Principal Axis Analysis Research Articles

Multiple Flux Rope Events at the High‐Latitude Magnetopause: Cluster/Rapid Observation on January 26, 2001

AbstractFrom 11:10 to 11:40UT on January 26, 2001 the four Cluster II spacecraft were located in the duskside high latitude regions of the magnetosheath and magnetosheath boundary layer (MSBL). During this time Interval the interplanetary magnetic field (IMF) had a negative Bz component. A detailed study on the multiple flux ropes (MFRs) observed in this period is conducted in this paper. It is found that: (1) The multiple flux ropes in the high latitude MSBL appeared quasi‐periodically with a repeated time period of about 78s, which is much shorter than the averaged occurring period (about 8–11min) of the flux transfer events (FTEs) at the dayside magnetopause (MP). (2) All the flux ropes observed in this event had a strong core magnetic field. The axial orientation of the most flux ropes is found to lie in the direction of the minimum magnetic field variance; a few flux ropes had their axes lying in the direction of the middle magnetic field variance; while for the remainders their principle axes could not be determined by the method of Principal Axis Analysis (PAA). The reason that causes this complexity relys on the different trajectories of the spacecraft passing through the flux ropes. (3) Each flux rope had a good corresponding HT frame of reference in which it was in a quasi‐steady state. All flux ropes moved along the surface of the MP in a similar direction indicating that these flux ropes all came from the dawnside low latitude. Their radial scale is 1– 2RE, comparable to the normal diameter of FTEs observed atthe dayside MP. (4) The energetic ions originated from the magnetosphere flowed out to the magnetosheath on the whole, while the solar wind plasma flowed into the magnetosphere along the axis of the flux ropes. The flux ropes offered channels for the transport of the solar wind plasma into the magnetosphere and the escaping of the magnetospheric plasma into the interplanetary space. (5) Each event was accompanied by an enhanced reversal of the dusk‐dawn electric field, which could be identified to be the convective electric field in nature.

Work-Relevant Values Strengthen the Stressor–Strain Relation in Elite Army Units

We examined in this research whether possessing work-relevant values would lead to stronger relations between different types of stressors and outcomes. U.S. Army Rangers completed the Rokeach Value Survey (Rokeach, 1973) and measures assessing work overload, role clarity, and amount of sleep. Rangers also completed measures of job satisfaction, morale, and psychological distress (depression, somatization, and anxiety). Due to the nature of our sample, we concentrated on the instrumental values (ways individuals attain desired states) contained in the Rokeach Value Survey. A principal axis analysis of these values revealed factors reflecting achievement-related values and affiliation-related values. Moderated multiple regressions revealed that Rangers who scored higher on the achievement value evidenced a stronger relation between the following variables: role clarity and job satisfaction, morale, and somatization; work overload and job satisfaction and morale; and between amount of sleep and anxiety, depression, and somatization. Thus, the achievement value moderated eight stressor–strain relations. In contrast, scores on the affiliation value only strengthened the stressor–outcome relation on three occasions. Discussion of the results focuses on how work-relevant values might amplify the impact of work-relevant experiences.

Ring current oxygen ions escaping into the magnetosheath

Storm‐related magnetospheric oxygen bursts were observed in the dayside magnetosheath during the coronal mass ejection on January 10, 1997. These singly charged oxygen ion events exhibited a clear antisunward flow. The oxygen ions are associated with a strong negative interplanetary magnetosheath field (IMF). The average Bz was almost − 50 nT, and the field projection in the x – y plane (GSE) was nearly constant in the Sun/dawn sector forming an angle of 45° relative to the Earth‐Sun axis. The magnetopause was identified as a rotational discontinuity by using the principal axis analysis (PAA) method. The three‐dimensional polar versus azimuthal angle distribution of the oxygen ions showed that the oxygen flow has a north to south velocity component. The observations suggest that the dayside reconnection process is generally steady. The energy dispersion can be explained with the time‐of‐flight (TOF) effect assuming oxygen ions are escaping from the magnetosphere along the reconnected field lines. The lack of hydrogen and helium ions during the observed oxygen bursts can be explained, as only oxygen ions are resupplied by the gradient drift in the inner magnetosphere because of their larger bounce periods with respect to hydrogen and helium ions. Therefore only oxygen ions are observed continuously in the magnetosheath. The estimated oxygen escape rate amounts to 0.61 × 1023 ions/s, about 33% of the input rate of the ring current. The observations imply that the stormtime ring current is asymmetric. A large amount of ring current oxygen ions escape from the magnetosphere into the magnetosheath.

