1979 年 31 巻 1 号 p. 5-27
A study of the residential structure of the American city has produced an increasing literature under the technique of factorial ecology. The study of large cities however is not enough compared to that of smaller cities because of the labor dealing vast information when taken a small area like a census tract as a observation unit.
The auther investigated the residential structure and its spatial pattern for the Detroit metropolitan area by performing factor analysis upon 1960 and 1970 census data. Change in the structure and pattern is also studied by comparing the extracted factors and factor scores obtained at different points in time.
The area studied is the entire Detroit Standard Metropolitan Statistical Area. (Fig. 1) The census tract is employed as a observation unit. After omission and consolidation a total of 762 tracts constitutes the analysis in 1960 and 986 in 1970. 56 variables from population characteristics available in the U.S. census of population were selected for the study. (Table 1) The same variables were chosen in the analysis for both 1960 and 1970. They are classified into 10 major categories: (1) sex and age, (2) family and household, (3) marrige status, (4) race and ethnicity, (5) mobility, (6) labor force, (7) occupation, (8) working status, (9) education and (10) family income.
Product-moment correlation coefficients were computed for all variables. These matrixes were then subjected to principal factor method factor analysis. Eight factors were extracted in 1960 and nine in 1970, accounting cumulatively for 83% and 81% of the total variance respectively. Those factors were rotated to orthogonally to simple structure. Varimax rotation was employed. The matrixes of factor loadings are shown in Tables 2 and 3.
The 1960 factors were interpreted as follows: (I) Family Life Cycle, (II) Racial Composition, (III) Socio-economic Status, (IV) Women in Labor Force, (V) Eastern European Immigrants, (VI) Youth Predominance, (VII) Sexual Composition and (VIII) Italians. The first three factors accounted cumulatively for more than 60% of the total variance and there was a sizable difference in significance between each of them and each of the rest.
The 1970 factors were interpreted as follows: (I) Socio-economic Status, (II) Racial Composition, (III) Family Life Cycle, (IV) Women in Labor Force, (V) Residential Mobility, (VI) Eastern Europian Immigrants, (VIII) Sexual Composition, (IX) Youth Predominance/Italians. The first three factors were also observed as significant and accounted for about 58% of the total variance.
In order to test the relationship between 1960 and 1970 factors, correlation coefficients were calculated and are shown in Table 4. Factor I in 1960 has strong correlation to Factor III in 1970, Factor II in 1960 to Factor II in 1970, and Factor III in 1960 to Factor I in 1970. Therefore it was confirmed that the first three factors of both years, which were Socio-economic Status, Racial Composition and Family Life Cycle were the major stable factors that explain the residential differentiation of Detroit. Minor factors of each year do not correspond clearly with each other except the factors of Women in Labor Force and East European Immigrants, which are considered to be the stable minor factors.
The spatial patterns of the major three factors were then analysed. Prior to it the entire metropolitan area was devided into seven concentric zones numbered 1 through 7 from the C.B.D. outward and seven sectors numbered 1 through 7 from southwest to northeast, which made 49 cells. (Fig. 2) The spatial patterns of factor score distributions were examined by three steps. First, a series of analysis of variance were undertaken to judge objectively whether the factor score distributions of Socio-economic Status and Family Life Cycle correspond to concentric model or sector model.