Why does SAS give negative eigenvalues in Proc Factor

Why does SAS give - Why do some softwares give negative eigenvalues when doing an Exploratory Factor Analysis Depending on which factor extraction

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Why do some softwares give negative eigenvalues when doing an Exploratory Factor Analysis Depending on which factor extraction method is used, the eigenvalues that SAS (and STATA) and maybe some other softwares (I don’t know about SPSS) produces are different than simply the eigenvalues of the correlation matrix. NOTE: Mplus only produces the eigenvalues of the correlation matrix. Here I detail the different eigenvalues produced (and why) by SAS Proc FACTOR… By default if no method = option is given, SAS Proc Factor will perform principal component analysis. In this case, the eigenvalues it presents are the eigenvalues for the observed correlation matrix. This is because the eventual q factors it will present (rotated or unrotated) are simply the first q eigenvectors. Hence the concept of “variability explained by the q factors” is represents the proportion of total variability in the standardized observed variables (which is equal to the sum of the diagonal of the correlation matrix,i.e. p) that can be accounted for by the first q factors (which is the sum of the first q eigenvalues). When we ask for a different extraction method, for example method = prinit which performs “Iterated Principal Factor Analysis” or method = ml which performs “Maximum Likelihood”, then SAS will present two sets of eigenvalues the first being “Preliminary eigenvalues” and the second being the “Eigenvalues of the Reduced Correlation Matrix”. Given these extraction methods, the software is now performing a true Common Factor Model and not Principal Component Analysis. Recall that the Common Factor Model assumes that each observed variable is explained by the factors it shares in common with the other observed variables PLUS its own unique random measurement error which is independent of all the other measurement errors. That is, Σ = ΛΛ + ψ . So, the factors that are extracted are not extracted from Σ, but from Σ − ψ which is called the “reduced correlation matrix”. Note that the diagonal elements of Σ − ψ are equal to the “communalities” whereas the diagonal elements of Σ are equal to 1. Here I present the Genetic Testing Worry data analyzed using the different extraction methods… method = principal (principal component analysis), method = prinit (iterated principal factor analysis), and method = ml (maximum likelihood) ( is used Method = principal
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This note was uploaded on 11/21/2011 for the course PUBH 7435 taught by Professor Melaniewall during the Fall '08 term at Minnesota.

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Why does SAS give - Why do some softwares give negative eigenvalues when doing an Exploratory Factor Analysis Depending on which factor extraction

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