A general method for analysis of covariance structures
TL;DR: In this article, a general multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix is proposed, where any parameter of the model may be fixed, free or constrained to be equal to other parameters.
Abstract: SUMMARY It is assumed that observations on a set of 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 maximum likelihood. A wide range of models is obtained from the general model by imposing various specifications on the parametric structure of the general model. Examples are given of areas and problems, especially in the behavioural sciences, where the method may be useful. 1. GENERAL METHODOLOGY 11. The general model We consider a data matrix X = {xOq} of N observations on p response variables and the following model. Rows of X are independently distributed, each having a multivariate normal distribution with the same variance-covariance matrix E of the form
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TL;DR: The aims behind the development of the lavaan package are explained, an overview of its most important features are given, and some examples to illustrate how lavaan works in practice are provided.
Abstract: Structural equation modeling (SEM) is a vast field and widely used by many applied researchers in the social and behavioral sciences. Over the years, many software packages for structural equation modeling have been developed, both free and commercial. However, perhaps the best state-of-the-art software packages in this field are still closed-source and/or commercial. The R package lavaan has been developed to provide applied researchers, teachers, and statisticians, a free, fully open-source, but commercial-quality package for latent variable modeling. This paper explains the aims behind the development of the package, gives an overview of its most important features, and provides some examples to illustrate how lavaan works in practice.
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Cites background from "A general method for analysis of co..."
...The three traditions were ultimately merged in the early 1970s and although many different researchers have made significant contributions (Jöreskog 1970; Hauser and Goldberger 1971; Zellner 1970; Keesling 1973; Wiley 1973; Browne 1974), it was the work of Karl Jöreskog (Jöreskog 1973), that came to dominate the field....
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TL;DR: The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or differentiation criteria.
Abstract: Several issues relating to goodness of fit in structural equations are examined. The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or...
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TL;DR: PLS path modeling can be used for analyzing multiple tables so as to be related to more classical data analysis methods used in this field and some new improvements are proposed.
4,839 citations
TL;DR: In this paper, the applicability of five 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, within-construct correlations must be greater than between construct correlations, and (e) linear composites of indicators can replace latent variables.
Abstract: 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.
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TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
Abstract: © The British Computer Society Issue Section: Articles Download all figures A powerful iterative descent method for finding a local minimum of a function of several variables is described. A number of theorems are proved to show that it always converges and that it converges rapidly. Numerical tests on a variety of functions confirm these theorems. The method has been used to solve a system of one hundred non-linear simultaneous equations. Related articles in Web of Science
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TL;DR: In this paper, the authors describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method.
Abstract: We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large samplex
2 test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.
2,326 citations
TL;DR: In this paper, the usual MANOVA (multivariate analysis of variance) model (see equation (1)) may be generalized by allowing for the appending of a post-matrix in the expectation equation.
Abstract: The usual MANOVA (multivariate analysis of variance) model (see equation (1)) may be generalized (equation (3)) by allowing for the appending of a post-matrix in the expectation equation. As explained in ? 1, this generalized model (3) is applicable particularly to many kinds of growth curve problems, as well as to other problems. Section 2 is theoretical, and develops techniques of analysis under the generalized model. A numerical example involving growth curves is worked out in ? 3.
997 citations
908 citations