Development and validation of the anger rumination scale

The Anger Rumination Scale was constructed to measure the tendency to focus attention on angry moods, recall past anger experiences, and think about the causes and consequences of anger episodes. Principal axis analysis demonstrated a four factor structure of the scale, which was also supported with a subsequent confirmatory factor analysis. The Anger Rumination Scale was demonstrated to have adequate internal consistency and one month test-retest reliability. The convergent and discriminant validity of the scale were supported by an expected pattern of correlations between the Anger Rumination Scale and the measures of anger experience, anger expression, negative affectivity, emotional attention, satisfaction with life, and social desirability. Normative data is provided for a sample of 408 college-age men and women.

Factor Analysis of the Minnesota Infant Development Inventory Based on a Hispanic Migrant Population

The Minnesota Infant Development Inventory (MIDI), a parental report instrument, was completed for 168 Hispanic migrant workers’infants ranging in age from 1 to 15 months. This study analyzed MIDI scores to determine the extent to which it measures the five domains postulated by its authors. Principal axis analysis with varimax and orthotran rotations was used to obtain pattern coefficients. The scree test and a parallel analysis were used to estimate the proper numbers of factors to extract. Three solutions were presented: (a) a one-factor solution, as indicated by the parallel analysis; (b) a three-factor solution, as indicated by the scree test; and (c) a five-factor solution, as recommended by MIDI’s authors. Based on several considerations (e.g., lack of empirical support for the MIDI five domain scores, parsimony, and ease of use), the one-factor solution was judged best for infants from Hispanic migrant families until future research supports other practices.

Longitudinal Changes in Corneal Asphericity in Myopia

To report the change in shape of the peripheral cornea (asphericity, Q) as it relates to myopia progression in adolescence. Forty-eight subjects with initial ages between 11 and 13 years of age were observed for 5 years. Each subject had participated in a variety of soft contact lens studies and all had worn daily wear soft contact lenses successfully for the 2 years before collection of the second data set. Myopia increased by an average of 1.46 D and was strongly correlated with a 0.56-mm increase in axial length. There was no contribution to the change in myopia from the change in central radius of the cornea. A significant (p < 0.01, one tail) correlation was found between Q and the progression of myopia. Principal axis analysis yielded a slope of -0.04 in Q per diopter of increase in myopia. These data show a shift to a more positive Q (in the oblate direction) with increased myopia.

The personal disturbance scale (DSSI/sAD): structural cross-validation and proposed short forms

The Personal Disturbance Scale (DSSI/sAD) is administered to 132 consecutive first attenders at a psychiatric outpatient clinic in a District General Hospital. The principal components and axis analyses of their item scores are compared with those of Bedford and Deary, 1997[Bedford, A., and Deary, I. J. (1997). The Personal Disturbance Scale (DSSI/sAD): development, use and structure. Personality and Individual Differences, 22, 493–510.]. From the congruent results of both data bases a subset of items is presented to give brief, factorially-purer independent measures of the clinical states of anxiety and depression as opposed to one general psychological distress score. Contrariwise, indication is given as to which items scores should be summated if concern is for a global personal disturbance scale dependent on the type of client group. The Shevlin et al. (1998)[Shevlin, M., Brunsden, V., and Miles, J. N. V. (1998). Alternative factor models of the Personal Disturbance Scale (DSSI/sAD). Personality and Individual Differences, 25, 569–574.] alternative structural equation model of a single factor solution (general psychological distress) is tested and found to be inadequate when applied to these data. However, the Bedford and Deary, 1997nested, three factor model does provide a close and acceptable fit both to this and our previous data set. The question of the balance between psychometric and clinical considerations in determining the length of scales is raised.

