Principal Axis Method Research Articles

CROSS-CULTURAL VALIDATION OF THE MICHILL ADJECTIVE RATING SCALE (MARS)

Data on the Michill Adjective Rating Scale (MARS) were collected from 413 persons in the United States and 353 persons in Pakistan. The Americans were given the English version and the Pakistanis, the Urdu version of the MARS on which each person rated self and several significant others. The Pearson rs among the 48 MARS items were computed separately for the ratings of self, father, mother, worst teacher, and Mao Tsetung for subjects classified into 10 groups on the basis of their culture, sex, and educational level. The r matrices were analyzed to extract four factors for each of the 10 groups and for each of the five types of ratings by means of the principal axis method. Tucker's coefficients of congruence were computed for each of the 10 groups and for each of the five ratings. Comparison of the coefficients of congruence for the various pairings indicated a reasonable degree of generality in most cases.

Dimensionality of the Body Symptom Questionnaire.

A good deal of recent research on somatic discomfort has employed the Body Symptom Questionnaire of Fisher and Greenberg to quantify the perceived location of the somatic discomfort. Certain formal psychometric properties of the instrument have not yet been established, and it is the purpose of this paper to do so. Specifically, since the independence of the questionnaire scales has not been determined, it is a primary focus of this discussion. A principal axis method of factoring showed that the Body Symptom Questionnaire scales are orthogonal to each other.

DISTRIBUTION AND SPATIAL STRUCTURE OF RETAIL TRAND IN METROPOLISES

Since 1960's studies of the distribution and the spatial structure of retail establishments in metropolises have been carrledi on in Japan, but the classification of retail locations and the spatial structure of retail trade have scarcely been examined. Particularly, there have been few studies on the locational classification of retail shops and the components of spatial retail structure. The aim of the present article, therefore, is to examine the classification of the retail locations and the spatial retail structure in the metropolises, making a comparison of Fukuoka City with Sapporo City. Data used in this article are the number of shops which are classi fied into thirty retail groups derived from the Census of Commerce for 1976 (Table 1), and the areal units (statistic units) are based on the census tracts as of 1975. The results are follows. 1. The results of the calculation of localization coefficients for each retail group in bothh cities reveal that every retail group in Sapporo City is a little more localized than in Fukuoka City, but the distributions of the retail groups in both cities show generally similar patterns. and retails groups are roughly classified into four types (Table 2) . The calculation of the specialization coefficient of each retail group by zones (city core area, built-up area, suburbs, and outer zone) in each city (Table 1) suggests that the locational types of retail shops can be classified into three groups and general food retail. As a result of above two analyses in ref erence to the distribution of retail establishments, it has come to be clear that the locational types of the retail groups in both cities are composed of “centripetal retail groups”, “dispersedd retail groups”, “street-oriented retail groups” and “centrifugal retail groups”. The distributionn of “centripetal retail groups” decreases with the distance from the city core area, while “dispersed retail groups” are found uniformly throughout the city. The distribution of “streetoriented retail groups” is concentrated in the area along the main streets in the suburbs and outer zone, and the distribution of “centrifugal retail groups” (supermarkets) increases with. the distance from the city core area. 2. As a result of grouping the retail stores by the R-mode cluster analysis (Figs. 1 and 2) the linkage tree of the retail groups in Fukuoka City is similar to that in Sapporo City, though the termination of clustering in Sapporo City is earlier than in Fukuoka City, and the similarity in distribution between retail groups is more remarkable in Sapporo City than in Fuku oka City. The grouping of the retail stores in both cities is composed of two main groups (sub-cluster) and five isolated groups (motor vehicle retail, bicycle retail including motorcycle and agricultural articles retail, etc.). The two main groups are follows : “centripetal retail groups” (i.e. department store, ladies' and children's dress retail, and glass and ceramics, retail, etc.), and “dispersed retail groups” (i.e. sea food retail, vegetable and fruit retail and hard and kitchen-ware retail, excluding agricultural equipments, etc.). 3. The spatial retail structures in both cities were examined by the use of the factor analysis (principal axis method). As a result, four dominant factors with eigenvalue greater than 1.00 were extracted in Fukuoka City and two in Sapporo City (Table 3). The first and second factors in Fukuoka City are similar to those in Sapporo City, and these two factors which are labelled as “higher central function” and “ubiquitously located function”, respectively are main components which yield the locational differentiation of retail establishments in both cities. On the other hand, however, there are some other retail groups which don't correspond to this factor structure.

