta MI, Marakas GM (2014) Research note—Partial least squares and models with formatively specified endogenous constructs: A cautionary note. Inform. Systems Res. 25(4):761–778] aim to evaluate the performance of partial least squares (PLS) path modeling when estimating models with formative endogenous constructs, but their ability to reach valid conclusions is compromised by three major flaws in their research design. First, their population data generation model does not represent “formative measurement” as researchers generally understand that term. Second, their design involves a PLS path model that is misspecified with respect to their population model. Third, although their aim is to estimate a composite-based PLS path model, their design uses simulation data generated via a factor analytic procedure. In consequence of these flaws, Aguirre-Urreta and Marakas' (2014) study does not support valid inference about the behavior of PLS path modeling with respect to endogenous formatively measured constructs.

http://misq.org/discovering-unobserved-heterogeneity-in-structural-equation-models-to-avert-validity-threats.html

A large proportion of information systems research is concerned with developing and testing models pertaining to complex cognition, behaviors, and outcomes of individuals, teams, organizations, and other social systems that are involved in the development, implementation, and utilization of information technology. Given the complexity of these social and behavioral phenomena, heterogeneity is likely to exist in the samples used in IS studies. While researchers now routinely address observed heterogeneity by introducing moderators, a priori groupings, and contextual factors in their research models, they have not examined how unobserved heterogeneity may affect their findings. We describe why unobserved heterogeneity threatens different types of validity and use simulations to demonstrate that unobserved heterogeneity biases parameter estimates, thereby leading to Type I and Type II errors. We also review different methods that can be used to uncover unobserved heterogeneity in structural equation models. While methods to uncover unobserved heterogeneity in covariance-based structural equation models (CB-SEM) are relatively advanced, the methods for partial least squares (PLS) path models are limited and have relied on an extension of mixture regression — finite mixture partial least squares (FIMIX-PLS) and distance measure-based methods — that have mismatches with some characteristics of PLS path modeling. We propose a new method — prediction-oriented segmentation (PLS-POS) — to overcome the limitations of FIMIX-PLS and other distance measure-based methods and conduct extensive simulations to evaluate the ability of PLS-POS and FIMIX-PLS to discover unobserved heterogeneity in both structural and measurement models. Our results show that both PLS-POS and FIMIX-PLS perform well in discovering unobserved heterogeneity in structural paths when the measures are reflective and that PLS-POS also performs well in discovering unobserved heterogeneity in formative measures. We propose an unobserved heterogeneity discovery (UHD) process that researchers can apply to (1) avert validity threats by uncovering unobserved heterogeneity and (2) elaborate on theory by turning unobserved heterogeneity into observed heterogeneity, thereby expanding theory through the integration of new moderator or contextual variables.

doi:10.1016/j.lrp.2012.10.001

Partial least squares structural equation modeling (PLS-SEM), or partial least squares path modeling (PLS) has enjoyed increasing popularity in recent years. In this context, the use of hierarchical latent variable models has allowed researchers to extend the application of PLS-SEM to more advanced and complex models. However, the attention has been mainly focused on hierarchical latent variable models with reflective relationships. In this manuscript, we focus on second-order hierarchical latent variable models that include formative relationships. First, we discuss a typology of (second-order) hierarchical latent variable models. Subsequently, we provide an overview of different approaches that can be used to estimate the parameters in these models: (1) the repeated indicator approach, (2) the two-stage approach, and (3) the hybrid approach. Next, we compare the approaches using a simulation study and an empirical application in a strategic human resource management context. The findings from the simulation and the empirical application serve as a basis for recommendations and guidelines regarding the use and estimation of reflective-formative type hierarchical latent variable models in PLS-SEM.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1879141

Since its first introduction in the Schmalenbach Business Review, Hahn et al.’s (2002) finite mixture partial least squares (FIMIX-PLS) approach to response-based segmentation in variance-based structural equation modeling has received much attention from the marketing and management disciplines. When applying FIMIX-PLS to uncover unobserved heterogeneity, the actual number of segments is usually unknown. As in any clustering procedure, retaining a suitable number of segments is crucial, since many managerial decisions are based on this result. In empirical research, applications of FIMIX-PLS rely on information and classification criteria to select an appropriate number of segments to retain from the data. However, the performance and robustness of these criteria in determining an adequate number of segments has not yet been investigated scientifically in the context of FIMIX-PLS. By conducting computational experiments, this study provides an evaluation of several model selection criteria’s performance and of different data characteristics’ influence on the robustness of the criteria. The results engender key recommendations and identify appropriate model selection criteria for FIMIX-PLS. The study’s findings enhance the applicability of FIMIX-PLS in both theory and practice.