Maximum likelihood estimation in covariance structure analysis with truncated data

We study an estimation procedure for maximum likelihood estimation in covariance structure analysis with truncated data, and obtain the statistical properties of the estimator as well as a test of the model structure. Truncated data with and without knowledge about the number of unmeasured observations are both considered. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which requires only first derivatives, is proposed to obtain the maximum likelihood estimates. We illustrate the statistics and parameter estimates by a fictitious example. The maximum likelihood method is compared to an alternative two-stage method.