ABSTRACT
The primary factors or "ideal" tests lie entirely in the first-order common-factor space, with vector lengths and communalities unity. Each test has a specific factor and an error factor, and these specific factors and error factors are lumped together in the unique factors. As the error factors of the tests lie entirely outside the first-order common-factor space, any error factors in the second-order analysis can be due only to imperfect first-order analysis, leading to the injection of a little of the error variance into the second-order common factors. The second-order specific-factor space, in turn, lies outside the second-order common-factor space. As in first-order analysis, the solution is indeterminate if the number of second-order factors equals or exceeds one-half the number of first-order factors. What is the correlation between each test and each second-order general factor? The hierarchical orthogonal solution answers these questions.
