British Journal of Mathematical and Statistical PsychologyVolume 38, Issue 1 p. 120-121 Some comments on structural equation models† P. M. Bentler, Corresponding Author P. M. BentlerDepartment of Psychology, University of California, Los Angeles, California, 90024, USA.Search for more papers by this authorD. G. Weeks, D. G. Weeks Washington University, St Louis, MO, USA.Search for more papers by this author P. M. Bentler, Corresponding Author P. M. BentlerDepartment of Psychology, University of California, Los Angeles, California, 90024, USA.Search for more papers by this authorD. G. Weeks, D. G. Weeks Washington University, St Louis, MO, USA.Search for more papers by this author First published: May 1985 https://doi.org/10.1111/j.2044-8317.1985.tb00821.xCitations: 5 † Invited by the editor. Supported in part by USPHS grants DA00017 and DA01070. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume38, Issue1May 1985Pages 120-121 RelatedInformation

The intelligence, academic achievement, and classroom behavior of 158 children were assessed in a sample that is being followed longitudinally. The sample included children at high risk for mental disorder by virtue of having a parent with a psychiatric diagnosis of schizophrenia or affective disorder, children at moderate risk, and children at low risk, A series of path analyses indicated that in this sample (1) classroom behavior was more likely an affect than a cause of academic achievement, and (2) the influence of parental psychopathology on classroom behavior was mediated by a child's intelligence and academic achievement. We were unable to substantiate an unmediated causal link between parental psychopathology and children's academic achievement or classroom behavior.

This study examined teachers' evaluations of adolescent children of parents who had been hospitalized for mental disorder. Classroom behavior of these children as well as that of children of parents with physical illness was compared to that of adolescents whose parents had not been hospitalized for mental disorder. Both DSM-III and DSM-II categorizations were used. Two teacher-rated instruments were used. Adolescents with a parent with DSM-III diagnoses of schizophrenia and major affective disorder, as compared to children of nonill parents, were rated as less motivated, less harmonious, less stable, more dogmatic, and more verbally negative. Differences among children of parents with other diagnoses were generally less striking. Results using DSM-II diagnoses were similar to but weaker than those using DSM-III.

Restricted multidimensional scaling models [Bentler & Weeks, 1978] allowing constraints on parameters, are extended to the case of asymmetric data. Separate functions are used to model the symmetric and antisymmetric parts of the data. The approach is also extended to the case in which data are presumed to be linearly related to squared distances. Examples of several models are provided, using journal citation data. Possible extensions of the models are considered.

Data are presented from the intellectual assessment of 153 children at two test periods in the St. Louis Risk Research Project. At phase I (1967-72) the Wechsler tests of intelligence were administered to offspring in families with one schizophrenic parent, one parent with affective disorder, one parent with schizoaffective disorder, one physically ill parent, or to offspring with two normal parents (mean age, 8 years). At phase II (1975-78) the intelligence of offspring was tested again at a mean age of 16 years. Differences between children as a function of parental diagnoses were assessed using a repeated measures analysis of covariance. The analyses yielded significant time effects. A time-by-parental-diagnosis effect was found for Verbal IQ, with children of parents with schizophrenia, affective disorder, or physical illness all showing a greater decrease in their scores at the second testing than offspring in the other groups. Offspring of psychotic mothers had lower IQ scores than those of psychotic fathers. Children of schizophrenics and children of schizoaffectives had the lowest stability in IQ scores from the first to the second testing.

This study examined the applicability of Weiner's model of causal attributions to lay explanations for the causes of loneliness. Weiner posits three dimensions (Internatily, Stability, and controllability) along which causes vary and links each dimension to distinct consequences for the actor. To test the salience of these dimensions in lay perceptions of causality, 180 college students made judgments about the causes of loneliness. As predicted, both exploratory and confirmatory multidimensional scaling analyses found that dimensions of Internality and Stability were perceived by respondents. Contrary to recent theorizing, Controllability was not independent of the other two dimensions; instead, controllable causes were both internal and unstable. Confirmation of Internality and Stability as dimensions underlying attributions for loneliness supported the extension of Weiner's model to the domain of affiliative behavior.

This chapter focuses on models in which both manifest and latent variables are continuous. This restriction still generates a large class of models when they are considered simultaneously in several populations and when certain variables are considered fixed rather than random. The field of multivariate analysis with continuous latent and measured random variables has made substantial progress in recent years, particularly, from mathematical and statistical points of view. Mathematically, clarity has been achieved in understanding representation systems for structured linear random variable models. Statistically, large sample theory has been developed for a variety of competing estimators, and the associated hypothesis testing procedures have been developed. The applied statistician, who is concerned with utilizing the above theory in empirical applications, will quickly find that causal modeling is a very finicky methodology having many pitfalls.

Research on loneliness has been hampered by its strong association with depression. The two states frequently co-occur, and measures of the two states are substantially correlated. Inability to manipulate experimentally loneliness or depression makes it difficult to untangle the causal influence of one on the other. The combination of longitudinal design and structural equation methodology is proposed as a solution to this general problem. Measures of loneliness and depression were administered to undergraduates at two points 5 weeks apart. Data from 333 subjects were correlated and analyzed under a succession of structural equation models. Results indicated that loneliness and depression were correlated but clearly different constructs; neither was a direct cause of the other, though both probably share some common origins; both were highly stable over to 5-week-period.

Olsson and Bergman (1977) presented a structural equation model for the development of intellectual abilities between the ages of 10 and 13. Their model proposed four correlated factors, each of which was stable over time. They also found that development on each factor was a function of that factor alone, independent of the other factors. The present paper describes a reanalysis of these data, under a structural model which assumed that a second-order general-intelligence factor (G) could account for the correlations among factors. It was found that, for the sample used, only G and the verbal and spatial ability factors were stable over time. It was concluded that much of the stability found by Olsson and Bergman could be accounted for by the stability of G, and that development on each primary factor was heavily dependent on development of G.

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.

Factor analysis in several populations, covariance structure models, three-mode factor analysis, structural equation systems with measurement model, and analysis of covariance with measurement model are all shown to be specializations of a general moment structure model published previously in this journal. Some new structured linear models are also described; they may be considered either generalizations or special cases of existing models. Simple representations are developed for complex linear models, and some applications to behavioral data are cited.

A class of multidimensional scaling models are developed wherein certain parameters may be fixed as known constants, or proportional to one another. Traditional multidimensional scaling can be obtained as a special case by fixing only the orientation and origin of a configuration. Methods of obtaining least-square estimates of the parameters via nonlinear programming are discussed, and an effective computer program is developed to implement application of the models to data. Several well-known data sets are reanalyzed under various restricted models, and the results demonstrate the possibility of achieving insight not attainable under the traditional approach. The potential distortion arising from inadequate model specification is discussed, and the importance of substantive theory to multidimensional scaling research is emphasized.