Anne Boomsma

Reporting Analyses of Covariance Structures

This contribution is focused on how to write a research paper when structural equation models are being used in empirical work. The main question to be answered is what information should be reported and what results can be deleted without much loss of judgment about the quality of research and the validity of conclusions being made. The major conjecture is that all information should be reported, or referred to, that enables each member of the scientific community, at least in principle, to replicate the analysis as it is published. The recommendations are ordered in the framework of the empirical research cycle. They are meant for authors, in particular students employing structural equation models for their dissertation, as well as for editors and reviewers.

Robustness studies in covariance structure modeling - An overview and a meta-analysis

In covariance structure modeling, several estimation methods are available. The robustness of an estimator against specific violations of assumptions can be determined empirically by means of a Monte Carlo study. Many such studies in covariance structure analysis have been published, but the conclusions frequently seem to contradict each other. An overview of robustness studies in covariance structure analysis is given, and an attempt is made to generalize findings. Robustness studies are described and distinguished from each other systematically by means of certain characteristics. These characteristics serve as explanatory variables in a meta-analysis concerning the behavior of parameter estimators, standard error estimators, and goodness-of-fit statistics when the model is correctly specified.

Nonconvergence, improper solutions, and starting values in lisrel maximum likelihood estimation

In the framework of a robustness study on maximum likelihood estimation with LISREL three types of problems are dealt with: nonconvergence, improper solutions, and choice of starting values. The purpose of the paper is to illustrate why and to what extent these problems are of importance for users of LISREL. The ways in which these issues may affect the design and conclusions of robustness research is also discussed.

Bayesian estimation and testing of structural equation models

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, for example, output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters underidentified models, as we illustrate on a simple errors-in-variables model.

Essays on item response theory

1 The Life of Georg Rasch as a Mathematician and as a Statistician.- 2 The Growing Family of Rasch Models.- 3 Gain Scores Revisited Under an IRT Perspective.- 4 Modeling Learning in Short-Term Learning Tests.- 5 An IRT Model for Multiple Raters.- 6 Conditional Independence and Differential Item Functioning in the Two-Parameter Logistic Model.- 7 Differential Item Functioning Depending on General Covariates.- 8 Statistical Tests for Differential Test Functioning in Raschs Model for Speed Tests.- 9 Expected Response Functions.- 10 A Logistic IRT Model for Decreasing and Increasing Item Characteristic Curves.- 11 Using Parameter Expansion to Improve the Performance of the EM Algorithm for Multidimensional IRT Population-Survey Models.- 12 Cross-Validating Item Parameter Estimation in Adaptive Testing.- 13 Imputation of Missing Scale Data with Item Response Models.- 14 On the Interplay Between Nonparametric and Parametric IRT, with Some Thoughts About the Future.- 15 Reversibility Revisited and Other Comparisons of Three Types of Polytomous IRT Models.- 16 Progress in NIRT Analysis of Polytomous Item Scores: Dilemmas and Practical Solutions.- 17 Two-Level Nonparametric Scaling for Dichotomous Data.- 18 The Circles of Our Minds: &&A Nonparametric IRT Model for the Circumplex.- 19 Using Resampling Methods to Produce an Improved DIMTEST Procedure.- 20 Person Fit Across Subgroups: An Achievement Testing Example.- 21 Single-Peaked or Monotone Tracelines? On the Choice of an IRT Model for Scaling Data.- 22 Outline of a Faceted Theory of Item Response Data.- Abbreviations.