Gender, Somatization, and Psychopathic Traits in a College Sample

The structure of psychopathic traits and their association with somatization symptoms were investigated in a sample of 199 undergraduate college students enrolled in introductory psychology classes. Using multiple measures of psychopathic traits, an iterated principal axis (IPA) analysis revealed two dimensions of psychopathy that were similar to ones typically found in forensic samples. One dimension focused on a cold, callous, and unemotional interpersonal style and the second dimension focused on an impulsive and antisocial lifestyle. These two dimensions emerged for both men and women, although the correlation between the two was somewhat higher for men than women. Also, the callous and unemotional dimension was negatively correlated with somatization symptoms, and the impulsive and antisocial dimension was positively associated with somatization symptoms. This pattern of associations was similar for both men and women and it suggests that somatization symptoms may be one aspect of the high rate of negative affectivity experienced by antisocial individuals.

Magnetotail response during a strong substorm as observed by GEOTAIL in the distant tail

Abstract. Simultaneous energetic particle and magnetic field observations from the GEOTAIL spacecraft in the distant tail (XGSM≈ –150 Re) have been analysed to study the response of the Earth's magnetotail during a strong substorm (AE ≤ 680 nT). At geosynchronous altitude, LANL spacecraft recorded three electron injections between 0030 UT and 0130 UT, which correspond to onsets observed on the ground at Kiruna Ground Observatory. The Earth's magnetotail responded to this substorm with the ejection of five plasmoids, whose size decreases from one plasmoid to the next. Since the type of magnetic structure detected by a spacecraft residing the lobes, depends on the Z extent of the structure passing underneath the spacecraft, GEOTAIL is first engulfed by a plasmoid structure; six minutes later it detects a boundary layer plasmoid (BLP) and finally at the recovery phase of the substorm GEOTAIL observes three travelling compression regions (TCRs). The time-of-flight (TOF) speed of these magnetic structures was estimated to range between 510 km/s and 620 km/s. The length of these individual plasmoids was calculated to be between 28 Re and 56 Re. The principal axis analysis performed on the magnetic field during the TCR encountered, has confirmed that GEOTAIL observed a 2-D perturbation in the X-Z plane due to the passage of a plasmoid underneath. The first large plasmoid that engulfed GEOTAIL was much more complicated in nature probably due to the external, variable draped field lines associated with high beta plasma sheet and the PSBL flux tubes surrounding the plasmoid. From the analysis of the energetic particle angular distribution, evidence was found that ions were accelerated from the distant X-line at the onset of the burst associated with the first magnetic structure. Key words. Magnetospheric physics (magnetospheric configuration and dynamics; magnetotail).

Magnetotail response during a strong substorm as observed by GEOTAIL in the distant tail

Simultaneous energetic particle and magnetic field observations from the GEOTAIL spacecraft in the distant tail (XGSM≈ –150 Re) have been analysed to study the response of the Earth's magnetotail during a strong substorm (AE ≤ 680 nT). At geosynchronous altitude, LANL spacecraft recorded three electron injections between 0030 UT and 0130 UT, which correspond to onsets observed on the ground at Kiruna Ground Observatory. The Earth's magnetotail responded to this substorm with the ejection of five plasmoids, whose size decreases from one plasmoid to the next. Since the type of magnetic structure detected by a spacecraft residing the lobes, depends on the Z extent of the structure passing underneath the spacecraft, GEOTAIL is first engulfed by a plasmoid structure; six minutes later it detects a boundary layer plasmoid (BLP) and finally at the recovery phase of the substorm GEOTAIL observes three travelling compression regions (TCRs). The time-of-flight (TOF) speed of these magnetic structures was estimated to range between 510 km/s and 620 km/s. The length of these individual plasmoids was calculated to be between 28 Re and 56 Re. The principal axis analysis performed on the magnetic field during the TCR encountered, has confirmed that GEOTAIL observed a 2-D perturbation in the X-Z plane due to the passage of a plasmoid underneath. The first large plasmoid that engulfed GEOTAIL was much more complicated in nature probably due to the external, variable draped field lines associated with high beta plasma sheet and the PSBL flux tubes surrounding the plasmoid. From the analysis of the energetic particle angular distribution, evidence was found that ions were accelerated from the distant X-line at the onset of the burst associated with the first magnetic structure. Key words. Magnetospheric physics (magnetospheric configuration and dynamics; magnetotail).

