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that convenient constructs that help our generation relate to the data consistencies we nd in our discipline. And because they are our constructs, we choose to de ne them by the CA model. Another rationale for CA is a set of pragmatics. One such pragmatic is that using CA instead of CFA seldom makes much difference. Many factor analyses are of 25 or more variables with, if the study is designed well, reasonably high communalities. In such cases, the results of CA and CFA lead to the same conclusions. Compare the CA in Table 6.6 against the CFA of Table 6.4. Is there really an interpretable difference And in fact do not the high loadings stand out better from the low ones in the CA Other rationales for CA arise as much from classical limitations of CFA as from the CA model. A major limitation arises from the communality problem. Because we never know the communalities but only estimate them, there are a set of solutions that t the data equally well. And iterating for communalities can produce Heywood cases. As the communalities can only be estimated, the further mathematical conclusion is that there are an in nite number of factor scores that could be computed that would ful ll the ECFA model equally well for any given data set (a result of what is called the indeterminacy problem). With CA, the factor scores are a linear combination of the variables of which there is only one set.

Action Loops Loops Declares the name and arguments for a Function procedure Reads data from a text file Branches Branches Processes statements conditionally Specifies an interface or class that will be implemented in a class module Reads data from a sequential text file Deletes a file from a disk Assigns the value of an expression to a variable or property Reads a line of data from a sequential text file Loads an object but doesn t show it Controls access to a text file Left-aligns a string within a string variable Replaces characters in a string with other characters Creates a new directory Renames a file or directory Branches on an error Branches on a condition Branches on a condition Opens a text file Changes default lower limit Declares the default comparison mode when comparing strings

printf( Bitmap header: Bytes 14 - %3d\n , 13+BMPInfo.size); printf( Color map: Bytes %3d - %3d\n , 14+BMPInfo.size, 13+BMPInfo.size+4*BMPInfo.ColorsUsed); printf( Image data: Bytes %3d - %3d\n\n , BMPHead.offset, BMPHead.offset-1+ (BMPInfo.width*BMPInfo.height*BMPInfo.BitsPerPixel+7)/8); } if (dup_color < 100) printf( Data has NOT been hidden in this file with STools ); if (dup_color >= 100)printf( *** Data HAS BEEN HIDDEN in this file with STools *** ); printf ( \n\n );

1 In the same way the coef cient R12 is the estimate that the child parity check node 1 sends to its parent symbol node 2, and is calculated assuming that its corresponding parity check equation, which is c2 c4 c6 c7 c8 c12 = 0 , is satis ed, when the bit or symbol 2 is in state c2 = 1. In this sense, there are again 16 combinations (odd number of 1 s) of the bits c4 , c6 , c7 , c8 and c12 that can satisfy such a condition. The probabilities associated with each

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(9.94) + i ) is attained when (9.95)

consisting of (m; x nj) submatrices Aij, I,) = l, ... ,q, is a block band matrix if Aij =: 0 for i j ~ s and for j i ~ p. Here s, p < q.