A loading matrix has perfect simple structure if each row has at most one nonzero element. It is shown that if there is an orthogonal rotation of an initial loading matrix that has perfect simple structure, then orthomax rotation with 0 ≤γ ≤ 1 of the initial loading matrix will produce the perfect simple structure. In particular, varimax and quartimax will produce rotations with perfect simple structure whenever they exist.

Consider the case where J instruments are used to classify each of I objects relative to K nominal categories. The conditional grade-of-membership (GoM) model provides a method of estimating the classification probabilities of each instrument (or “judge”) when the objects being classified consist of both pure types that lie exclusively in one of K nominal categories, and mixtures that lie in more than one category. Classification probabilities are identifiable whenever the sample of GoM vectors includes pure types from each category. When additional, relatively mild, assumptions are made about judgment accuracy, the identifiable correct classification probabilities are the greatest lower bounds among all solutions that might correspond to the observed multinomial process, even when the unobserved GoM vectors do not include pure types from each category. Estimation using the conditional GoM model is illustrated on a simulated data set. Further simulations show that the estimates of the classification probabilities are relatively accurate, even when the sample contains only a small percentage of approximately pure objects.

This paper provides a statistical framework for estimating higher-order characteristics of the response time distribution, such as the scale (variability) and shape. Consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology (e.g., Luce, 1986). RT distribution for a single participant depends on certain participant characteristics, which in turn can be thought of as arising from a distribution of latent variables. The present work focuses on the three-parameter Weibull distribution, with parameters for shape, scale, and shift (initial value). Bayesian estimation in a hierarchical framework is conceptually straightforward. Parameter estimates, both for participant quantities and population parameters, are obtained through Markov Chain Monte Carlo methods. The methods are illustrated with an application to response time data in an absolute identification task. The behavior of the Bayes estimates are compared to maximum likelihood (ML) estimates through Monte Carlo simulations. For small sample size, there is an occasional tendency for the ML estimates to be unreasonably extreme. In contrast, by borrowing strength across participants, Bayes estimation “shrinks” extreme estimates. The results are that the Bayes estimators are more accurate than the corresponding ML estimators.

The aim of this note is to show that the centroid method has two optimality properties. It yields loadings with the highest sum of absolute values, even in absence of the constraint that the squared component weights be equal. In addition, it yields scores with maximum variance, subject to the constraint that none of the squared component weights be larger than 1.