stat-factor analysis - Alicia Deal 1 CJ737 Ch 9 factor...

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Alicia Deal CJ737 03-29-06 Ch 9 factor analysis Chapter 9: Factor Analysis 1.) a.) Assess the eigenvalue criteria. How many components were retained? Is the eigenvalue appropriate, considering the number of factors and the commonalities? Three components were retained: component 1 had an eigenvalue of 2.423, component 2 had a value of 1.426, and component 3 had a value of 1.021. No, they are not appropriate because only two variables, degree (.933) and educ (.939), are greater than 0.7. The other variables are less than .3. The variables would be appropriate if (for its factor size being less than 30) all the factors were greater than . 7. b.) Assess the variance explained by the retained components. What is the total variability explained by the model? Is this amount adequate? The total variability of the 3 variables is 60.875%. The extraction sum of square loadings indicate that component 1 explains 30.293%, component 2 17.822%, and component 3 12.76%. This amount is not adequate because the retained factors need to account for at least 70% of the total variance. The rotation sum of square loadings indicate that comp. 1 explains 23.488% of the total variance, comp 2: 21.677%, and comp 3: 15.710% which displays more similar levels of explained variance between the components. c.) Assess the scree plot. At which component does the plot begin to level off? At component three is where the plot begins to level off. It appears to level off at component 3 yet the plot descends sharply at component 7. d.) Assess the residuals. How many residuals exceed the .05 criteria? There are 12 or 42% of residuals that exceed the .05 criteria. The residuals suggest that a 4 th variable could improve the model to decrease the number of residuals that exceed .05. e.) Having applied the four criteria, do you believe the number of components retained in this analysis is appropriate? If not, what is your recommendation?
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