Anon

Factor Analysis and Principal Components Analysis 239

where

=





     





     

Y

yy

yy

yy

N

tNt

TNT

11 1

1

1











is the matrix of the data, in which every row corresponds to an observa-

tion of all N variables, and each column corresponds to all T observa-

tions of each variable; and where

=





      





      

F

ff

ff

ff

1

1

1

q

tqt

TqT

11 1

1

1











is the matrix of factors where we add a column of ones to include the

constant terms a (note that the terms of this matrix are not observable)

=





































C

aa

bb

bb

N

N

qNq

1

11 1

1

is the matrix of factor loadings plus the terms a in the first row.

=

εε

εε

εε





     





     

E

N

tNt

TNT

11 1

1

1











is the matrix of error terms, which are not observable.