The Revolution

In: English and Literature

Submitted By shoaib
Words 4231
Pages 17
Factor Analysis - SPSS(
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• First Read Principal Components Analysis.

The methods we have employed so far attempt to repackage all of the variance in the p variables into principal components. We may wish to restrict our analysis to variance that is common among variables. That is, when repackaging the variables’ variance we may wish not to redistribute variance that is unique to any one variable. This is Common Factor Analysis. A common factor is an abstraction, a hypothetical dimension that affects at least two of the variables. We assume that there is also one unique factor for each variable, a factor that affects that variable but does not affect any other variables. We assume that the p unique factors are uncorrelated with one another and with the common factors. It is the variance due to these unique factors that we shall exclude from our FA.

Iterated Principal Factors Analysis

The most common sort of FA is principal axis FA, also known as principal factor analysis. This analysis proceeds very much like that for a PCA. We eliminate the variance due to unique factors by replacing the 1’s on the main diagonal of the correlation matrix with estimates of the variables’ communalities. Recall that a variable’s communality, its SSL across components or factors, is the amount of the variable’s variance that is accounted for by the components or factors. Since our factors will be common factors, a variable’s communality will be the amount of its variance that is common rather than unique. The R2 between a variable and all other variables is most often used initially to estimate a variable’s communality.

Using the beer data, change the extraction method to principal axis:

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Take a look at the initial communalities (for each variable, this is the R2 for predicting that variable from an optimally weighted linear…...

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