Structural equation models incorporating unmeasured variables make possible the rigorous testing of theories previously difficult to test adequately because of fallible measures of the theoretic variables. This paper first discusses a simple causal model; incorporating a single unmeasured variable for the purpose of exposition. A substantive example follows, incorporating several unmeasured variables for which multiple indicators were available. Joreskog's LISREL model for the analysis of linear structural relationships was used. The problem studied concerned the processes of educational attainment among several ethnic groups. The most important substantive conclusion was that measurement errors differ between ethnic groups and that ignoring errors leads to biased estimates of structural effects. However, application of LISREL depends on the collection of appropriate data. Unless the data have been collected by appropriate procedures, and unless the model is adequately specified, LISREL is unlikely to produce definitive results. (Author/CTM)