Conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly, but must be inferred from fallible or incomplete data. For example, responses to mental test items may depend upon latent aptitude variables, which modeled in turn as functions of demographic effects in the population. A method of estimating such effects by means of marginal maximum likelihood, implemented by means of an EM algorithm, is proposed. Asymptotic standard errors, likelihood ratio tests of alternative models, and computing approximations are provided. The procedures are illustrated with data for tests from the Armed Services Vocational Aptitude Battery administered to a national probability sample of American youth. (Author)