On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme

A new approach for the estimation and the validation of a structural equation model with a formative-reflective scheme is presented. The basis of the paper is a proposal for overcoming a potential deficiency of PLS path modeling. In the PLS approach the reflective scheme assumed for the endogenous latent variables (LVs) is inverted; moreover, the model errors are not explicitly taken into account for the estimation of the endogenous LVs. The proposed approach utilizes all the relevant information in the formative manifest variables (MVs) providing solutions which respect the causal structure of the model. The estimation procedure is based on the optimization of the redundancy criterion. The new approach, entitled redundancy analysis approach to path modeling (RA-PM) is compared with both traditional PLS Path Modeling and LISREL methodology, on the basis of real and simulated data.     

Lower bounds on sample size in structural equation modeling

Computationally intensive structural equation modeling (SEM) approaches have been in development over much of the 20th century, initiated by the seminal work of Sewall Wright. To this day, sample size requirements remain a vexing question in SEM based studies. Complexities which increase information demands in structural model estimation increase with the number of potential combinations of latent variables; while the information supplied for estimation increases with the number of measured parameters times the number of observations in the sample size – both are non-linear. This alone would imply that requisite sample size is not a linear function solely of indicator count, even though such heuristics are widely invoked in justifying SEM sample size. This paper develops two lower bounds on sample size in SEM, the first as a function of the ratio of indicator variables to latent variables, and the second as a function of minimum effect, power and significance. The algorithm is applied to a meta-study of a set of research published in five of the top MIS journals. The study shows a systematic bias towards choosing sample sizes that are significantly too small. Actual sample sizes averaged only 50% of the minimum needed to draw the conclusions the studies claimed. Overall, 80% of the research articles in the meta-study drew conclusions from insufficient samples. Lacking accurate sample size information, researchers are inclined to economize on sample collection with inadequate samples that hurt the credibility of research conclusions. Guidelines are provided for applying the algorithms developed in this study, and companion software encapsulating the paper’s formulae is made available for download.     

A priori molecular descriptors in QSAR: a case of HIV-1 protease inhibitors. II. Molecular graphics and modeling

Molecular graphics and modeling methods illustrated the chemical background of the a priori approach from part I, and visualized steric and electronic enzyme-inhibitor relationships at qualitative and quantitative level for 34 and its derivatives. The enzyme-inhibitor electron density overlap occurs at 1.5–5.5 Å cut-off distance, beyond van der Waals radii. Derivatives of 34 exhibit linear relationships between biological activity, molecular size and number of intermolecular interactions.