Kaiser's Measure of Sampling Adequacy (MSA) for factor-analytic correlation matrices is studied for several levels each of p, the number of variables, q, the number of factors, and rfl, the root-mean-square off-diagonal correlation. The major influence for MSA is p, in agreement with theory; the joint main effect influences of p, q, and rfl to the total SSs remains greater than 84% under various choices of the levels of p, q, and rfl.
Guttman's classic lower bound for the number of common factors is extended to the completely general case where communalities may lic in the closcd interval frorri zero to one. Guttmaii [2] has established a lower bound for the number of common factors.Givcn R, the correlation matrix of order n, let I?, =H -I, and G2 =the diagonal matrix of squared multiple correlations of cach variable with the rcmaining n -1 : then the number of non-negative latent roots of Ro +CP is a lower bound to r, the rank of the matrix Ro +H2, where 121 GUTTMAN, L. (1954). Some necessary conditions for common-factor analysis. 13 I GUTTMAN, I,. (1956).
Psyclio-ponents. l'sychometrika, V, 75-99. XIX,[149][150][151][152][153][154][155][156][157][158][159][160][161] ntetrika, XSI, 273-285. ' Best possil,lc ' systematic estimates of comrnunalitics.
I'sychoinetrika,
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.