Properties of hydromagnetic waves in the polar caps: Ulysses

Properties of the large amplitude Alfvén waves which are a dominant feature of the high latitude solar wind have been studied during the pole-to-pole passage of Ulysses. In addition, an effort has begun to identify magnetosonic waves at high latitude in spite of their expected small amplitude and the presence of the large amplitude Alfvén waves. The power in the latter is essentially the same in both solar hemispheres without evidence of any significant north-south asymmetry. The increased power as Ulysses approached the poles is not, in fact, dependent on latitude but is caused by a power law dependence on distance. The Alfvénicity of the fluctuations, as indicated by the covariance of the field and velocity, increases to high levels (0.8) at high latitudes. Principal axis analyses indicate that the field vector appears to wander randomly over a hemisphere whose radius is the nearly constant field magnitude. This behavior is consistent with a stochastic model introduced by Barnes as demonstrated by a statistical analysis of the field variations observed by Ulysses. The principal axis analysis also shows that the direction associated with the minimum eigenvalue is nearly radial. The strategy for identifying magnetosonic waves involves searching for them in the weak interaction regions accompanying microstreams. Simultaneous variations in the magnetic, kinetic, and total pressures are qualitatively consistent with the presence of magnetosonic waves.

Plasmoids as magnetic flux ropes

Observational constraints on the magnetic topology and orientation of plasmoids is examined using a magnetic field model. We develop a magnetic flux rope model to examine whether principal axis analysis (PAA) of magnetometer signatures from a single satellite pass is sufficient to determine the magnetic topology of plasmoids and if plasmoid observations are best explained by the flux rope, closed loop, or large‐amplitude wave picture. Satellite data are simulated by extracting the magnetic field along a path through our model of a magnetic flux rope. We then examine the results using PAA. We find that the principal axis directions (and therefore the interpretation of structure orientation) is highly dependent on several parameters including the satellite trajectory through the structure. Because of this we conclude that PAA of magnetometer data from a single satellite pass is insufficient to differentiate between magnetic closed loop and flux rope models. We also compare our model results to ISEE 3 magnetometer data of plasmoid events in various coordinate frames including principal axis and geocentric solar magnetospheric. We find that previously identified plasmoid events that have been explained as closed loop structures can also be modeled as flux ropes. We also searched the literature for previously reported flux rope and closed loop plasmoid events to examine if these structures had any similarities and/or differences. The results of our modeling efforts and examination of both flux rope and plasmoid events lead us to favor the flux rope model of plasmoid formation, as it is better able to unify the observations of various magnetic structures observed by ISEE 3.

A comparison of right-wing authoritarianism, conformity and conservatism

Study aims were (a) to test the Altemeyer Right-Wing Authoritarianism Scale (RWAS) for unidimensionality and (b) to compare RWAS with two related Constructs of Conformity and sociopolitical Conservatism. A sample of 339 university students completed all three measures on an 80-item survey form. A principal axis analysis of the 30 RWAS items alone isolated two factors with pro-trait items loading on the first and con-trait items loading on the second factor. Since the two factors correlate 0.40 an underlying higher order dimension is implied. Analysis of the three scales combined disclosed four factors interpretable as Right-Wing Authoritarianism. Freedom of Expression, Conservatism on Military Issues and Political Liberalism. The results indicate that RWAS measures two factors and a slender higher-order dimension.

