Latent-variable models in criminological research: Applications and a generalization of Joreskog's LISREL model

This paper examines issues in LISREL models involving latent, or unobserved, variables. We discuss estimating parameters in multiple-indicator models, various approaches to assessing goodness of fit, different types of linear measurement models, using LISREL to correct for attenuation in models involving single indicators with known reliabilities, and estimating parameters in structural equation models involving latent exogenous and endogenous variables. Finally, we present a generalization of the standard LISREL model which explicitly identifies implicit constraints on parameters in the standard LISREL model. We argue that the generalization can accommodate a wider range of models and provide additional diagnostic information on some assumptions in the standard LISREL model. By example, we show how the more general model can be estimated using Joreskog's LISREL program.