Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.     

The rank of reduced dispersion matrices

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historial discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.Financial support by the Netherlands Organization for the Advancement of Pure Research (ZWO) is gratefully acknowledged.     

Application of model-selection criteria to some problems in multivariate analysis

A review of model-selection criteria is presented, with a view toward showing their similarities. It is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model-selection criteria. Consideration is given to application of model-selection criteria to some problems of multivariate analysis, especially the clustering of variables, factor analysis and, more generally, describing a complex of variables.     

Retrospective questions and correlations

In survey research it is not uncommon to ask questions of the following type: “How many times did you undertake actiona in reference periodT of length τ?.” The relationship is established between τ and the correlation of the number of reported actions with some background variable. To this end it is assumed that the process of actions satisfies a renewal model with individual heterogeneity. Also a model has to be formulated for possible recall effects. Applications are given in the field of medical consumption.     

Factor analysis by instrumental variables methods

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. These procedures are justified by the method of least squares. Formulas for asymptotic standard errors of factor loadings are derived. The procedures are empirically compared to the method of maximum likelihood. The conclusion, based on the data used in this study, is that two of the procedures seem to work well.     

Initial response to rape: The impact of factors within the rape situation

The relationship between specific aspects of the rape situation and immediate post-rape measures of depression, fear, anxiety, and social and interpersonal functioning in 50 recent victims of sexual assault was examined. The data failed to reveal any significant relationships between rape situation variables (e.g., stranger vs. known assailant, weapon vs. no weapon) and the nature or severity of the victims' psychological response. It is emphasized that this negative finding contradicts previous and current clinical lore, and has a number of implications for the assessment and treatment of rape victims.This research was supported by a grant from the National Institute of Mental Health (MH#29692) to the first two authors.     

Life stories managing chronic illness: Young adults’ lived experiences with type 1 diabetes

This study aimed to characterise diabetes management experiences of South African young adults living with well-controlled type 1 diabetes (n = 8, female = 5, male = 3, age range = 20–25). The young adults told life stories managing their type 1 diabetes. Thematic analysis revealed the young adults to construct personal identities as people living with type 1 diabetes, to mostly utilise emotion-focused management strategies and social support for successful living with type 1 diabetes. Behavioural health strategies appear important for living well with this chronic insulin deficiency condition.     

国外心理契约破坏及结果变量与调节变量：述评与展望

心理契约破坏是个体对组织未能履行其在心理契约中应承担责任的认知评价。文章首先结合以往研究探讨了心理契约破坏与相应结果变量的关系,然后探讨了调节变量的作用,最后从被试群体、研究方法及理论模型的构建上对未来研究进行了展望。     

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.