Factor Structure of the Comrey Personality Scales, the Personality Research Form—E, and the Five-Factor Model

According to McCrae and Costa, Norman's 1963 five-factor model of personality based on peer ratings provides a universal and comprehensive framework for describing individual differences in personality and also for interpreting different personality systems. This study tested the generality and comprehensiveness of the five-factor model using Comrey Personality Scales and Jackson's 1984 Personality Research Form-E. Separate principal axis analyses of scales from each inventory indicated three factors for the Comrey scales and five for the Research Form—E. The three Comrey factors were similar to Agreeableness, Conscientiousness, and Extraversion in the five-factor model, and the five Research Form—E factors were similar to those in the five-factor model. These results provided strong empirical evidence for the generality and comprehensiveness of the five-factor model.

CDAW 8 observations of plasmoid signatures in the geomagnetic tail: An assessment

A primary objective of the Coordinated Data Analysis Workshop 8 (CDAW 8) was the critical assessment of the plasmoid hypothesis. In this study, various types of magnetic phenomena, including closed loops and flux ropes, were considered as candidates for producing the north‐then‐south magnetic field perturbations characteristic of the “plasmoids” observed in the magnetotail by ISEE 3 during the CDAW 8 A and G events. For these two events the principal axis analyses of the magnetic field data and supporting energetic particle and plasma measurements are found to be consistent with the closed‐loop model of plasmoids for which the plane of rotation for B lies near the GSE X‐Z plane and only small field components lie in the minimum variance direction oriented largely along the Y direction. While small pitch angle spiraling of the field lines within these structures such as suggested by Hughes and Sibeck (1987) and Birn et al. (1989) cannot be definitively measured using single‐spacecraft magnetometer observations, the ISEE 3 measurements are not consistent with moderate strength or Venus‐type, strong core field flux ropes. The event A and G plasmoids were preceded by smoothly draped lobe field lines and followed by strong southward fields in the postplasmoid plasma sheet as predicted by the reconnection model of substorms. This latter feature of the observations is consistent with plasmoids moving down the tail, at least in part, due to the Maxwell stress exerted by lobe field lines which were disconnected at the near‐tail neutral line and have draped about the earthward side of the plasmoid. Calculations, based upon typical plasmoid and tail parameters, are presented which indicate that the J×B force associated with these disconnected lobe field lines may be sufficient to accelerate plasmoids up to the speeds observed by ISEE 3. A new characteristic of the plasmoid signature identified in this study is the presence of enhanced internal magnetic fields which can exceed the magnitude of the adjacent lobe fields by as much as 10–20%. While the internal structure of plasmoids remains poorly understood, an extension of the traveling compression region model (Slavin et al., 1984) is proposed to explain these high field regions. Finally, the relationship between the nature of individual substorms and the characteristics of the plasmoids observed in the tail by ISEE 3 is considered. The event A observations suggest that during isolated substorms the magnetotail may undergo an interval of intense reconnection which results in the creation of a single large plasmoid. Extended substorm intervals, exemplified by event G, may produce numerous smaller plasmoids as X lines form in the cislunar tail and retreat tailward while the magnetosphere continues to draw energy from the solar wind. Overall, the energy expended in accelerating the plasmoid down the tail appears comparable to that dissipated in the inner magnetosphere and ionosphere. Additional studies of plasmoid structure and dynamics as a function of substorm activity and distance down the tail should be conducted to determine the general validity of the conclusions reached on the basis of the CDAW 8 events.

Principal axis analysis of gene frequency data.

When a set of populations are compared in respect of gene frequencies, and the chi-square test of heterogeneity is found to be significant, it is pertinent to find out whether the heterogeneity can be explained by a few linear combinations of the gene frequencies, and the total heterogeneity chi-square value can be partitioned as the sum of heterogeneity chi-square values contributed by the linear combinations. The present report describes such a method, and the linear combination that explains the maximum heterogeneity is called the principal axis. An application of this method is presented to find clusters of 31 Mongoloid tribal populations of eastern India using ABO gene frequency data.

