Context Of Maximum Likelihood Estimation Research Articles

On the Relation Between the Linear Factor Model and the Latent Profile Model.

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the unconditional covariances. In particular, a 2-class latent profile model with Gaussian components underestimates the observed covariances but not the variances, when the data are consistent with a unidimensional Gaussian factor model. In explanation of this phenomenon we provide some results relating the unconditional covariances to the goodness of fit of the latent profile model, and to its excess multivariate kurtosis. The analysis also leads to some useful parameter restrictions related to symmetry.

Some observations on instrumental variable methods of time-series analysis

It. is becoming increasingly clear that in the area of environmental systems analysis, where systems are often badly defined and models are subject to considerable uncertainty, recursive methods of time-series analysis can be particularly useful both in the initial and critical stages of system identification, as well as in the final stages of parameter estimation and model validation. Of the existing methods of time-series analysis, those based upon the method of instrumental variables are amongst the simplest and. at the same time, demonstrably most useful in practical applications. This paper discusses the instrumental variable (IV) and approximate maximum likelihood (AML) methods of recursive time-series analysis and shows how they can be unified to some extent within the context of maximum likelihood estimation. In this manner the virtues and limitations of the existing IV and AML techniques become more apparent and possible procedures for improving their statistical efficiency are exposed.