A note on distributional properties of the Jöreskog-Sörbom fit indices

In introducing the LISREL model for systems of linear structural equations, Jöreskog and Sörbom proposed two goodness-of-fit indices, GFI and AGFI. Their asymptotic distributions and some statistical properties are discussed.The authors would like to acknowledge the helpful comments and suggestions from the Associate Editor and two anonymous reviewers.     

Effect analysis and causation in linear structural equation models

This paper considers total and direct effects in linear structural equation models. Adopting a causal perspective that is implicit in much of the literature on the subject, the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature. Drawing a distinction between concomitants and factors, the paper concludes that a concomitant has neither total nor direct effects on other variables. When a variable is a factor and one or more intervening variables are concomitants, the notion of a direct effect is not causally meaningful. Even when the notion of a direct effect is meaningful, the usual estimate of this quantity may be inappropriate. The total effect is usually interpreted as an equilibrium multiplier. In the case where there are simultaneity relations among the dependent variables in tghe model, the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers, and thus, the usual interpretation is incorrect. To remedy some of these deficiencies, a new effect, the total effect of a factorX on an outcomeY, holding a set of variablesF constant, is defined. When defined, the total and direct effects are a special case of this new effect, and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier.For helpful comments, I am grateful to G. Arminger, K. Bollen, W. Faris, R. m. Hauser, T. Petersen, three anonymous Psychometrikas reviewers, and the Editor. For computational assistance, I am grateful to B. D. Kim.     

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.     

Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

The genetic architecture of effortful control and its interplay with psychological adjustment in adolescence

The role of genes and environment in the relation between self-regulation and adjustment is unclear. We investigated, with the twin design, genetic and environmental components of the association between effortful control (EC) and indicators of psychological adjustment using adolescents’ and parents’ reports for 774 twins. Genetic factors explained a substantial proportion of variance in EC (58%) and the outcome variables of optimism (55%), general self-esteem (45%), happiness (48%), and self-derogation (29%). Perceived competence had no significant genetic component. Aside from perceived competence, uncorrelated with EC, phenotypic correlations of EC with measures of well-being/adjustment were moderate and predominantly explained by shared genetic effects. Results suggest a significant genetic contribution in adolescents’ EC and in its relation to various aspects of adjustment.     

To Use or Not to Use: The Prenatal Genetic Technology/Worry Conundrum

We conducted an exploratory, qualitative study investigating the factors influencing the use of genetic counseling and prenatal genetic testing for two groups: pregnant women 35 years of age and over (AMA) at the time of delivery and pregnant women with an abnormal maternal serum triple screen (MSAFP3). The convenience sample consisted of 25 semistructured interviews of women/couples and 50 observations of genetic counseling sessions. Worry turned out to be the most important variable influencing decision making about prenatal genetic testing and was greater in the MSAFP3 group than in the AMA group. The women in the AMA group appeared to assign the risk of having a child with Down syndrome to their age category rather than to themselves individually, whereas, the risk perception for women with an abnormal MSAFP3 appeared to have shifted from a general population risk for pregnant women to an individual, personal risk. There was a general lack of understanding and also more misinformation about the MSAFP3 screen compared to amniocentesis. Women in both groups were torn between fear of an invasive test and worry about the health of their fetus for the rest of their pregnancy if they did not undergo amniocentesis.     

Neurogenetic approaches to habituation and dishabituation in Drosophila

We review work in the major model systems for habituation in Drosophila melanogaster, encompassing several sensory modalities and behavioral contexts: visual (giant fiber escape response, landing response); chemical (proboscis extension reflex, olfactory jump response, locomotory startle response, odor-induced leg response, experience-dependent courtship modification); electric (shock avoidance); and mechanical (leg resistance reflex, cleaning reflex). Each model system shows several of Thompson and Spencer’s [Thompson, R. F., & Spencer, W. A. (1966). Habituation: A model phenomenon for the study of neuronal substrates of behavior. Psychological Review, 73, 16–43] parametric criteria for habituation: spontaneous recovery and dishabituation have been described in almost all of them and dependence of habituation upon stimulus frequency and stimulus intensity in the majority. Stimulus generalization (and conversely, the delineation of stimulus specificity) has given insights into the localization of habituation or the neural architecture underlying sensory processing.The strength of Drosophila for studying habituation is the range of genetic approaches available. Mutations have been used to modify specific neuroanatomical structures, ion channels, elements of synaptic transmission, and second-messenger pathways. rutabaga and dunce, genes of the cAMP signal pathway that have been studied most often in the reviewed experiments, have also been implicated in synaptic plasticity and associative conditioning in Drosophila and other species including mammals. The use of the Gal4/UAS system for targeting gene expression has enabled genetic perturbation of defined sets of neurons. One clear lesson is that a gene may affect habituation differently in different behaviors, depending on the expression, processing, and localization of the gene product in specific circuits. Mutations of specific genes not only provide links between physiology and behavior in the same circuit, but also reveal common mechanisms in different paradigms of behavioral plasticity. The rich repertoire of models for habituation in the fly is an asset for combining a genetic approach with behavioral, anatomical and physiological methods with the promise of a more complete understanding.     

Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.1978 Psychometric Society Presidential Address.This research has been supported by the Bank of Sweden Tercentenary Foundation under the project entitledStructural Equation Models in the Social Sciences, Karl G. Jöreskog, project director.