Allometric scaling in palaeontology: A critical survey

Allometric scaling models, used to describe morphological and functional relationships between two sets of observations, are examined both in concept and in application. This paper focuses on the underlying assumptions and statistics of the methods most frequently used: linear regression, principal axis and standard major axis analysis. It is shown that the standard major axis (SMA) is the most appropriate bivariate linear model in palaeonotological research. Differences among the models discussed are illustrated by a morphometric analysis of dental dimensions in australopithecines.

Steepened magnetosonic waves at comet Giacobini‐Zinner

We examine intense hydromagnetic waves at comet Giacobini‐Zinner to investigate the mode and direction of wave propagation and thereby provide important constraints on potential mechanisms for wave origin in the vicinity of the comet. The character of the wave polarization changes from basically elliptical far from the comet to almost linear followed by either a rapid partial rotation (less than 360°) or multiple rotations (high‐frequency wave packets) in the vicinity of the bow wave. Simultaneous high‐resolution measurements of electron density fluctuations demonstrate that the long‐period (∼100 s) waves are propagating in the magnetosonic (fast MHD) mode. Principal axis analyses of the long‐period waves and accompanying partial rotations show that the sum of the wave phase rotations is 360°. This indicates that both are parts of the same wave. The change in polarization characteristics near the comet is simply a consequence of wave steepening. From the time sequence of the steepened waveforms observed by ICE, we demonstrate that the waves must propagate in the general direction along the magnetic field toward the Sun with phase velocities less than the solar wind speed. They are consequently blown back across the spacecraft and observed with a left‐hand sense of rotation. All available observations are therefore consistent with wave generation by the right‐hand resonant ion ring instability which predicts waves propagating in the ion beam (solar) direction. Based on the Wu‐Davidson linear growth rate expression, the total convective gain is shown to exhibit a weak (logarithmic) dependence on distance from the comet reaching a maximum of 30 e‐folding in the vicinity of the bow wave. Conditions necessary for the origin of multiple rotations currently are not well understood. Arguments for their being standing whistler waves consisting of a partial rotation plus multiples of 360° rotations are presented. Models of such emissions should be able to explain them as integral parts of the steepened magnetosonic waves. The large amplitudes, ΔB/|B| ∼ O(1), and small‐scale sizes (rotational discontinuities) of the cometary waves suggest that rapid pitch angle scattering and energy transfer with energetic ions should occur. Since the waves are highly compressive, Δ|B|/|B| ≃ O(0.5), one can also anticipate possible first‐order Fermi and gradient B drift acceleration.

Coastal atmospheric forcing in the northern Gulf of Alaska

A comparison of winds over the northern Gulf of Alaska found measured winds to be significantly weaker than calculated geostrophic winds. The latter required more than the standard 30% reduction to correct for frictional effects in the maritime boundary layer. An additional 11% is calculated based on principal axis analysis. A counterclockwise rotation of the instantaneous geostrophic wind vectors of 44° (59° total) beyond the standard 15° was required to align them with those measured at a coastal weather station. However, events in these two wind sets were well correlated throughout the year, and the rotary coherence was significant for frequencies lower than 0.895 cpd. On the basis of empirical orthogonal function analysis, most of the seasonal variability in this coastal current is associated with wind changes. Freshwater discharge is also important in driving the alongshore baroclinic flow and a secondary cross‐shelf flow.

A Simulation Study of Factor Score Indeterminacy

Though factor analysis continues to be one of the most frequently used multivariate techniques, its value has been questioned because of the indeterminacy of factor scores. The authors review the literature on factor score indeterminacy and discuss the implications of indeterminacy for research practice. A simulation experiment is used to investigate the effects of characteristics of the factor analytic data set on the accuracy of factor score estimation. Indeterminacy is found to depend critically on the level of communality and to be detected more accurately via image factoring than by principal axis or principal component analysis.