Factor analysis and principal component analysis are usually followed by simple structure rotations of the loadings. These rotations optimize a certain criterion (e.g., varimax, oblimin), designed to measure the degree of simple structure of the pattern matrix. Simple structure can be considered optimal if a (usually large) number of pattern elements is exactly zero. In the present paper, a class of oblique rotation procedures is proposed to rotate a pattern matrix such that it optimally resembles a matrix which has an exact simple pattern. It is demonstrated that this method can recover relatively complex simple structures where other well-known simple structure rotation techniques fail.

In the behavioral sciences, many research questions pertain to a regression problem in that one wants to predict a criterion on the basis of a number of predictors. Although in many cases, ordinary least squares regression will suffice, sometimes the prediction problem is more challenging, for three reasons: first, multiple highly collinear predictors can be available, making it difficult to grasp their mutual relations as well as their relations to the criterion. In that case, it may be very useful to reduce the predictors to a few summary variables, on which one regresses the criterion and which at the same time yields insight into the predictor structure. Second, the population under study may consist of a few unknown subgroups that are characterized by different regression models. Third, the obtained data are often hierarchically structured, with for instance, observations being nested into persons or participants within groups or countries. Although some methods have been developed that partially meet these challenges (i.e., principal covariates regression (PCovR), clusterwise regression (CR), and structural equation models), none of these methods adequately deals with all of them simultaneously. To fill this gap, we propose the principal covariates clusterwise regression (PCCR) method, which combines the key idea’s behind PCovR (de Jong & Kiers in Chemom Intell Lab Syst 14(1–3):155–164, 1992) and CR (Späth in Computing 22(4):367–373, 1979). The PCCR method is validated by means of a simulation study and by applying it to cross-cultural data regarding satisfaction with life.

A model for four-mode component analysis is developed and presented. The developed model, which is an extension of Tucker's three-mode factor analytic model, allows for the simultaneous analysis of all modes of a four-mode data matrix and the consideration of relationships among the modes. An empirical example based upon viewer perceptions of repetitive advertising shows the four-mode model applicable to real data.

In component analysis solutions, post-multiplying a component score matrix by a nonsingular matrix can be compensated by applying its inverse to the corresponding loading matrix. To eliminate this indeterminacy on nonsingular transformation, we propose Joint Procrustes Analysis (JPA) in which component score and loading matrices are simultaneously transformed so that the former matrix matches a target score matrix and the latter matches a target loading matrix. The loss function of JPA is a function of the nonsingular transformation matrix and its inverse, and is difficult to minimize straightforwardly. To deal with this difficulty, we reparameterize those matrices by their singular value decomposition, which reduces the minimization to alternately solving quartic equations and performing the existing multivariate procedures. This algorithm is assessed in a simulation study. We further extend JPA for cases where targets are linear functions of unknown parameters. We also discuss how the application of JPA can be extended in different fields.

Cureton & Mulaik (1975) proposed the Weighted Varimax rotation so that Varimax (Kaiser, 1958) could reach simple solutions when the complexities of the variables in the solution are larger than one. In the present paper the weighting procedure proposed by Cureton & Mulaik (1975) is applied to Direct Oblimin (Clarkson & Jennrich, 1988), and the rotation method obtained is called Weighted Oblimin. It has been tested on artificial complex data and real data, and the results seem to indicate that, even though Direct Oblimin rotation fails when applied to complex data, Weighted Oblimin gives good results if a variable with complexity one can be found for each factor in the pattern. Although the weighting procedure proposed by Cureton & Mulaik is based on Landahl's (1938) expression for orthogonal factors, Weighted Oblimin seems to be adequate even with highly oblique factors. The new rotation method was compared to other rotation methods based on the same weighting procedure and, whenever a variable with complexity one could be found for each factor in the pattern, Weighted Oblimin gave the best results. When rotating a simple empirical loading matrix, Weighted Oblimin seemed to slightly increase the performance of Direct Oblimin.

Both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous Guttman-scalable items can be expressed as simple functions of the number of items if the score distribution is uniform and there is an equal number of items at each difficulty level. Even when these special conditions do not hold, the correlations can often be expressed in a simple form by assuming a particular score distribution.

Data obtained from two experiments were used to identify and describe factors affecting crop loss due to weeds in forage stands. Timothy (Phleum pratense L. ‘Champ′) was established in presence or absence of barley (Hordeum vulgare L. ‘Bruce′), red clover (Trifolium pratense L. ‘Florex′), broadleaf weeds, and grass weeds. Botanical composition, soil water, soil nutrients, light interception, and plant cover were determined 4 and 6 weeks after seeding, and crop yield was determined at periodic forage harvest dates. Principal components analyses permitted the extraction of 12 factors and regression analyses demonstrated that these factors can be used to describe crop yield. Each factor can be estimated either by obtaining the rotated factor scores or by selecting a representative variable that can be substituted for the rotated factor scores in the regression models. The approach described in this paper should be tested with other crops and other weed complexes. It is suggested to use weed density in combination with weed and crop cover data to predict crop loss.

Introduction. Pescabivona is the name of an autochthonous peach [Prunus persica (L.) Batch] population of the central west of Sicily. In a previous work, this fruit was submitted to chemical analysis, while in this paper, sensory evaluation is considered. Materials and methods. Samples of four Pescabivona landraces were harvested throughout the harvest season. A trained panel outlined the sensory profiles and the data were processed by ANOVA and Principal Component Analysis (PCA). A correlation between sensory analysis and instrumental data was finally carried out. Results and discussion. The results demonstrated a high standard of quality for the four landraces studied, with some differences in aroma intensity and in some other parameters, with sweetness and aroma being highly correlated with overall liking. PCA did not clearly separate the different landraces as they have the same origin. Some correlations between sensory analysis and instrumental data were verified. The sensory liking was correlated with the main ripeness parameters, as well as with the pulp firmness. Conclusion. The data obtained contribute to outlining a complete fruit profile for product comparison and shelf-life monitoring. As previously verified for chemical parameters, the sensory evaluation indicates a substantial similarity among the landraces. The good agreement between sensory evaluation and composition makes sensory analysis a precious tool to assess quality of Pescabivona landraces.

Full-field electroretinograms were recorded from five normal human subjects using white light (mean luminance: 250 cd/m2) sine wave stimuli at different frequencies and contrasts. In agreement with previous studies, we found that the amplitude of the fundamental component displayed a dip at about 12 Hz, coinciding with a maximum in the second harmonic component, indicating frequency doubling of the responses. By including measurements at different contrasts, we were able to recognize two (sine-like and transient) response components. We found that the waveform of the transient response was relatively frequency independent. An algorithm to separate the two components was developed. The interaction between these two components can explain the frequency-doubled responses around 12 Hz. The sine-like component is more linear and prominent in the low-frequency region, whereas the transient seems to be more nonlinear and prominent in the high-frequency region.