Factor analysis

Question 1

What is factor analysis?

Answer 1

• A statistical technique that takes a large number of variables and puts them into a small number of “factors” (groups) with which all of the variables are related to

Question 2

What’s the general main principle when performing factor analysis?

Answer 2

• Must identify the basic underlying variables which account for the correlations between the actual test scores

Question 3

When do we use factor analysis?

Answer 3

• Simplify a large data set
• Map out the most important variables
• Theory testing

Question 4

What’s the conceptual procedure for factor analysis?

Answer 4

1) Complete a correlation matrix for all variables
2) Extract factors from this correlation matrix
3) Decide how many factors are necessary to represent the correlation matrix “best”, often a very important and sometimes difficult decision
4) Once decided, must rotate the factor loading matrix
5) Interpret the rotated factors and label them

Question 5

What’s important to know when extracting the first factor?

Answer 5

• The first factor is obtained by linear combining the variables so that the factor has the largest variance (i.e., it will encapsulate the largest number of values)

Question 6

T/F: Want to capture the most variance possible while extracting the fewest factors possible

Answer 6

• TRUE

Question 7

What are factor loadings?

Answer 7

• The simple correlation between factors and the variables
• We can interpret factors based on factor loadings

Question 8

What are Eigenvalues?

Answer 8

• The sum of the squared factor loadings of unrotated factors (columnwise)
• This indicates the overall factor size/impact
• Important to use when determining the number of factors to extract

Question 9

What’s the Eigenvalue-greater-than-one rule?

Answer 9

• A strategy to use when deciding how many factors you want to extract
• You extract factors that only have an Eigenvalue greater than one
• Downside: Can cause you to over extract factors

Question 10

What’s the Scree plot method?

Answer 10

• Plots Eigenvalues, then select factors that are found before the “elbow” of the graph

Question 11

What do reproduced correlations mean?

Answer 11

• Depending on how many factors you extract, you can create a new correlation matrix estimated entirely from the two factors retained
• A correlation between any two variables can be estimated by finding the sum of cross-products of factor loadings of the two variables on the same factor

Question 12

What can residual correlations tell us?

Answer 12

• Original correlation - reproduced correlation
• If residual correlations are small, that means that the factors extracted do a good job at explaining the original observed correlations quite well
• i.e., want the residual correlations to be as small as possible

Question 13

Why do we rotate factors?

Answer 13

• Want to achieve a simple structure, meaning we want to obtain factors that have high loadings for some variables, but low loadings for other variables
• SImple structure solution = each variable loads highly on only one factor

Question 14

Why do we want to obtain a simple solution with our factors?

Answer 14

• Want to increase interpretability
• Remember: loadings = simple correlations

Question 15

What’s orthogonal rotation?

Answer 15

• Means that the 90-degree angles between axes are maintained in the rotations

Question 16

What does the term varimax orthogonal rotations indicate?

Answer 16

• The factors are rotated in such a way that the variance of the squared loadings on the factors is maximized

Question 17

T/F: Must calculate the sum of the squared factor loadings after the factors have been rotated

Answer 17

• TRUE

Question 18

What’s communality?

Answer 18

• The extent to which a variance is explained by the factors you obtained (shows proportions of variance = reliability)

Question 19

What are factor scores?

Answer 19

• For subsequent analyses, factor scores can be computed by a method of regression
• Can be used to make predictions
• SPSS can also do this

Question 20

What can be the main issue when using factor scores to make predictions?

Answer 20

• Want to ensure that there are enough cases in the data so that the predictions have some validity
• The sample should be reasonably representative of the population for which you want to draw conclusions on
• Sample size should be large

Question 21

What does an Eigenvalue of less than one represent?

Answer 21

• This means that a factor is accounting for less than a variables worth of variance

Question 22

What’s the theory behind using the Scree plot method?

Answer 22

• The idea is that real, meaningful factors should be noticeably larger than chance, spurious factors
• Should stop extracting factors when the eigenvalues of the next factors start to look identical

Question 23

What does the term orthogonal rotation mean in terms of the factors?

Answer 23

• Varimax orthogonal rotation preserves the independence of the factors