A new model for simultaneous component analysis (SCA) is introduced that contains the existing SCA models with common loading matrix as special cases. The new SCA-T3 model is a multi-set generalization of the Tucker3 model for component analysis of three-way data. For each mode (observational units, variables, sets) a different number of components can be chosen and the obtained solution can be rotated without loss of fit to facilitate interpretation. SCA-T3 can be fitted on centered multi-set data and also on the corresponding covariance matrices. For this purpose, alternating least squares algorithms are derived. SCA-T3 is evaluated in a simulation study, and its practical merits are demonstrated for several benchmark datasets.

Given two matrices, A and B, each with n rows, and with p and q columns, respectively, a very common goal is the comparison of these matrices in a subspace of dimension s, 1 ≤ s ≤ min p, q. That is, assuming linear mappings of A and B into the subspace, the comparison involves the choice of two transformation matrices L and M of dimensions p by s and q by s, respectively, and the subsequent comparisons of the images AL and BM in some fashion.

Concise formulas for the asymptotic standard errors of component loading estimates were derived. The formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations. The formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances/correlations is available. The estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices.

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. “Simple structure” is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.

This paper considers the reflection unidentifiability problem in confirmatory factor analysis (CFA) and the associated implications for Bayesian estimation. We note a direct analogy between the multimodality in CFA models that is due to all possible column sign changes in the matrix of loadings and the multimodality in finite mixture models that is due to all possible relabelings of the mixture components. Drawing on this analogy, we derive and present a simple approach for dealing with reflection in variance in Bayesian factor analysis. We recommend fitting Bayesian factor analysis models without rotational constraints on the loadings—allowing Markov chain Monte Carlo algorithms to explore the full posterior distribution—and then using a relabeling algorithm to pick a factor solution that corresponds to one mode. We demonstrate our approach on the case of a bifactor model; however, the relabeling algorithm is straightforward to generalize for handling multimodalities due to sign invariance in the likelihood in other factor analysis models.

It has been shown by Kaiser that the sum of coefficients alpha of a set of principal components does not change when the components are transformed by an orthogonal rotation. In this paper, Kaiser's result is generalized. First, the invariance property is shown to hold for any set of orthogonal components. Next, a similar invariance property is derived for the reliability of any set of components. Both generalizations are established by considering simultaneously optimal weights for components with maximum alpha and with maximum reliability, respectively. A short-cut formula is offered to evaluate the coefficients alpha for orthogonally rotated principal components from rotation weights and eigenvalues of the correlation matrix. Finally, the greatest lower bound to reliability and a weighted version are discussed.

Correspondence analysis (CA) is a statistical method for depicting the relationship between two categorical variables, and usually places an emphasis on graphical representations. In this study, we discuss a CA formulation based on canonical correlation analysis (CCA). In CCA-based formulation, the correlations within and between row/column categories in a reduced dimensional space can be expressed by canonical variables. However, in existing CCA-based formulations, only orthogonal rotation is permitted. Herein, we propose an alternative CCA-based formulation that permits oblique rotation. In the proposed formulation, the CA loss function can be defined as maximizing the generalized coefficient of determination, which is a measure of proximity between two variables. Simulation studies and real data examples are presented in order to demonstrate the benefits of the proposed formulation.

The Procrustes criterion is a common measure for the distance between two matrices X and Y, and can be interpreted as the sum of squares of the Euclidean distances between their respective column vectors. Often a weighted Procrustes criterion, using, for example, a weighted sum of the squared distances between the column vectors, is called for. This paper describes and analyzes the performance of an algorithm for rotating a matrix X such that the column-weighted Procrustes distance to Y is minimized. The problem of rotating X into Y such that an aggregate measure of Tucker's coefficient of congruence is maximized is also discussed.

This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.

Bioethics education in residency helps trainees achieve many of the Accreditation Council for Graduate Medical Education milestones and gives them resources to respond to bioethical dilemmas. For this purpose, The Providence Center for Health Care Ethics has offered a robust clinical ethics rotation since 2000. The importance of bioethics for residents was highlighted as the COVID-19 pandemic raised significant bioethical concerns and moral distress for residents. This, combined with significant COVID-19-related practical stressors on residents led us to develop a virtual ethics rotation. A virtual rotation allowed residents flexibility as they were called to help respond to the unprecedented demands of a pandemic without compromising high quality education. This virtual rotation prioritized flexibility to support resident wellbeing and ethical analysis of resident experiences. This article describes how this rotation was able to serve residents without overstraining limited bandwidth, and address the loci of resident pandemic distress. As pandemic pressures lessened, The Providence Center for Health Care Ethics transitioned to a hybrid rotation which continues to prioritize resident wellbeing and analysis of ongoing stressors while incorporating in-person elements where they can improve learning. This article provides a description of the rotation in its final form and resident feedback on its effectiveness.

