Journal of Data Science

Abstract: Hyperplane fitting factor rotations perform better than conventional rotations in attaining simple structure for complex configurations. Hyperplane rotations are reviewed and then compared using familiar exam es from the literature selected to vary in complexity. Included is a new method for fitting hyperplanes, hypermax, which updates the work of Horst (1941) and Derflinger and Kaiser (1989). Hypercon, a method for confirmatory target rotation, is a natural extension. These performed very well when compared with selected hyperplane and conventional rotations. The concluding sections consider the pros and cons of each method.

Factor analysis (FA) is the most commonly used pattern recognition methodology in social and health research. A technique that may help to better retrieve true information from FA is the rotation of the information axes. The purpose of this study was to evaluate whether the selection of rotation type affects the repeatability of the patterns derived from FA, under various scenarios of random error introduced, based on simulated data from the Standard Normal distribution. It was observed that when applying promax non - orthogonal rotation, the results were more repeatable as compared to the orthogonal rotation, irrespective of the level of random error introduced in the model.

Abstract: The study of factor analytic models often has to address two im portant issues: (a) the determination of the “optimum” number of factors and (b) the derivation of a unique simple structure whose interpretation is easy and straightforward. The classical approach deals with these two tasks separately, and sometimes resorts to ad-hoc methods. This paper proposes a Bayesian approach to these two important issues, and adapts ideas from stochastic geometry and Bayesian finite mixture modelling to construct an ergodic Markov chain having the posterior distribution of the complete col lection of parameters (including the number of factors) as its equilibrium distribution. The proposed method uses an Automatic Relevance Determi nation (ARD) prior as the device of achieving the desired simple structure. A Gibbs sampler updating scheme is then combined with the simulation of a continuous-time birth-and-death point process to produce a sampling scheme that efficiently explores the posterior distribution of interest. The MCMC sample path obtained from the simulated posterior then provides a flexible ingredient for most of the inferential tasks of interest. Illustrations on both artificial and real tasks are provided, while major difficulties and challenges are discussed, along with ideas for future improvements.

Abstract: In maximum likelihood exploratory factor analysis, the estimates of unique variances can often turn out to be zero or negative, which makes no sense from a statistical point of view. In order to overcome this difficulty, we employ a Bayesian approach by specifying a prior distribution for the variances of unique factors. The factor analysis model is estimated by EM algorithm, for which we provide the expectation and maximization steps within a general framework of EM algorithms. Crucial issues in Bayesian factor analysis model are the choice of adjusted parameters including the number of factors and also the hyper-parameters for the prior distribution. The choice of these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a Bayesian factor analysis model. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. We observe that our modeling procedure prevents the occurrence of improper solutions and also chooses the appropriate number of factors objectively.