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After discussing the similarities and differences between covariance structural analysis and exploratory factor analysis, the relative superiority of the former is shown both for the generation, as well as for the testing of the hypothesis. Covariance structural analysis provides an objective axiomatic approach for the testing of structural hypotheses because, unlike exploratory factor analysis, it presupposes an explicit prior formulation of the hypothetical partitioning of data into factors. The two techniques are also compared in terms of scientific parsimony and the interpretation of results. It appears that though covariance structural analysis is more promising than exploratory factor analysis in theory building, a systematic joint use of both may lead to a more meaningful interpretation of intercorrelation data than can be reached by factor analysis alone.

An approach to the analysis of multivariate time series is presented in which linear structural relationships among multiple stochastic variables are investigated. A number of alternative structural models are considered for the case of two stochastic variables. Each model represents a possible hypothesis concerning the relationship of growth in one variable to growth in the second. Both symmetric and asymmetric models are considered. Extensions of two of the models to three variables are illustrated by means of a numerical example. Implications of the models for the problem of detecting change in multivariate time series are discussed.

4 different procedures are commonly employed with sample data to reduce a set of predictor variables. In the present study these procedures were repeatedly applied to computer-simulated samples to provide comparative data pertaining to two questions: (a) Which procedure can be expected to produce an equation that yields the most accurate predictions for the population? (b) Which procedure is most likely to identify the optimal set of independent variables? The samples were drawn from 12, mathematically defined, multivariate normal populations. Each population consisted of 1 criterion and 10 predictor variables. Five or fewer independent variables constituted the optimal set in each case. With respect to both questions small differences among the procedures were observed. However, the forward selection and stepwise procedures consistently produced more favorable results than the 2 backward elimination procedures. The question of the number of sampling units to use is discussed.

In a variety of problems, it is desirable to have a single coefficient summarize the causal effects of a set of variables when other variables are controlled. The "sheaf coefficient" presented here does this and can be employed meaningfully in the context of path analysis models.

The factor analysis model is rewritten as a system of linear structural relations with errors in variables. The method of instrumental variables is applied to this revised form of the model to obtain estimates of the factor loading matrix. The relation between this method and interbattery analysis, proportional profile analysis, and canonical factor analysis is pointed out. In addition, an estimation procedure based on replicated sampling different from proportional profile analysis is given.

Two multivariate statistical methods, factor analysis and canonical analysis, are compared on selected statistical concepts and an example is presented illustrating differences in interpretation arising from the use of the two methods. Only one factor analytic model is considered, this being the principal factor solution based upon the theory of principal components. A review of the statistical theory reveals that both methods call for the solution of characteristic equations to obtain the coordinate system which exhibits the correlations among multiple variables. They differ in the partitioning of the variables into sets, in the scalar quantity to be maximized in solving the characteristic equations, and in the linear regression models. An empirical example is presented to illustrate possible effects of these statistical differences on the interpretation of data. The illustration suggests that factor analysis may be more appropriate for hypothesis generating and exploratory studies, while canonical analysis should have wider application in research involving hypothesis testing and prediction.

A method is indicated by which multiple factor analysis may be used in determining a number,r, and then in selectingr “predicting” variables out ofn variables so that each of the remainingn-r variables may be predicted almost as well from ther variables as it could be predicted from all then—1 variables.

Factor analysis has been traditionally utilized for three broad purposes: First, as a data reduction technique which will hopefully simplify a multivariate situation to a smaller set of dimensions and enable the researcher to utilize data on a large number of variables; second, as an indexing device in which overtly manifested data are transformed to provide the latent or unobservable trait of a phenomenon; finally, as a cluster technique which helps the researcher to classify a variety of observations into a small set of clusters which are also generally ordered. All three approaches have used a common starting point, namely, a matrix of correlations either among the variables (R type factor analysis) or among the observations (Q type factor analysis). In other words, factor analysis has been limited to associative relations. The same technique can be used in functional relations, especially to estimate parameters of all linear and several nonlinear functions. It, therefore, essentially seems to...