The barrier to internal rotation of the methyl group in methyl thiolformate from microwave spectroscopy

Some low- J μ a R-branch lines of the E torsional substate of the ground vibrational state of methyl thiolformate were assigned. Calculations using the Internal Axis Method (IAM) and the Principal Axis Method (PAM) reproduce the observed line frequencies within a few MHz. The barrier to internal rotation of the methyl group is determined to be 1.78 ± 0.03 kJ mole −1.

Acetic acid: Microwave spectra, internal rotation and substitution structure

The internal rotation splittings in the microwave spectrum of acetic acid have been re-examined, using both principal axis method (PAM) and internal axis method (IAM) treatments. It is shown how individual terms in the PAM equation can be correlated to the first terms in an expansion of the corresponding IAM formula. When centrifugal distortion was allowed for, both methods reproduced the A-type frequencies within experimental error. For the E-type lines the r.m.s. deviation was 1.64 MHz in the PAM (using W vσ ( n) -terms with n = 1, 2, …, 14, d, e, f) and 0.70 MHz in the IAM. To derive the substitution structure eight isotopic species were studied. The inertial moments of the molecules with various degrees of methyl group deuteration are not consistent with each other, so these data could not be fully used. Therefore, the structure was derived with the assumption of a cylindrically symmetric methyl group, although there is some evidence that the HCH angles differ by a few degrees. The geometry, which is in agreement with earlier electron diffraction results, is compared with the substitution structures of other carboxylic acids.

Is the state-trait anxiety inventory multidimensional?

The factor structure of the State-Trait Anxiety Inventory (STAI) was investigated to determine whether the STAI State and Trait Anxiety scales were multidimensional. The STAI (Form Y) was administered to a heterogeneous sample of Air Force recruits ( N = 1728); the scores for all 40 STAI items were factor-analyzed together, using the principal axis method and varimax rotation. Two- and four-factor solutions were found to be equally good in simple structure and psychological meaningfulness. Clearly defined state and trait anxiety factors were found in the more parsimonious two-factor solution. In the four-factor solution, the factors were: State Anxiety-Present, State Anxiety-Absent, Trait Anxiety-Present and Trait Anxiety-Absent. Using Cattell's (1966) confactor method, these factors were found to be congruent with similar factors previously identified for high school students by Spielberger et al. (1980). The anxiety-present and anxiety-absent factors were interpreted as reflecting either ‘item method’ variance or ‘item-intensity specificity’. There was no evidence in the present study that the STAI scales were multidimensional in terms of item content.

Principal axis analysis of dental attrition data

AbstractThe principal axis method is an age independent analysis method for dental attrition data which avoids many problems associated with earlier methods of analysis, correlation and regression. A principal axis equation is determined from the scatter of M1 on X and M2 on Y, and the slope of the equation can be used to indicate rate of wear. High slopes indicate rapid rates of wear. Because rate of wear rather than degree of wear is the parameter of interest, the procedure is age independent. Confidence regions can be calculated to test the distinctness of the slopes. Dental data from three Amerind skeletal samples, Indian Knoll, Hardin Site and Campbell Site, are used to illustrate the technique. Because least squares fits such as the principal axis solution are strongly influenced by the magnitude of variance in the data, two different methods of ordinal data collection are used in this test: Molnar's 1–8 and Scott's 4–40 scales. The Scott scoring system provides more satisfactory results when used in the principal axis analysis technique because of smaller confidence regions. The testing of the technique on other samples is urged.

Higher-Order Personality Factors Of The ISI.

To determine the higher order factors defined by scales of the Interpersonal Style Inventory (ISI), data from two male samples and from one female sample were separately analyzed. Intercorrelations of 14 of the scales were analyzed by the method of principal axes. The five rotated factors established were highly similar across samples. They were interpreted as Socialized vs. Unsocialized, Interpersonally Involved vs. Withdrawn, Autonomous vs. Conforming, Controlled vs. Spontaneous, and Stable vs. Anxious. The findings are compared to constructs established in the PRF and 16 PF.

