Structural equation modeling (SEM) has become a quasi-standard in marketing and management research when it comes to analyzing the cause-effect relations between latent constructs. For most researchers, SEM is equivalent to carrying out covariance-based SEM (CB-SEM). While marketing researchers have a basic understanding of CB-SEM, most of them are only barely familiar with the other useful approach to SEM-partial least squares SEM (PLS-SEM). The current paper reviews PLS-SEM and its algorithm, and provides an overview of when it can be most appropriately applied, indicating its potential and limitations for future research. The authors conclude that PLS-SEM path modeling, if appropriately applied, is indeed a "silver bullet" for estimating causal models in many theoretical models and empirical data situations.

PLS-SEM: Indeed a Silver Bullet

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

Experimental Design and Data Analysis for Biologists

Structural Equations with Latent Variables.

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Monographs on statistics and applied probability

Solving Least Squares Problems.

The ideal method of science is the study of the direct influence of one condition on another in experiments in which all other possible causes of variation are eliminated. Unfortunately, causes of variation often seem to be beyond control. In the biological sciences, especially, one often has to deal with a group of characteristics or conditions which are correlated because of a complex of interacting, uncontrollable, and often obscure causes. The degree of correlation between two variables can be calculated by well-known methods, but when it is found it gives merely the resultant of all connecting paths of influence. The present paper is an attempt to present a method of measuring the direct influence along each separate path in such a system and thus of finding the degree to which variation of a given effect is determined by each particular cause. The method depends on the combination of knowledge of the degrees of correlation among the variables in a system with such knowledge as may be possessed of the causal relations. In cases in which the causal relations are uncertain the method can be used to find the logical consequences of any particular hypothesis in regard to them. CORRELATION

Correlation and Causation.

Classification and Clustering.

Many textbooks on regression analysis include the methodology of principal components regression (PCR) as a way of treating multicollinearity problems. Although we have not encountered any strong justification of the methodology, we have encountered, through carrying out the methodology in well-known data sets with severe multicollinearity, serious actual and potential pitfalls in the methodology. We address these pitfalls as cautionary notes, numerical examples that use well-known data sets. We also illustrate by theory and example that it is possible for the PCR to fail miserably in the sense that when the response variable is regressed on all of the p principal components (PCs), the first (p − 1) PCs contribute nothing toward the reduction of the residual sum of squares, yet the last PC alone (the one that is always discarded according to PCR methodology) contributes everything. We then give conditions under which the PCR totally fails in the above sense.

Some cautionary notes on the use of principal components regression

Many of the existing measures for influential subsets in univariate ordinary least squares (OLS) regression analysis have natural extensions to the multivariate regression setting. Such measures may be characterized by functions of the submatrices H I of the hat matrix H, where I is an index set of deleted cases, and Q I , the submatrix of Q = E(E T E)−1 E T , where E is the matrix of ordinary residuals. Two classes of measures are considered: f(·)tr[H I Q I (I − H I − Q I ) a (I − H I ) b ] and f(·)det[(I − H I − Q I ) a (I − H I ) b ], where f is a scalar function of the dimensions of matrices and a and b are integers. These characterizations motivate us to consider separable leverage and residual components for multiple-case influence and are shown to have advantages in computing influence measures for subsets. In the recent statistical literature on regression analysis, much attention has been given to problems of detecting observations that, individually or jointly, exert a disproportionate ...

https://www.jstor.org/stable/pdfplus/2290468.pdf

Robert F. Ling

Papers

Solving Least Squares Problems.

Correlation and Causation.

Classification and Clustering.

Some cautionary notes on the use of principal components regression

General Classes of Influence Measures for Multivariate Regression