Small-Sample Robust Estimators of Noncentrality-Based and Incremental Model Fit

Traditional estimators of fit measures based on the noncentral chi–square distribution (root mean square error of approximation [RMSEA], Steigers γ, etc.) tend to overreject acceptable models when the sample size is small. To handle this problem, it is proposed to employ Bartletts (1950), Yuans (2005), or Swains (1975) correction of the maximum likelihood chi–square statistic for the estimation of noncentrality–based fit measures. In a Monte Carlo study, it is shown that Swains correction especially produces reliable estimates and confidence intervals for different degrees of model misspecification (RMSEA range: 0.000–0.096) and sample sizes (50, 75, 100, 150, 200). In the second part of the article, the study is extended to incremental fit indexes (Tucker–Lewis Index, Comparative Fit Index, etc.). For their small–sample robust estimation, use of Swains correction is recommended only for the target model, not for the independence model. The Swain–corrected estimators only require a ratio of sample size to estimated parameters of about 2:1 (sometimes even less) and are thus strongly recommended for applied research. R software is provided for convenient use.

The Model-Size Effect on Traditional and Modified Tests of Covariance Structures

According to Kenny and McCoach (2003), chi-square tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range of 48 to 960 degrees of freedom it was found that the traditional maximum likelihood ratio statistic, T ML , overestimates nominal Type I error rates up to 70% under conditions of multivariate normality. Some alternative statistics for the correction of model-size effects were also investigated: the scaled Satorra–Bentler statistic, T SC ; the adjusted Satorra–Bentler statistic, T AD (Satorra & Bentler, 1988, 1994); corresponding Bartlett corrections, T MLb , T SCb , and T ADb (Bartlett, 1950); and corresponding Swain corrections, T MLs , T SCs , and T ADs (Swain, 1975). The empirical findings indicate that the model test statistic T MLs should be applied when large structural equation models are analyzed and the observed variables have (approximately) a multivariate normal distribution.

On person parameter estimation in the dichotomous Rasch model

An overview is given of person parameter estimation in the Rasch model. In Section 4.2 some notation is introduced. Section 4.3 presents four types of estimators: the maximum likelihood, the Bayes modal, the weighted maximum likelihood, and the Bayes expected a posteriori estimator. In Section 4.4 a simulation study is presented in which properties of the estimators are evaluated. Section 4.5 covers randomized confidence intervals for person parameters. In Section 4.6 some sample statistics are mentioned that were computed using estimates of θ. Finally, a short discussion of the estimators is given in Section 4.7.

CROSS-VALIDATION IN REGRESSION AND COVARIANCE STRUCTURE-ANALYSIS - AN OVERVIEW

This article gives an overview of cross-validation techniques in regression and covariance structure analysis. The method of cross-validation offers a means for checking the accuracy or reliability of results that were obtained by an exploratory analysis of the data. Cross-validation provides the possibility to select, from a set of alternative models, the model with the greatest predictive validity, that is, the model that cross-validates best. The disadvantage of cross-validation is that the data need to be split in two or more parts. This can be a serious problem when sample size is small. Various authors have therefore tried to find single sample criteria that provide the same kind of information as the cross-validation criteria but that do not require the use of a validation sample. Several of these criteria will be discussed, along with some results from studies comparing cross-validation and single sample criteria in covariance structure analysis.

On the structure of motor symptoms of Parkinson's disease

This study aims to investigate the structure of the motor symptoms of Parkinsons disease (PD), as measured by the Motor Section of the Unified Parkinsons Disease Rating Scale (UPDRS). The dimensionality of the Motor Section of the UPDRS was studied using structural equation modeling. The UPDRS measures were obtained from 405 patients with PD [237 men (39 “off”, 170 “on”, 28 unknown) and 168 women (21 “off”, 140 “on”, 7 unknown)]. The ordinal character of UPDRS scores and sample size substantiated the use of robust diagonally weighted least squares model estimation. It was shown that the Motor Section of the UPDRS incorporates five main latent symptom factors (rigidity, tremor, bradykinesia of the extremities, axial/gait bradykinesia, speech/hypomimia) plus two additional factors for laterality, which account for asymmetry of tremor, rigidity and bradykinesia of the extremities. Tremor seems to be an independent symptom factor of PD. Other latent variables are substantially correlated.