Microwave spectrum, structure, dipole moment and centrifugal distortion of nitrosomethane. Dipole moment of acetaldehyde

The microwave spectra of ten isotopic species of nitrosomethane have been measured enabling structures for CH3NO and CD3NO to be determined independently. The mean of these structures is found to be : NO = 1.211, C—N = 1.480, C—Hi(in plane)= 1.094, C—H0(out-of-plane)= 1.094 A, ∠CNO = 113.2, ∠HiCN = 111.0, ∠H0CN = 107.2 and ∠H0CH0= 109.2°. The methyl group is tilted by 2.5° away from the oxygen atom. The orientation of the dipole moment in nitrosomethane has been determined from isotopic measurements. For CH315NO, higher order Stark perturbation terms, arising through an accidental near degeneracy, had to be included to obtain an accurate dipole moment. The components of the dipole moment are; µa= 2.262, µb= 0.516 and µ= 2.320 ± 0.004 D. The orientation of the dipole moment in the related molecule acetaldehyde has been determined from isotopic work and previous Stark effect measurements have been refined to give µa= 2.537, µb= 1.062 and µ= 2.750 ± 0.006 D. A, E splittings in the microwave spectra of CH3NO and CD3NO have been analysed by both the principal axis method (PAM) and the internal axis method (IAM) for a rigid top–rigid frame model. An attempt to fit the spectrum of CD3NO was made using Woods' IAM treatment in conjunction with Watson's centrifugal distortion theory. More precise distortion constants were then obtained from the spectra of sym-CH2DNO and sym-CHD2NO and used to determine a preliminary harmonic force field for nitrosomethane. A few perturbations in the spectra of the symmetric species have been observed due to sym–asym interactions. The structure, bonding and vibrational properties of nitrosomethane are discussed.

A Study on the Techniques of Nodal and Functional Regionalization

Several methods for the regionalization of nodal and functional regions and the classification of hierarchical orders of central places have been developed recently. In order to understand clearly the characteristics of each of the following five methods the writer conducted such a study by using data for telephone calls among 66×66 areas in the Chugoku District, Southwestern Japan.The main results are summarized as follows:(a) Direct connection method. This method has been generally used to demarcate the tributary areas of central places and to classify the hierarchical order by analysing only the nodal flows without considering the indirect flows for each place. The regionalization using this method was not satisfactory, because telephone districts as a basic unit of the analysis were often established artificially. It seems better to rank the order of each place while comparing with the central place of the highest order, Hiroshima, in the research area.(b) Graph theory method. In this method as it was used by Nystuen and Dacey indirect flows were added to the analysis basing on the graph theory. However, some problems, like the mathematical assignment of indirect flows to each route and the indefiniteness of indirect connection, are encountered in considering the volume of total association for each area. Again, with this method as with the direct connection method, there are some problems in the hierarchical ordering of central places, because only the largest flows are utilized. However, since the analyses of both matrices B'(=Y+Y2+Y3) and B arrived at the same result, the usefulness of matrix B analysis was verified, In addition, Fig. 2 which shows the distribution of nodal regions analysed by this method, was almost the same as Fig. 1 which shows the regionalization by the direct connection method.(c) Functional distance method. This method is used to measure the accessibility between each area by using mean first passage time (MFPT), to classify nodal and functional regions and to clarify the hierarchical structure of central places. The regionalization of nodal regions by the cluster analysis among places of origin in the matrix of MFPT is similar to that analysed by the direct connection and graph theory methods, except for a tendency toward the isolation of one or two remote rural areas from the main groups (Fig. 5). On the other hand, the hierarchical ordering of each area by the cluster analysis among places of destination in the matrix of MFPT as well as among column vectors of average MFPT did not correspond to the central place order because they do not measure the centrality of places but the accessibility itself within the research area. In addition, many of the higher order centres were integrated to one group contrary to Christaller's theory.Moreover, since the elements of standardized column vectors of MFPT have no tendency to be extremely low to the neighbouring area of large central cities the neighbouring effect of functional distance is emphasized for the nodal regionalization using shortest functional distance and the nodal regions for large central cities tend to be delimited narrowly (Fig. 6).(d) Factor analysis method. Factor analysis (principal axis method with varimax rotation) as well as the functional distance method extracts functional regions based on the similarity of the patterns of places of origin or destination. Since the origin-destination matrix contains many zero values it is necessary for the factor analysis to approach the normal distribution by some means of transformation. In Fig. 7, which shows the spatial distribution of areas with factor loadings over 0.5 and standardized factor scores over 1.0 for each factor within 13 factors extracted by R-method, some partial overlappings occur to functional regions of small factors.

