Rubin and Thayer (Psychometrika, 47:69–76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one, when the covariance matrix to be analyzed and the initial matrices including unique variances and inter-factor correlations are positive definite. We further numerically demonstrate that the EM algorithm yields proper solutions for the data which lead the prevailing gradient algorithms for factor analysis to produce improper solutions. The numerical studies also show that, in real computations with limited numerical precision, Rubin and Thayer’s (Psychometrika, 47:69–76, 1982) original formulas for confirmatory factor analysis can make factor correlation matrices asymmetric, so that the EM algorithm fails to converge. However, this problem can be overcome by using an EM algorithm in which the original formulas are replaced by those guaranteeing the symmetry of factor correlation matrices, or by formulas used to prove the above fact.

As the literature indicates, no method is presently available which takes explicitly into account that the parameters of Lazarsfeld's latent class analysis are defined as probabilities and are therefore restricted to the interval [0, 1]. In the present paper an appropriate transform on the parameters is performed in order to satisfy this constraint, and the estimation of the transformed parameters according to the maximum likelihood principle is outlined. In the sequel, a numerical example is given for which the basis solution and the usual maximum likelihood method failed. The different results are compared and the advantages of the proposed method discussed.

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300.

Exit wave restoration using focus series of images has become a widely used technique to improve image resolution and interpretation. To understand the effects of the imaging approximations used, we have critically compared the specimen exit wave functions restored using the efficient linear Wiener filter, with a general nonlinear maximum likelihood method.

The objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson model in order to use all available information in the estimation of the distribution. In a second step, a random variable is included in the regression component of the Poisson model and a negative binomial model with a regression component is derived. We then present our main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. We show how net premium tables can be derived from the model. Examples of tables are presented.