Community, opportunity, and crime on school property: A quantitative case study

Educational Foundations, Fall 2001 by Bickel, Robert, Dufrene, Roxane

All the independent variables except high school size (HIGHSIZE) and the HIGHSIZE-by-SES interaction term (INTERACT) are composites created with principal components analysis. Table I describes the constituents of each composite variable.

Principal Components and Multicollinearity

Use of composite variables enables us to avoid inflated standard errors due to multicollinearity (Hadi, Chatterjee, & Price, 2000: 245-269). This is of special concern in the present analysis because we have comparatively few cases, West Virginia's fifty-five school districts (Stevens, 1997: 365-366). Moreover, before construction of the seven composites, there were twenty-four independent variables, a large number by any standard, and certain to exacerbate statistical difficulties attributable to multicollinearity (Gujurati, 1994: 319-345). In addition, important variables, such as economic opportunity (ECONOPP) and socioeconomic status (SES) are closely related conceptually, making fairly strong intercorrelations more likely.

As reported in Table 2, however, with eight independent variables and a multiplicative interaction term, our Condition Index is only 6.2. Furthermore, the largest Variance Inflation Factor (not included here) is only 4.9, and seven of the remaining eight are below 2.0. All measures of multicollinearity are well within acceptable limits (Fox, 1997: 338-343; Chatterjee, Hadi, & Price, 236-241 and 247-249).

Principal Components and Multi-Faceted Concepts

Some of the independent variables, moreover, are best understood as composites, multi-faceted phenomena which cannot be captured in one manifest measure. (See Tables 2 through 8). This is conspicuously the case with the variable MODERN, a measure of the degree to which school districts and the counties with which they are coterminous approximate or depart from traditional patterns of social organization and practice for West Virginia communities. (See Table 8.)

Selection of the variables which make up the MODERN composite is based on characteristics of traditional West Virginia communities (Bickel, Smith, & Eagle, 2001). Most have been rural, isolated, and sparsely populated. Racially and ethnically they have lacked diversity, made up almost exclusively of West Virginia-- born whites. While high school completion rates have been roughly the same as the national average, college enrollment rates have consistently been among the lowest in the U.S. Among those who have gone to college, very few matriculated outside of West Virginia. Most workhas been in mining, timbering, manufacturing, and self-- employed agriculture. Service sector employment has been uncommon (Bickel, Large, Weaver, & Williams, 1997; Bickel & McDonough, 1997; Bickel & McDonough, 1999).

Thus, as with our previous work, MODERN is used as the measure of out-of-- school community. Higher values on this composite correspond to diminished out-- of-school community, while lower values correspond to stronger out-of-school community.

The other composites are intended to gauge economic opportunity (ECONOPP), educational opportunity (EDOPP), school resources (SCHLRES), school achievement (SCHLACH), socioeconomic status (SES), and social pathology (SOCLPATH). The principal components results for each of these additional composites are given in Tables 2 through 7. All measures are aggregated to the school district level.