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.

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...

It is shown that if a random p-vector x conforms to an r-common factor model and an external variable Z is given, then there exists a family of linear combinations X of x and Z such that [x': X]' conforms to an r-common factor model

Recent research of asymptotic robustness shows that the likelihood ratio (LR) test statistic for test-of-independence based on normal theory remains valid for a general case where only independence is assumed. In contrast, under elliptical populations the LR statistic is correct if a kurtosis...