How many factors were extracted in this PCA? What percentage of variance do these factors account for?

In this exercise, you will undertake a principal components analysis of the CES-D items, using all 20 original items (no reversed items). Go to Analyze ➜ Data Reduction ➜ Factor Analysis. Select the 20 CES-D items, being careful not to select reversed items, and move them into the box for Variables. Click the Descriptives pushbutton and in the next dialog box select Univariate descriptives and Initial solution under Statistics; and KMO Bartlett’s test and Anti-image under Correlation Matrix. Click Continue and then on the original dialog click the Extraction pushbutton. In this dialog box, select Methods ➜ Principal Components; Analyze ➜ Correlation Matrix; Display ➜ Unrotated factor matrix and Scree plot; and Extract ➜ Eigenvalues over 1. Then click Continue and select Rotation from the original dialog box. Select Method ➜ Varimax and Display ➜ Rotated solution. Click Continue and then click the Options pushbutton. Select Missing values ➜ Delete listwise and, for Coefficient Display Format, select Sorted by Size and Suppress absolute values less then .30. Click Continue, then OK to run the analysis, and then answer the following questions: (a) What was the value of the KMO measure of sampling adequacy for the entire set of items? What does this suggest about the factorability of the items? (b) Was Bartlett’s test significant? (c) Look at the anti-image correlation matrix and inspect the measures of sampling adequacy (MSA) of individual items along the diagonal. What is the lowest value—and does this support a factor analysis? (d) In terms of communalities, how many items had extraction communalities exceeding .50? Which item had the highest communality, and which had the lowest? (e) How many factors were extracted in this PCA? What percentage of variance do these factors account for? What are the eigenvalues for the extracted factors? (f) Examine the scree plot. Does the plot suggest the same number of factors as were originally extracted? (g) Looking at the unrotated factor matrix (the Component Matrix), are there items with high loadings on more than one factor? (h) Interpret the rotated component matrix. What does the pattern of loadings suggest about the adequacy of the factor solution?

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