It is shown that the maximum likelihood and generalized least-squares estimators of unique variances in the conditional model are asymptotically equivalent to those in the marginal model in factor analysis. The asymptotic covariance matrices of the estimators are expressed in matrix form.

Identifiability of full factor analysis model for x = (x1, x2T)T is discussed, when the marginal model for x2 and/or the conditional model for x2 given x1 conform to factor analysis models. Two numerical examples are given for illustrative purposes.

The structure of maximum likelihood estimators in the Heywood case is investigated without any restrictions on parameters. It is shown that this structure is identical to that obtained by Jöreskog (1967) under the restriction that some uniquenesses are zero. As a result, the structure of...

A new implementation of the Marquardt method for the nonlinear least-squares problem is presented. The algorithm is very simple but its performance with nine test functions is at least comparable with either Davidon-Fletcher-Powell's method or Moré's adaptive Marquardt method.

Three popular methods to estimate the unknown parameters in the factor analysis model, simple (SLS) and weighted (WLS) least-squares methods and the maximum likelihood method (ML), are compared by a Monte Carlo study. The experiments were conducted with 200 replications for every combination of...

A new Gaussian graphical modeling that is robustified against possible outliers is proposed. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its likelihood. Test statistics associated with the...