This paper proposes an improved procedure for factor analysis applied to flow data in terms of solving relevant technical problems, and attempts to systematize it (see Fig. 5).
After confirming the proposed procedure's validity, the utility of higher-order factor analysis is examined, taking as a case study automobile traffic flows in the Keihanshin Metropolitan Area with a complicated connectivity structure. Compared with the orthogonal rotation which results in identifying uncorrelated functional regions, higher-order factor analysis has advantages of being able to extract correlated functional regions and to clarify the hierarchical structure of functional regions.
The proposed procedure of factor analysis applied to the Origin-Destination data matrix is as follows: i) as to the form of the O-D data matrix, an asymmetrical matrix including diagonal elements or intra-flows is preferable; ii) as to the input data matrix in extracting the initial factors, the result of factor analysis of a hypothetical O-D data matrix reveals that the cross-product standardized by the sum of squares (ΣX_j²=1.0) matrix may be more adequate than the correlation matrix; iii) as to the number-of-factors which is one of the most intractable problems on factor analysis, the number of factors showing the most interpretable factor structure are regarded as the number of common factors to be extracted, based on three criteria of 1) each area's communality value of greater than 0.1, 2) the change of percentage of the accumulated variance explained and 3) existence or not of bipolar factors; iv) in interpreting factors, under the assumption that the high factor loadings may specify groups of destinations receiving trips from common origins, and that the high factor scores specify these (groups of) origins, the internal structure of each functional region (the primate central area-type, the multiprimate central areas-type and the interdependent-type) is identified based on the ranking of the factor scores and their differences from the first ranking factor score.
Next, higher-order factor analysis with oblique rotation is applied to the 212×212 O-D data matrix of automobile traffic flows in the Keihanshin Metropolitan Area in 1979. As a result of the analysis, it turned out that the Keihanshin Metropolitan Area consisted of 30 first-order functional regions with the above-mentioned internal structures, and that these first-order functional regions were integrated into 13 relatively independent second-order functional regions.
First, as for the first-order functional regions (see Fig. 9), the northern part of Osaka City whose central area is Osaka-Kita Ward, is classified as the primate central area-type, the southern part of Osaka City is classified as the interdependent-type, Kyoto City is classified as the interdependent-type, and Kobe City whose central areas are Kobe-Ikuta and Kobe-Hyogo Wards is classified as the multi-primate central areas-type. They are identified as functional regions corresponding to the three metropolitan areas of Osaka, Kyoto and Kobe respectively.
In addition, ‘satellite cities’ of Himeji, Nara and Wakayama located in periphery of the Metropolitan Area are characterized as functional regions classified as the primate central area-type. One set of ‘satellite cities’ surrounding Osaka City such as Higashi-Osaka, Sakai and Tondabayashi, and another set of ‘satellite cities’ such as Toyonaka-Suita-Ibaragi, Hirakata-Neyagawa-Moriguchi-Kadoma and Amagasaki-Nishinomiya, show different internal structures. The former is the primate central area-type, and the latter is the multi-primate central areas-type.
Second, as for the second-order functional regions (see Fig. 10), it could be pointed out that they integrate a few neighboring first-order functional regions, and that some boundaries between them correspond to the boundaries of prefectures.

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This paper presents a study of Japanese rural-urban migration based on Mabogunje's systematic scheme and discusses the rural development policy, especially as it pertains to mountainous areas.
In Japan, many mountain villages have experienced consistent and serious depopulation in the course of postwar economic development. However there have hardly been any theoretical studies which investigated the process of population decrease. We have today several studies which successfully make clear from an economic point of view the causes of the emigration from mountainous areas. They explain the causes by the economic decline of mountain villages and also the increasing demand for labor force in metropolitan areas. This framework seems to apply well to macroscopic studies, but not to microscopic studies. For the latter, Mabogunje's theoretical framework of rural-urban migration is more appropriate. Therfore we now propose to adopt this one and examine the existence of rural control sub-systems in Japan. In this study, stress was placed especially on Agricultural Cooperatives and town offices as the control sub-systems and the following issues were examined: 1) the reorganization process of agriculture under the direction of the Agricultural Cooperative and town office; 2) the spatial pattern of agriculture and farm management; 3) the trends among farmers in a settlement where agricultural production has been developed in recent years; 4) the control of the Agricultural Cooperative and town office over the rural-urban migration.
The study area, Oyama-machi is a mountain village which is located in Oita prefecture, northern Kyushu Island.
The following results were obtained:
1. In this village, since 1961 the Agricultural Cooperative and town office have worked together to make agricultural plans and to carry them out. As a result of their efforts, agricultural production, in particular of fruits and“Enokidake”mushrooms, has remarkably been increased and the local economy has been revitalizea. The success can be attributed to the following features of the plans: 1) the first project (Ume-Kuri movement) was carried out by the original finance of the town office; 2) The authorities encouraged farmers to cultivate crops besides rice, in particular plums and chestnuts; 3) agricultural plans aimed at raising all the farmers' incomes; 4) agricultural products were mainly shipped to the local market (northern Kyushu); 5) the improvement of the economic imbalance among settlements was considered in policy making. The point is that above mentioned issues differ greatly from the agricultural policy of the central government. The case of this town suggests the necessity for changing agricultural policy, especially for mountain farming.
2. A successful case such as Oyama-machi is very rare in mountain villages, but the author found that this village had several problems that were common to other villages. Dam construction in the 1960's caused the emigration or the increase of non-agricultural part-time jobs among farmers. Then the inducement of small factories in 1973 had a bad influence on agricultural production through the outflow of female workers from agriculture. Therefore the revitalization of the local economy could not easily be realized in spite of the efforts. “Enokidake” mushroom production which was set about in 1973 played an important role in the improvement of the economic condition and realized the return migration and the population increase. During this development process, the Agricultural Cooperative and town office strengthened their function as the rural control sub-system in rural-urban migration.
3. Oyama-machi has remarkably developed in recent years, but there is a wide difference in farm management among settlements and also among farm households.

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