A COMPREHENSIVE FACTOR ANALYSIS OF PERSONALITY QUESTIONNAIRE ITEMS: A TEST OF TWENTY PUTATIVE FACTOR HYPOTHESES

The purpose of the present study was to evaluate twenty putative factor hypotheses (PFH's) of personality using various rotation methods, both orthogonal and oblique. In order to obtain a representative item pool, the literature was surveyed, with special attention to factor analytic studies. The test sources provided 1726 non-repeated items, from which 400 items, representing 20 PFH's, were selected. A balanced questionnaire consisting of items reworded for general consistency of presentation and answer format was administered to a cross-continent sample from which 1003 complete data sets were obtained. Factoring of 401 variables was carried out by principal axis method followed by four rotation procedures: two orthogonal, two oblique. Results across the various solutions indicated the following factors: Sociability (SY), Adjustment-Emotionality (AE), Dominance (AD), Superego (SG), Hypochondriac-Medical (HM), Impulsiveness (IP), Cooperativeness-Considerateness (CC), Inferiority (IF), Persistence (PS), Trust vs. Suspicion (TS), General Activity (GA). In addition, other factors were found, which although of lesser variance, have been reported in the literature.

PAM analysis of the microwave spectra of thioacetic acid, CH 3COSH and CH 3COSD

The microwave spectra of two isotopic species of thioacetic acid, CH 3COSH and CH 3COSD, have been studied. Using the principal axis method (PAM), including terms through n = 6 in the perturbation series and the denominator correction, the spectra were analyzed and 45 lines for CH 3COSH and 40 lines for CH 3COSD were assigned. The parameters obtained by the least-squares analysis are A = 9913.29 ± 0.56 MHz, B = 4923.11 ± 0.23 MHz, C = 3354.60 ± 0.24 MHz, θ = 57.080 ± 0.030°, s = 6.2980 ± 0.0012, and I α = 3.198 ± 0.020 amu A ̊ 2 for CH 3COSH, and A = 9662.80 ± 0.78 MHz, B = 4810.74 ± 0.26 MHz, C = 3273.92 ± 0.18 MHz, θ = 55.097 ± 0.024°, s = 5.9742 ± 0.0016, and I α = 3.171 ± 0.020 amu A ̊ 2 for CH 3COSD. The barrier to internal rotation of the methyl group is V 3 = 222.6 ± 1.4 cal/mole for CH 3COSH and V 3 = 212.9 ± 1.4 cal/mole for CH 3COSD. The Stark effect measurements of A species transitions for CH 3COSH led to the dipole moment μ = 1.821 ± 0.013 D with the components μ a = 0.191 ± 0.010 D and μ b = 1.811 ± 0.013 D.

Student attitudes toward language, learning, and language learning

The purpose of this study was to discover student attitudes toward language, learning, and language learning. The subjects were 155 entering first year students, women and men aged 18–24, enrolled in a program leading to a B.A. in English at the University of Isfahan, Isfahan, Iran. A questionnaire of 50 statements concerning language, its nature and functions, and learning, particularly language learning, based on a five-point scale, was given by teachers in the classroom during 1974. A Pearson product-moment coefficient of correlation was computed. The matrix was factor analyzed by the principal axis method and then rotated to varimax criteria. Twelve factors were extracted. The attitudes of the students are pragmatic, informal, and somewhat unformed, but they demonstrate a sophistication developed by experienced language learners. These attitudes seem generally favorable to foreign language learning, with the exception of two factors. Students place a strong reliance on vocabulary memorizing as a way of learning to comprehend language. They also fail to grasp the importance of syntax in the comprehension of language, especially reading comprehension. The study suggests that students and teachers might well give some time to the consideration of concepts of language and language learning.

