The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addit...

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

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Structural equation modeling in practice: a review and recommended two-step approach

The metafor package provides functions for conducting meta-analyses in R. The package includes functions for fitting the meta-analytic fixed- and random-effects models and allows for the inclusion of moderators variables (study-level covariates) in these models. Meta-regression analyses with continuous and categorical moderators can be conducted in this way. Functions for the Mantel-Haenszel and Peto's one-step method for meta-analyses of 2 x 2 table data are also available. Finally, the package provides various plot functions (for example, for forest, funnel, and radial plots) and functions for assessing the model fit, for obtaining case diagnostics, and for tests of publication bias.

Conducting Meta-Analyses in R with the metafor Package

Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.

/pdf/missing-data-our-view-of-the-state-of-the-art-3xnwc88wmd.pdf

Missing data: Our view of the state of the art.

Age-specific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies.

The question of how to analyze unbalanced or incomplete repeated-measures data is a common problem facing analysts. We address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within-subject covariances. Models that can be fit include standard univariate and multivariate models with incomplete data, random-effects models, and models with time-series and factor-analytic error structures. We describe Newton-Raphson and Fisher scoring algorithms for computing maximum likelihood estimates, and generalized EM algorithms for computing restricted and unrestricted maximum likelihood estimates. An example fitting several models to a set of growth data is included.

Unbalanced repeated-measures models with structured covariance matrices

Existing analytic oblique rotation schemes proceed by optimizing a simplicity function applied to the reference structure. This article suggests optimizing a simplicity function applied to primary loadings directly. The feasibility of the suggestion is demonstrated using the quartimin criterion. An algorithm to implement the optimization is derived and the existence of an admissible solution proved. Practical comparisons with the biquartimin method are made using Thurstone's Box Problem and Holzinger and Swineford's Twenty-Four Psychological Tests Problem.

Rotation for simple loadings

Almost all modern rotation of factor loadings is based on optimizing a criterion, for example, the quartimax criterion for quartimax rotation. Recent advancements in numerical methods have led to general orthogonal and oblique algorithms for optimizing essentially any rotation criterion. All that is required for a specific application is a definition of the criterion and its gradient. The authors present the implementations of gradient projection algorithms, both orthogonal and oblique, as well as a catalogue of rotation criteria and corresponding gradients. Software for these is downloadable and free; a specific version is given for each of the computing environments used most by statisticians. Examples of rotation methods are presented by applying them to a loading matrix from Wehmeyer and Palmer.

Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis

Derivative-free nonlinear least squares algorithms which make efficient use of function evaluations are important for fitting models defined by systems of nonlinear differential equations. A new Gauss-Newton-like algorithm with these properties is developed. The performance of the new algorithm (called Dud for “doesn't use derivatives”) is evaluated on a number of standard test problems from the literature. On these problems Dud competes favorably with even the best derivative-based algorithms.

https://www.jstor.org/stable/pdfplus/1268154.pdf

Dud, A Derivative-Free Algorithm for Nonlinear Least Squares

An asymptotic χ2 test for the equality of two correlation matrices is derived. The key result is a simple representation for the inverse of the asymptotic covariance matrix of a sample correlation matrix. The test statistic has the form of a standard normal theory statistic for testing the equality of two covariance matrices with a correction term added. The applicability of asymptotic theory is demonstrated by two simulation studies and the statistic is used to test the difference in the factor patterns resulting from a set of tests given to retarded and non-retarded children. Two related tests are presented: a test for a specified correlation matrix and a test for equality of correlation matrices in two or more populations.

Robert I. Jennrich

Papers

Unbalanced repeated-measures models with structured covariance matrices

Rotation for simple loadings

Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis

Dud, A Derivative-Free Algorithm for Nonlinear Least Squares

An Asymptotic χ2 Test for the Equality of Two Correlation Matrices