3C. Case Study

Question 1

What case study was used for an EFA?

Answer 1

Shopping Behaviour

12 variables measured on a likert scale (1-7),
n = 490 (respondents)

Question 2

Two of the variables had an * next to them, to indicate they were reverse coded, why is reverse-coding carried out?

Answer 2

Two main reasons:

1. Make scoring consistent: If higher scores should mean “more of the trait” (e.g., more satisfaction), a negatively worded item like “I am unhappy” needs reversing so a high response doesn’t lower the total score the wrong way.
2. Check attention / careless responding: If someone answers “Strongly agree” to both “I feel confident” and “I feel useless,” that’s a red flag.

Question 3

What are the 3 assumptions we have to be aware of?

Answer 3

1. Measurement level: Interval or ratio scales
2. Standardised data (mean = 0, standard deviation = 1)
3. Sample size: rule of thumb > 100 observations

Question 4

What are the 3 preliminary analyses that determine whether it makes sense to conduct an EFA?

Answer 4

1. There should be high correlations among sets of variables
2. Sample adequacy (Kaiser-Meyer-Olkin KMO)
3. Bartlett’s test of sphericity

Question 5

What is the scaled to determine whether the variables are sufficiently correlated with one another?

Answer 5

> 0.5: moderately high
0.6: high
0.7: very high

Question 6

If there is no correlation between the variables, why does an EFA not make sense?

Answer 6

Well an EFA’s entire purpose is GROUPING variables into underlying factors, if there is no correlation between variables… it undermines the entire purpose of this analysis!

Question 7

What is the scale used for “Sample Adequacy” (preliminary analysis)?

Answer 7

Kaiser-Meyer-Olkin KMO, (scale as listed in picture)

Question 8

What does Bartlett’s test need to be?

Answer 8

Significant!

Question 9

Does this KMO and Bartlett’s preliminary analysis show an EFA makes sense?

Answer 9

YES.

Because Bartlett’s test is significant
and
KMO is at 0.82, which is >0.8, and therefore “deserving” according to the scale

Question 10

What is step 2 (following the preliminary analysis)?

Answer 10

DETERMINING the NUMBER of FACTORS

Question 11

What are the two main ways the number of factors are determined?

Answer 11

1. Kaiser Criterian
2. Scree Plot

Question 12

What is the “Kaiser Criterion”?

Answer 12

Helps us determine number of factors

Select all factors with an eigenvalue GREATER than 1

Question 13

What is the problem with factors that have an eigenvalue SMALLER than 1?

Answer 13

They are NO better than a SINGLE variable - since each variable has a variance of 1.0 due to standisation

Question 14

What is a “Scree Plot”?

Answer 14

Helps us determine number of factors

Plot of Eigenvalues against the number of factors in order of extraction. Select one factor LESS than the ELBOW.

Question 15

Why is it said that the number of factors should exceed a “cumulative percentage variance” of 50% (preferably 75%)?

Answer 15

So the rule-of-thumb “≥50% (and ~75% is nicer)” is basically saying:

If your factors explain very little (e.g., 20–30%), you’ve reduced the data too aggressively and the factors may not represent the variables well.

If they explain a lot, the factor solution is doing a decent job summarizing the dataset

Question 16

Using the “Kaiser Criterion”, how many factors should you choose?

Answer 16

3 factors, because they are each >1

After this, the three together have a cumulative % of 59.774%

Question 17

Using the “Scree Plot”, how many factors should you choose?

Answer 17

1 LESS THAN ELBOW

so… in this case elbow is at 3, so only 2 factors

Question 18

If the “Kaiser Criterion” shows to use 3 factors, but the “Scree Plot” shows to use 2, what should you do?

Answer 18

COMPARE THE 3-FACTOR SOLUTION, AND 2-FACTOR SOLUTION, determine WHICH is more SUITABLE!

Question 19

What is done to facilitate the interpretation of a factor solution?

Answer 19

ROTATING THE FACTORS (using VARIMAX)!

Varimax makes a factor solution easier to interpret by “cleaning up” the loadings so each variable tends to belong clearly to one factor.

Question 20

What does “VARIMAX” do?

Answer 20

Varimax doesn’t change the overall fit/communality much—it mainly redistributes how variables load across factors to make the pattern clearer.

Before rotation: a variable loads .45 on Factor 1 and .40 on Factor 2 (ambiguous).

After varimax: it might load .70 on Factor 1 and .10 on Factor 2 (clear).

Question 21

What is this called?

Answer 21

CROSS-LOADING

Question 22

What is “CROSS-LOADING”?

Answer 22

Cross-loading is when one item/variable loads noticeably on more than one factor—so it doesn’t clearly “belong” to a single factor.

Question 23

Is this problematic?

Answer 23

Whilst cross-loading is problematic, the secondary loading is really low (only 0.2), so its not really problematic in this case

Question 24

What are the steps to interpreting (and comparing 2 vs 3 factor in this case)?

Answer 24

1. Check for high cross loadings (>0.4) and low absolute factor loadings (<0.5)
2. Assign each variable to a certain factor based on its maximum absolute factor loading
3. Find an umbrella term for each factor to describe the set of variables associated with that factor

Question 25

Why is the 2 factor choice more reasonable in this case?

Answer 25

Even though 3 factors DONT load in the 2 factor solution... Logically the umbrella terms make more sense in the 2-factor solution than the 3-factor solution. So the 2-factor solution is logically more meaningful even though it has more problematic variables! (look at the 3rd factor... it just doesnt make much logical sense)

Question 26

What is the LAST step to an EFA?

Answer 26

EVALUATE GOODNESS OF FIT

Question 27

What is the first step to a "Goodness Of Fit"?

Answer 27

REMOVE PROBLEMATIC ITEMS!!! -> remove those items and run the analysis again!

Question 28

From the final solution, find (name) the umbrella terms, and evaluate the goodness of fit:

Answer 28