In this research, it is shown that the graphical modeling is able to be run by the software of structural equation modeling. Its software is Mx. The data for analysis were three correlation matrices used in the Japanese Society for Quality Control (1999), and using Mx, these data was analyzed by graphical modeling. In case 1, reproduction of a result was possible, but furthermore it was possible to carry out covariance selection from perspective of fit index. In case 2 and case 3, reproduction of a result was almost completely possible. In this result, the graphical modeling was able to be analyzed by framework for structural equation modeling, and it can be included for lower model of SEM. A program of Mx and its manual was shown as an appendix in the last of this article.
Angular analysis (ANA) of correlation matrices is proposed in which variables are represented as vectors in a low-dimensional space and inter-variable correlation coefficients are approximated only by the cosines of the angles between variable vectors. ANA can be viewed as a method which approximates correlation coefficients with least parameters and as a constrained version of principal component analysis (PCA). Solutions of ANA are obtained with an alternate least squares procedure in which an algorithm for oblique Procrustes rotation is used. The performance of the procedure is assessed in a simulation study. ANA is compared theoretically and empirically with PCA.
The standing broad jump test performed by infants can apparently be too easy or too difficult for those with high and low motor abilities, respectively. This causes test subjects to become frustrated or bored, and leads to difficulties with evaluations. Therefore, the present study aimed to use item response theory to create a reliable and feasible two-phase subjective evaluation of the standing broad jump performed by infants. Kindergarten children (n=196) performed a standing broad jump that was measured and videotaped. Nineteen measures (items) of body movement during the jump were categorically evaluated as ‘success’, ‘no opinion’, or ‘failure’. The correlation matrix among the movement measures was analyzed using principal factor solution, and a one-dimensional structure among the measures was confirmed. The difficulty parameter and ability characteristic values were then obtained by applying item response theory. The correlation was high among difficulty parameters obtained separately from samples that had been randomly divided into two. The correlation was also high among θ values separately obtained from groups of items that had also been randomly divided into two. These results confirmed sample and item invariance. The mean value of θ according to age significantly varied, indicating that θ would reflect increasing motor ability with growth. Based on the adaptive possibility to the item response theory data, the following types of two-phase testing were created that do not require complicated calculations : 1) A low-reliability, high feasibility type, in which the reliability coefficients of the first and second tests were 0.7 and 0.8, respectively. 2) A medium-reliability, medium-feasibility type, in which the reliability coefficients of the first and second tests were 0.8 and 0.85, respectively. 3) A high-reliability but low-feasibility type, in which the reliability coefficients of the first and second tests were 0.85 and 0.9, respectively.