Một âm mưu khác hữu ích là căn bậc hai của tổng của các ô vuông của tất cả các mối tương quan còn lại chia cho số lượng các mối tương quan như vậy còn lại, đó là p (p - 1) / 2. Nếu có một phá vỡ trong lô của các đường cong, sau đó chúng tôi sẽ chọn k để tối đa và các mối tương quan còn lại trung bình bình phương nhỏ | 616 PRINCIPAL COMPONENT ANALYSIS AND FACTOR ANALYSIS Figure Plot of the maximum absolute residual and the average root mean square residual. correlations. Another useful plot is the square root of the sum of the squares of all of the residual correlations divided by the number of such residual correlations which is p p 1 2. If there is a break in the plots of the curves we would then pick k so that the maximum and average squared residual correlations are small. For example in Figure we might choose three or four factors. Gorsuch suggests In the final report interpretation could be limited to those factors which are well stabilized over the range which the number of factors may reasonably take. INTERPRETATION OF FACTORS Much of the debate about factor analysis stems from the naming and interpretation of factors. Often after a factor analysis is performed the factors are identified with concepts or objects. Is a factor an underlying concept or merely a convenient way of summarizing interrelationships among variables A useful word in this context is reify meaning to convert into or to regard something as a concrete thing. Should factors be reified As Gorsuch states A prime use of factor analysis has been in the development of both the theoretical constructs for an area and the operational representatives for the theoretical constructs. In other words a prime use of factor analysis requires reifying the factors. Also The first task of any research program is to establish empirical referents for the abstract concepts embodied in a particular theory. In psychology how would one deal with an abstract concept such as aggression On a questionnaire a variety of possible aggression questions might be used. If most or all of them have high loadings on the same factor and other questions thought to be unrelated to aggression had low loadings one might identify that factor with aggression. Further the highest loadings might identify operationally the questions
