Bulletin Spring‧Summer 1996

A n Examp l e of Structural Equa t i on Mode l l i ng We can consider an example of the application of structural equation modelling. The path diagram below represents a model of student growth study conducted at the Education Testing Service in the USA based on some longitudinal data (see, e.g. Jöreskog & Sörbom, 1989). In this model, there are several latent variables: quantitative ability (Q) and verbal ability (V) at grades 7 and 9; and several observed variables which are the students' scores on the following tests at grades 7 and 9: mathematics (MATH) , science (SCI), social studies (SS )， reading (READ), the verbal (SCATV) and quantitative (SCATQ) parts of the Scholastic Aptitude Test. As can be seen in the path diagram, latent variables are all related to some appropriate observed variables: 'straight' arrows represent causations and 'curved' arrows represent correlations. Each of these arrows contributes a parameter in the model that requires to be estimated. Based on the analysis of the model, several conclusions can be drawn. For instance, the verbal ability at grade 7 (V 7 ) has no causal effect on the quantitative ability at grade 9 (Q 9 ), but it has a causal effect on the verbal ability at grade 9 (V 9 ) with a magnitude to be determined by the parameter β 42 . Similar path diagrams are normally adopted to facilitate the developing and specifying of structural equation models. In order to obtain detailed analyses of such models, a general computer program is also required. Data t h a t Precludes App l i c a t i on o f Structural Equa t i on Models Now, with the help of the efficient programs LISREL V II (Jöreskog & Söbom, 1989) and EQS (Bentler, 1992), structural equation models have been widely used to analyse practical situations. Like most statistical methods, correct applications are based on certain assumptions. Fo r this technique, the most important assumptions are that the variables are continuous and the observations are independently distributed. As this methodology has increased in popularity, there is a strong demand for its P a t h d i a g r am of a m o d e l of student g r o w t h . Observed and l a t e n t v a r i a b l e s are r e p r e s e n t e dby r e c t a n g l e s and c i r c l e s r e s p e c t i v e l y ; s t r a i g h t a r r o ws represen t c a u s a t i o n s a d c u r v ed a r r o ws represen t c o r r e l a t i o n s . 24