Nebraska is one of the top five corn-growing states in the United States, with the planting of corn on 3.5 to 4 million hectares annually. Harvest loss of corn results in volunteer corn interference in the crop grown in rotation. Estimating the extent of harvest loss and expected volunteer corn density is a key to planning an integrated volunteer corn management program. This study aimed to evaluate the harvest loss of corn and estimate the potential for volunteerism. Harvest loss samples were collected after corn harvest from a total of 47 fields in six counties, including 26 corn fields in 2020, and 21 fields in 2021, in south-central and southeastern Nebraska. An individual cornfield size was 16 to 64 ha. A total of 16 samples were collected from each field after corn harvest in 2020 and 2021. Harvest loss of corn was 1.5% and 0.7% of the average yield of 15,300 kg ha−1 in 2020 and 2021, respectively. Corn harvest loss was 191 and 80 kg ha−1 from dryland fields, and 206 and 114 kg ha−1 from irrigated fields in 2020 and 2021, respectively. An average kernel loss of 68 and 33 m−2 occurred in 2020 and 2021, respectively. The germination percentage of corn kernels collected from harvest loss was 51%, which implies that volunteer corn plants of 35 and 17 m−2 from 2020 and 2021, respectively, could be expected in successive years. A volunteer corn management plan is required, because if it is not controlled, this level of volunteer corn density can cause yield reduction depending on the crop grown in rotation.

During the last decade, our understanding of stellar physics and evolution has undergone a tremendous revolution thanks to asteroseismology. Space missions such as CoRoT, Kepler, K2, and TESS have already been observing millions of stars providing high-precision photometric data. With these data, it is possible to study the convection of stars through the convective background in the power spectrum density of the light curves. The properties of the convective background or granulation has been shown to be correlated to the surface gravity of the stars. In addition, when we have enough resolution (so long enough observations) and a high signal-to-noise ratio (SNR), the individual modes can be characterized in particular to study the internal rotational splittings and magnetic field of stars. Finally, the surface magnetic activity also impacts the amplitude and hence detection of the acoustic modes. This effect can be seen as a double-edged sword. Indeed, modes can be studied to look for magnetic activity changes. However, this also means that for stars too magnetically active, modes can be suppressed, preventing us from detecting them.

In this talk, I will present some highlights on what asteroseismology has allowed us to better understand the convection, rotation, and magnetism of solar-like stars while opening doors to many more questions.

Stellar activity depends on multiple parameters one of which is the age of the star. The members of open clusters are good targets to observe the activity at a given age of the stars since their ages are more precisely determined than that of field stars. Choosing multiple clusters, each with different age, gives us insight to the change in activity during the lifetime of stars. With the analysis of these stars we can also refine the parameters of gyrochronology (Barnes 2003), which is a method for estimating the age of low-mass, main sequence stars from their rotation periods.

Mercury is locked in an unusual 3:2 spin-orbit resonance and as such is expected to be in a state of equilibrium called Cassini state. In that state, the angle between the spin axis and orbit normal, called obliquity, remains almost constant while the spin axis remains almost in the plane, also called Cassini plane, defined by the normal to the Laplace plane and the normal to the orbital plane. The spin axis and the orbit normal precess together with a period of about 300 kyr. The orientation of the spin axis of Mercury has been estimated using different approaches: (i) Earth-based radar observations, (ii) Messenger images and altimeter data, and (iii) Messenger radio tracking data. The different estimates all tend to confirm that Mercury occupies the Cassini state. The observed obliquity is small and close to 2 arcmin. It indicates a normalized polar moment of inertia of about 0.34. This information, combined with the existence of a liquid iron core, as evidenced by the librations, allows to constrain the interior structure of Mercury. However, the different estimates of the orientation of the spin axis locate the spin axis somewhat behind or ahead of the Cassini plane, and it is difficult to reconcile and interpret them coherently in terms of detailed interior properties. We review recent models for the obliquity and spin orientation of Mercury, which include the effects of complex orbital dynamics, tidal deformations and associated dissipation, and internal couplings related to the presence of fluid and solid cores. We discuss some implications regarding the interpretations of the orientation estimates in term of interior properties.

This paper reviews our current knowledge about pulsating chemically peculiar (CP) stars. CP stars are slowly rotating upper main-sequence objects, efficiently employing diffusion in their atmospheres. They can be divided into magnetic and non-magnetic objects. Magnetic activity significantly influence their pulsational characteristics. Only a handful of magnetic, classical pulsating objects are now known. The only exceptions are about 70 rapidly oscillating Ap stars, which seem to be located within a very tight astrophysical parameter space. Still, many observational and theoretical efforts are needed to understand all important physical aspects and their interrelationships. The most important steps to reach these goals are reviewed.