Scaled and Adjusted Restricted Tests in Multi-Sample Analysis of Moment Structures

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Moment structure analysis is widely used in behavioural, social and economic studies to analyse structural relations between variables, some of which may be latent (i.e., unobservable); see, for example, Bollen (1989), Yuan and Bentler (1997), and references therein. Commercial computer programs to carry out such analysis, for a general class of structural equation models, are available, for example, LISREL of Jöreskog and Sörbom (1994) and EQS of Bentler (1995). In multi-sample analysis, data from several samples are combined into one analysis, making it possible, among other features, to test for across-group invariance of specific model parameters. One issue which is central in moment structure analysis is the goodness-of-fit test of the model and the test of restrictions on parameters.