Hierarchical models of ability at individual and class levels

Scores in ability tests administered to students in Grades 4–6 ( n = 1,274) and Grades 7–9 ( n = 1,310) were simultaneously factor analyzed at class and individual levels. Muthén's (1990) multilevel factor analysis was used to test hierarchical models of intelligence. At the individual level the general factor was most highly loaded on “fluid” abilities. Also, there were residual factors for speed, verbal comprehension, spatial visualization, and numerical facility as well as test-specific factors derived from parallel versions of the tests. At the class level three common factors were established: one general factor more highly loaded on “crystallized” than on fluid abilities, and residual common factors for speed and, in Grades 7–9, verbal comprehension. The between factors accounted for relatively more variance in Grades 7–9 than in Grades 4–6 due to an intervening reorganization of classes based on choice of more or less academic courses. Demographic differences between neighborhoods, self-selection between academic and general programs, and variations in instruction and test administration were used to explain the between-class factors.