Fixedeffect Linear Bilinear Models

Williams (1952) was the first to link the Eqn 14.1 model with principal components (PC) analysis by considering the model y = | + T + Xai Yj + ej where X is the largest singular value of ZZ' and Z'Z (for Z = yy - yy.), and ai and yi are the corresponding eigenvectors. Gollob (1968) and Mandel (1969, 1971) rediscovered and extended Williams' (1952) work by considering the bilinear GE term as (t 8) aik y jk. Thus, k=1

the general formulation of the linear-bilinear model is:

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