The Microwave Spectrum of anti-Acetaldehyde Oxime-d

Abstract The microwave spectrum of anti-acetaldehyde oxime-d was investigated in the frequency region from 9 to 36 GHz. The rotational transition lines widely split into the A and E species due to the tunneling of the methyl group through the low potential barrier hindering the internal rotation. The transition lines belonging to the A species were fitted to the rigid rotor Hamiltonian, and the following effective rotational constants in MHz were obtained: AA=17250, BA=6284.33, and CA=4704.96. All the observed transition frequencies were fitted to the Hamiltonian containing perturbation terms to the fourth order in order to obtain the internal-rotation parameters using the principal axis method. The potential barrier, V3, hindering the internal rotation was determined to be 373 cal mol−1. The dipole moment was determined to be 0.828 D from the Stark effect of the transitions belonging to the A species.

Effective hamiltonian and effective dipole operator in the principal axis method (PAM)

An alternative to ‘denominator corrections’ is developed using a recently published projector formulation of the Van Vleck transformation. The allowedness of torsional transitions in PAM-type molecules is attributed to higher-order terms in the dipole operator originating from the Van Vleck transformation. A formula which predicts a weak dependence of the molecular dipole moment on the torsional state is obtained. Acetaldehyde is considered as an example.

The Factorial Structure of Responses to Conceptual Complexity

A series of figures differing in complexity were exposed to 44 nursing students. Ss were monitored for GSR and heart rate while they looked at each figure for as long as they wished. They then rated each figure on 20 semantic differential-type scales. The data were factor analyzed by the principal axis method, with communalities iterated by refactoring followed by varimax rotation. Four factors were extracted and the first three were identified as Osgood’s activity, evaluative, and potency factors. It was suggested that the activity factor relates to arousal-raising stimulus properties, while the evaluative factor relates to arousal-reducing or -restraining stimulus properties.

A CLASSIFICATION OF MUNICIPALITIES IN HIROSHIMA PREFECTURE WITH USING MULTIVARIATE ANALYSIS

The regionalization approach which has been integrated by various criteria has been one of the major subjects for regional geography. Nowadays, with the remarkable devel-opment of quantitative geography, it has often been re-examined in various regions by a new method. The purpose of the present paper is to classify, as objectively as possible, the municipalities in Hiroshima Prefecture with the analyses of their demographic and socio-economic characteristics and their population changes, and also to make clear the regional structure. The main results are summarized as follows: 1) Examined the factor analysis (principal axis method) with 57 variables which refer to the regional characteristics such as population, household, age structure, migration, occupational-industrial structure, educational level, housing conditions, standard of living and so on (Tab. 1), the writer extracted nine factors by the rotation of factors with eigen value over unity and considered the highest three as main factors in detail. They can be labelled as urbanity, blue collar worker and suburban area factors. The urbanity factor which explains about 40 per cent of total variance is the primary factor. It seems that the occurrence of such a large first factor mainly stems from regional properties of Hiroshima Prefecture where the large regional capital, Hiroshima City, is sharply confronted with mountainous area of conspicuous depopulation. The writer assumes, however, that, if a similar analysis may be conducted in any prefecture of Japan, the urbanity factor would appear as the first factor. Because the improvement of rural life may be less effective due to the strong outflows of migration from country to large cities so that the spatial difference of life between rural and urban areas, especially large cities, may exist still obviously. 2) The spatial distribution of factor score for the urbanity factor shows a remarkable contrast between the coastal cities and the rural areas of inland and islands. A typical depopulation area such as Chugoku Mountains, Jinseki Plateau and Sera Upland records especially low values. These results coincide with the fact recognized in certain previous geographical surveys, too. The loading value of each variable for blue collar worker factor (explained 11 per cent) has shown similar tendency to that of the first factor and seems to be a sub-dimension of it. Therefore, this score distribution is also similar to it. Contrary to these two factors, the factor score of suburban area factor (explained 7 per cent) shows the highest values in the suburban area of Hiroshima City and is relatively high in its outside zone. A noticeable fact is that the highest value zone does not occur in the vicinity of Fu-kuyama City. On the other hand, the factor score of coastal cities as well as island and remote inland area is very low (Fig. 2abc) . The reason why coastal cities record low values, however, may be different from that of islands and inland area. 3) From the factor analysis about population change from 1920 to 1975 for each five year period which totalled 11 periods, th three factors were extracted. They represent the rapid economic growth period after 1960, the pre-war period, the convulsion period in wartime and post war period respectively (Tab. 4). It is noticeable that the population change rate between 1920 and 1925 is considerably similar to that of the convulsion period. In addition, the spatial pattern of the population change for pre-war time tends to be largely different each other compared with the population change of each five year period after 1960 (Tab. 5).

