PLS path modeling

The applicability of 5 conventional guidelines for construct measurement is critically examined: (a) Construct indicators should be internally consistent for valid measures, (b) there are optimal magnitudes of correlations between items, (c) the validity of measures depends on the adequacy with which a specified domain is sampled, (d) within-construct correlations must be greater than between-construct correlations, and (e) linear composites of indicators can replace latent variables. A structural equation perspective is used, showing that without an explicit measurement model relating indicators to latent variables and measurement errors, none of these conventional beliefs hold without qualifications. Moreover, a "causal" indicator model is presented that sometimes better corresponds to the relation of indicators to a construct than does the classical test theory "effect" indicator model.

Conventional wisdom on measurement: A structural equation perspective.

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The Evolution and Future of National Customer Satisfaction Index Models

The author proposes an alternative estimation technique for latent variable interactions and quadraties. Available techniques for specifying these variables in structural equation models require adding variables or constraint equations that can produce specification tedium and errors or estimation difficulties. The proposed technique avoids these difficulties and may be useful for EQS, LISREL 7, and LISREL 8 users. First, measurement parameters for indicator Ioadings and errors of linear latent variables are estimated in a measurement model that excludes the interaction and quadratic variables. Next, these estimates are used to calculate values for the indicator loadings and error variances ofthe interaction and quadratic latent variables. Then, these calculated values are specified as constants in the structural model containing the interaction and quadratic variables. Interaction and quadratic effects are routinely reported for categorical independent variables (i.e., in analysis of variance) frequently to aid in the interpretation of significant main effects. However, interaction and quadratic effects are less frequently reported for continuous independent variables.

Latent Variable Interaction and Quadratic Effect Estimation: A Two-Step Technique Using Structural Equation Analysis

Only true experiments offer definitive evidence for causal inferences, but not all educational interventions are readily amenable to experiments. Correlational evidence can at least tentatively inform evidence-based practice when sophisticated causal modeling or exclusion methods are employed. Correlational evidence is most informative when exemplary practices are followed as regards (a) measurement, (b) quantifying effects, (c) avoiding common analysis errors, and (d) using confidence intervals to portray the range of possible effects and the precisions of the effect estimates.

Evaluating the Quality of Evidence from Correlational Research for Evidence-Based Practice

A general model and an associated method of data analysis are presented. It is assumed that observations on a set of response variables have a multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix. Any parameter of the model may be fixed, free or constrained to be equal to other parameters. The free and constrained parameters are estimated by the maximum likelihood method. Approximate standard errors and confidence intervals for the estimated parameters may be obtained by computing the inverse of the information matrix. The adequacy of any specific model contained in the general model may be tested by the likelihood ratio technique, yielding a large sample chi-square test of goodness of fit.



Great generality and flexibility are obtained, in that a wide range of models is contained in the general model by imposing various specifications on the parametric structure of the general model. Part II of this paper deals with applications to various problems mainly from the field of psychology. In part I the general model is dealt with purely formally without reference to any particular specialization or application of it. Expressions for first-order derivatives and expected values of second-order derivatives of the likelihood function are derived, and the method of maximizing the likelihood function is described.

K. G. Jöreskog

Papers

A general method for analysis of covariance structures with applications: part i: general methodology*