Explicit formulas are derived for the asymptotic sampling variances and covariances of the maximum likelihood estimators for factor-analysis parameters in the special case where there is just one common factor. The effect of the number of variables on these variances and covariances is indicated. A formula is given showing to what extent the usual covariance between two of a set of variables can be estimated more efficiently when there is known to be just one common factor. (Author)

Purpose: Since 2000, the Korea University Medical College has conducted Comprehensive Basic Medical Sciences Examination as a summative test. Summative assessment must be dependable in that it meets the highest standards of reliability and validity. The purpose of this study were to examine the validity and reliability of Comprehensive Basic Medical Sciences Examination and to improve the quality of the examination. Methods: The subject of this study was the examination materials and scores of the test. We conducted exploratory factor analysis to testify validity. Cronbach a coefficient was used to examine the reliability. Results: Only one factor was extracted from exploratory factor analysis. Its eigen value was 4.61 and it explained 65.93% of total variance. We could infer the extracted factor as an ability of basic medical sciences knowledge. The reliability coefficient of the test was ranged from 0.45 to 0.74. Of the total 335 item, overall acceptable items were 206 (58.0%); the range of difficulty was 0.21~1.00 and discriminative indices were higher than 0.20. Conclusion: We confirmed the Comprehensive Basic Medical Sciences Examination in 2000 met the relative highest standards of reliability and validity. Item analysis could be of help to improve the quality of examination.

The current COVID-19 pandemic represents an accidental crisis of global proportions that requires humanity to adaptively cope with unknown and low-control stressors. This research aimed to explore coping mechanisms by first considering them in the domain of their factor structure and then examining their mediating role in the relationship between stress perception and precautionary measures in the context of a pandemic. The sample included a total of 582 adult respondents from Serbia (75.7% female), with an average age of 38.74 years (SD = 10.48). The Brief COPE (Coping Orientation to Problems Experienced) scale was used to measure coping mechanisms, the Perceived Stress Scale was used to assess the perception of the stress level, and the propensity to adhere to the prescribed precautions was examined with a scale constructed for the purpose of this study. The exploratory factor analysis extracted seven coping strategies. The first corresponded to problem-focused confrontation, the second referred to emotion-focused confrontation, three isolated dimensions were associated with avoidance coping strategies, while the functions of Humor and Religion could not be clearly defined. After conducting a higher-order factor analysis, two factors were singled out: the first, which combined problem-focused and emotion-focused coping, Humor, and Religion, and the second, which brought together mechanisms aimed at avoidance coping. The results of the hierarchical regression analysis suggested significant partial mediating effects of coping mechanisms. The first higher-order factor enhanced the effects of stress perception on the practice of precautionary behavior, while the second higher-order factor reduced these effects. The obtained results raise the question of adequacy of the standard coping mechanism measuring instruments in the assessment of stress caused by an accidental crisis and further question the possibility of an adequate response to stressors that are unknown and poorly controllable.

A variant of the method of principal components analysis, which is due to Hotelling (1933), is currently perhaps the most popular choice for analyzing a group of variables into "factors." The practitioner often refers to components analysis as "factor analysis with l's in the diagonal." Kaiser's suggestion (1960; 1964) to retain only the same number of factors as there are latent roots greater than one of the matrix, R, of intercorrelations among the variables has gained wide acceptance. In a large percentage of analyses performed today called "factor analysis," Kaiser's rule for selecting the number of factors to retain after the resolution of R into principal components is used, then these are rotated orthogonally by means of Kaiser's varimax procedure (Kaiser, 1958). Not all factor analysis experts would agree that the truth is thus revealed, but few of them object to this procedure on the grounds that it lacks good psychometric and statistical justification. However, the techniques often used by researchers to calculate "factor scores" as the final step in the analysis have the blessings of no factor analysis specialists. Many researchers operate under the misapprehension that following a components-type factor analysis scores on a factor are obtained by weighting scores on variables by the loadings of the variables on the rotated factor, or that scores on a factor are obtained by summing the scores on the variables which have "high" (in absolute value) loadings on the factor. As an illustration of these two procedures, suppose that four variables have the following loadings on a varimax rotated factor

The purpose of this study was to test a hypothesized factor structure for a number of test variables which have been used to assess strength. An analysis indicated that 11 factors might be present in this domain, but that only 8 of these could be readily represented by test variables. Data were collected on college women for 29 variables. Two derived oblique factor solutions were obtained. The results indicated that (a) the two solutions differed to some extent, and (b) some but not all of the hypothesized factors were supported.

Oblique and orthogonal transformational techniques are developed, for both exploratory and confirmatory factor analytic applications, that allow the investigator to maximize, for each factor, the distance between the mean square of the factor pattern coefficients of the salient variables for that factor and that of the coefficients of the non-salient variables. The saliency of each variable may be determined either a priori or empirically. Specific computing procedures are presented—including methods for differentially weighting the factors and variables—and are illustrated by their application to several well-known data sets. Implications for practice are discussed.