Microwave spectrum, conformation, barrier to internal rotation and dipole moment of pyruvic acid

Microwave spectra of CH 3COCOOH and CH 3COCOOD are reported. The preferred conformation of the molecule is demonstrated to possess a planar HCCOCOOH skeleton with two out-of-plane hydrogens. The two carbonyl groups are trans to each other and a weak five-membered hydrogen bond is formed between the carboxyl group hydrogen atom and the carbonyl group oxygen atom. The methyl group conformation is discussed. A computer programme based on “the principal axis method” is described in some detail and the results of a least squares analysis of the observed spectra are outlined. The barrier to internal rotation was determined as V 3 = 965±40 cal mol −1 for both isotopic species. Stark effect measurements yielded μ a = 2.27±0.02 D, μ b = 0.35±0.02 D and μ tot = 2.30±0.03 D for the dipole moment and its components along the principal axes.

Multivariate Analysis of Subjective and Physical Measures of Hall Acoustics

The purpose of this study is (1) to examine whether the differences of sound-field qualities among seats in a music hall are accountable by a kind of multivariate procedure, (2) to examine whether subjective characteristics of several music halls are comparable with this technique, and (3) to propose a new method to estimate sound-field characteristics of music halls from physical terms, in place of words used in conventional techniques. Experimental procedures: (1) First, program sources are recorded in an anechoic room, and those sources are reproduced through a omnidirectional loudspeaker system on the stage of a music hall, Yamaha Music Camp. Those reproduced sounds are recorded stereophonically at each seat. (2) Then the hearing tests for those reproduced sources are carried out with dynamic receivers in a sound-proof room. (3) At the same time acoustic characteristics of the room such as percent-articulation, directional diffusivity, definition, reverberation time, transmission characteristics, SPL variation, etc., at the respective seat are measured. Subjective characteristics were first analyzed by multidimensional scaling (MDS), which yielded three orthogonal factors. Then, principal axis method (PAM) was applied to the correlation matrix of these factors and the physical measurements. The results were that three factors were extracted by PAM; the first represents SPL level, the second reverberation time or definition, while the third is not interpreted. An interpretation of these subjective characteristics in terms of physical measurements is proposed.

性格表現用語580語の意味類似による多因子解析から作られた性格の側面

In the previous study (Aoki, 1971a) 455 personality trait words were selected and classified into 17 categories on the basis of their meanings. In the present study, in addition to the 455 trait words, 125 new trait words were added, and therefore, a total of 580 trait words were reclassified into 11 categories for the purpose of factor analysis.Subjects (Ss) were 107 male adults, aged 35 to 45. Each S was given two categories, each containing 49 to 63 words. Instructions given to the Ss were like the following: “The purpose of this study is to find out what words people commonly use to describe a characteristic of person. You will be given a list of words. Your task is to judge mutual similarities of meanings among these words and to select from the same list similar words for each word as many as you can. For example, when you were given the word “kind”, you might respond with such words as generous, friendly, tender, sympathetic, warm-hearted, and so on. The words are to be written to the right of the given word. This procedure will be continued through all the words in each category.All legible responses made by each S were tallied separately for each of the 11 categories. This procedure permitted an assessment of relative frequency of responses to the various words within each category. For each category the responses in terms of relative frequency were factor analysed by the principal axis method with geometric rotation (Kashiwagi, 1965). Four to six factors were extracted for each category, bringing the total to 57.From these results a set of 236 trait words was assembled. The set consisted of 57 trait words which had the highest loading for each obtained factor, plus 179 which did not fall into either obtained factor, having lower loadings than .15. In order to construct personality aspects from this set, the words were paired as many as possible in such a way that each word would have an antonym. 63 paired personality aspects were tentatively constructed and compared with Cattell's 42 spheres (1957) and Miyagi's 35 scales (1969). On the basis of this comparison, 66 personality aspects were finally determined.