On Ultrastructural Relationships Models

Abstract

In the long history of the errors-in-variables model, two types of models were considered, namely structural relationships and functional relationships models. Dolby (1976) combined these two models in the univariate case into a single model called the ultrastructural relationships model and found the maximum likelihood estimators of the parameters. We extend Dolby’s ultrastructural relationships model to the multivariate case, assuming the existence of an estimator for the error covariance matrix, independent of the observations. We find that the maximum likelihood method is unable to distinguish between the multivariate ultrastructural relationships model and the multivariate functional relationships model considered by Amemiya and Fuller (1984).