Publisher Summary Practical experience has shown that factor analysis can be of great value as an aid in the interpretation of large correlation matrices, but it is no miracle tool. It should be noted that in the analysis of cranio-facial variables, the number, identity, and magnitude of the factors may be arbitrarily determined by the investigator in the selection of variables. The common practice of using factor analysis for the detection and subsequent measurement of hidden biological factors is less fortunate, because the factors will often be fortuitous, reflecting the bias of the investigator. The most rewarding use of factor analysis in cephalometry is its application in the analysis of the relationships between different sources of variability. For technical reasons, this analysis should be carried out in two steps: (1) a selection of representative variables based upon one or more exploratory factor analyses of the initial set of variables and (2) a final analysis of these selected variables. This solution will then provide the key to understanding of the source of variability influencing each of the associations in the original matrix of correlations.

This study aims to present the development and validation process of a scale to explore the learning barriers of high school students in Turkey. For this purpose, a scale was developed and administered to 316 high school students studying in the different counties of Ankara in the spring term of 2014-2015 academic year. Gathering the data, an exploratory factor analysis was run through SPSS Package program to see the structure of the interrelationships among the variables under six tests. Furthermore, a reliability analysis was conducted to the items under each test in the scale. As a result, one factor appeared under each test when the eigenvalues and variance percentages were examined, making six factors in total. The Cronbach’s Alpha Reliability Coefficient was calculated as to be significant for each test, which showed that the tests were reliable. Finally, some items were excluded from the scale., This study aims to present the development andvalidation process of a scale to explore the learning barriers of high schoolstudents in Turkey. For this purpose, a scale was developed and administered to316 high school students studying in the different counties of Ankara in thespring term of 2014-2015 academic year. Gathering the data, an exploratoryfactor analysis was run through SPSS Package program to see the structure of the interrelationshipsamong the variables under six tests. Furthermore, a reliability analysis wasconducted to the items under each test in the scale. As a result, onefactor appeared under each test when the eigenvalues and variance percentageswere examined, making six factors in total. The Cronbach’s Alpha ReliabilityCoefficient was calculated as to be significant for each test, which showedthat the tests were reliable. Finally, some items were excluded from the scale.

Reflective thinking is important to young adolescents as they develop their thinking skills. Various instructional methods have been recommended to support reflective thinking, yet the nature of the underlying factors in these methods is unclear. Exploratory factor analysis was used to determine the factors prompting reflective thinking. Results of this study suggest that young students perceived three clusters of methods as supporting their reflection: reflective learning environments, reflective teaching methods, and reflective scaffolding tools. A one-way within subjects ANOVA showed that the most helpful factor was the reflective learning environment, with the most helpful elements being freedom and collaboration. Students’ perceptions of concept mapping and reflective question prompts were found to differ significantly across gender. Recommendations are provided for designing learning environments that prompt reflective thinking.

Factor analysis is re-applied, using relatively more rigorous methods, to a 15 × 15 correlation matrix reported by Mundy-Castle and containing 11 Wechsler-Bellevue subtest variables, 2 EEG variables, age and occupational level, for a sample of 34 employees of the South African National Institute for Personnel Research. Six common factors were extracted and subjected to orthogonal rotation in search of meaningful simple structure. Two age-related factors were found and respectively identified as “Experience” and “Deterioration.” (Factors I and II.) Within the residual four-space, the vectors for alpha Frequency in the EEG and Digit Span performance in the W-B were found to be comparable. (Factor III.) This result is discussed in relation to the excitability cycle hypothesis, primary vs. secondary function, and externalization vs. internalization. The vector for alpha Index was found to have a near perfect communality in the residual three-space, and is interpreted as measuring (inversely) strength of “Conditioned Attentiveness.” (Factor IV.) Picture Completion in the W-B is judged to depend partially on this factor. The remaining two factors are of minor interest since they are probably mixtures of things that could not be distinguished in this study using only 15 variables and 34 cases. It is suggested that a proper interpretation for common factors, when there have not been enough variables to preclude the existence of specific factors, is in terms of dynamic mechanisms presumptive of a cause-effect relationship between loaded variables, rather than in terms of hypothetical underlying variables. Factors I, IV, and V can be used to illustrate this principle.