SPSS Statistics

I've established that when FACTOR performs Promax rotation, it uses, as the initial configuration for itself, the rescaled rather than the raw loadings left by the preliminary varimax. (Rescaled loadings differ from the raw ones when the analysis is based on covariances, that is /METHOD=COVARIANCE in FACTOR procedure. Rescaled loadings are raw loadings divided by the respective variable's st. dev.)

Neither CSR document nor SPSS Algorithms do not mention it. But it is important. SPSS algorithms only states in the Promax section of FACTOR: "Varimax rotation is used to get an orthogonal rotated matrix Л_R = {л_ij}". Indeed, we know that promax starts with the results of varimax. But what results should it be? Raw loadings or rescaled loadings?

What do people here think?
What do SPSS statisticians think?
How other software solve the dilemma?
Why not add a due remark to SPSS Algorithms document?
Finally, why not add an option to FACTOR command - for a user to select whether promax should start from the rescaled or the raw loadings?

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Kirill Orlov
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#SPSSStatistics

My own tentative answer to the question why rescaled loadings are used, would be:
Promax obtains the target "sharpened" matrix (notated as P in the Algorithms doc.) first by Kaiser-normalizing the input matrix prior to raising its elements to power 4 (or whatewer k parameter is. This is seen in the first equation in the Algorithms doc.). The normalization has the aim not to let elements be above 1, so that the exponentiated elements are never bigger than the original ones, but easily less then those. Then, logically, the input matrix Л - the matrix to be procrustes-transformed towards P (see the second equation he Algorithms) - should better keep its elements not above 1, too. It is the rescaled loadings, but not the raw loadings, that are ever not above 1.

This is a guess and perhaps other answers will be better.

------------------------------
Kirill Orlov
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Original Message:
Sent: Fri July 15, 2022 01:13 PM
From: Kirill Orlov
Subject: Promax rotation of FACTOR: why is based on Rescaled varimax's loadings?

I've established that when FACTOR performs Promax rotation, it uses, as the initial configuration for itself, the rescaled rather than the raw loadings left by the preliminary varimax. (Rescaled loadings differ from the raw ones when the analysis is based on covariances, that is /METHOD=COVARIANCE in FACTOR procedure. Rescaled loadings are raw loadings divided by the respective variable's st. dev.)

Neither CSR document nor SPSS Algorithms do not mention it. But it is important. SPSS algorithms only states in the Promax section of FACTOR: "Varimax rotation is used to get an orthogonal rotated matrix Л_R = {л_ij}". Indeed, we know that promax starts with the results of varimax. But what results should it be? Raw loadings or rescaled loadings?

What do people here think?
What do SPSS statisticians think?
How other software solve the dilemma?
Why not add a due remark to SPSS Algorithms document?
Finally, why not add an option to FACTOR command - for a user to select whether promax should start from the rescaled or the raw loadings?

------------------------------
Kirill Orlov
------------------------------
#SPSSStatistics

Another and a simpler answer to the question why rescaled loadings are used, is:
Typically, we interpret factors looking on rescaled loadings, not raw loadings. Hence it is more natural to transform the former, not the latter, to a "simple structure". I've noticed that in orthogonal rotations (such as varimax) too, SPSS will rotate the rescaled and not the raw loadings. (Another matter is that when Kaiser normalization was requested, then an orthogonal rotation of the rescaled and raw loadings are equivalent by the mere fact that the normalization before a rotation removes the difference between these and those.)

------------------------------
Kirill Orlov
------------------------------

Original Message:
Sent: Fri July 15, 2022 01:13 PM
From: Kirill Orlov
Subject: Promax rotation of FACTOR: why is based on Rescaled varimax's loadings?

I've established that when FACTOR performs Promax rotation, it uses, as the initial configuration for itself, the rescaled rather than the raw loadings left by the preliminary varimax. (Rescaled loadings differ from the raw ones when the analysis is based on covariances, that is /METHOD=COVARIANCE in FACTOR procedure. Rescaled loadings are raw loadings divided by the respective variable's st. dev.)

Neither CSR document nor SPSS Algorithms do not mention it. But it is important. SPSS algorithms only states in the Promax section of FACTOR: "Varimax rotation is used to get an orthogonal rotated matrix Л_R = {л_ij}". Indeed, we know that promax starts with the results of varimax. But what results should it be? Raw loadings or rescaled loadings?

What do people here think?
What do SPSS statisticians think?
How other software solve the dilemma?
Why not add a due remark to SPSS Algorithms document?
Finally, why not add an option to FACTOR command - for a user to select whether promax should start from the rescaled or the raw loadings?

------------------------------
Kirill Orlov
------------------------------
#SPSSStatistics