The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of R factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence …

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary …

If the ratio m/p tends to zero, where m is the number of factors m and p the number of observable variables, then the inverse diagonal element of the inverted observable covariance matrix (σ pjj) -1 tends to the corresponding unique variance ψ jj for almost all of these (Guttman, 1956). If the smallest …

A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that B. F. Green's (1976) conjecture …

The subject of factor indeterminacy has a vast history in factor analysis (Guttman, 1955; Lederman, 1938; Wilson, 1928). It has lead to strong differences in opinion (Steiger, 1979). The current paper gives necessary and sufficient conditions for observability of factors in terms of the parameter matrices …

The CANDECOMP algorithm for the PARAFAC analysis of n × m × p three-way arrays is adapted to handle arrays in which n > rnp more efficiently. For such arrays, the adapted algorithm needs less memory space to store the data during the iterations, and uses less com- putation time than the original CANDECOMP …