Wk 3 - EFA 1

Question 1

What are the major objectives of EFA? (x2)

Answer 1

Simplify data set

Clarify constructs measured by vars used

Question 2

How does EFA simplify data sets? (x2)

Answer 2

Groups vars by assessing shared variance in responses

Meaning of hypothetical constructs based on var content and theory

Question 3

How does EFA clarify constructs? (x1)

Answer 3

Enables judgements of construct validity

Question 4

What are 2 things to remember when summarising data with factors?

Answer 4

o Factors directly summarize commonalities among different measures
o Not all measures contribute equally to a factor

Question 5

What 2 types of variance are involved in EFA? (plus define, x 1 each)

Answer 5

o Unique: Proportion that is not shared with other variables

o Communal: Proportion that is

Question 6

What determines the factor structure in EFA? (x1)

Because we assume that… (x1)

Answer 6

Patterns of communality that reflect subsets of variables with high correlations
Such patterns reflect underlying psych constructs

Question 7

What is the goal of EFA? (x1)

Which is achievesd by… (x1)

Answer 7

o To arrive at a parsimonious factor structure

 Boiling numerous tasks/items down to best number of underlying factors

Question 8

What are the 2 steps in EFA? (plus describe, x1 each)

Answer 8

Extraction of factors - capture max shared variance across factors
Rotation - simplify the resulting structure

Question 9

Define eigenvector (used in FA) (x1)

Answer 9

Best fitting regression line for each ‘largest amount of variance possible’

Question 10

Define Factor Loadings (x1)

Answer 10

Correlation between each observed varibale and a given factor

Question 11

What do eigenvalues do? (x1)

Calculatede by…(x1)

Answer 11

Quantify variance explained by each eigenvector

Sum of squared factor loadings

Question 12

Describe the extraction process in EFA (x4)

Answer 12

Plot k number of variables, giving hypothetical k-dimensional space
Pass k orthogonal eigenvectors (or enough to capture all variance, if

Question 13

What is the result of applying orthogonal eigenvectors in EFA? (x2)

Answer 13

Earlier eigenvectors account for more variance than later ones
So each new eigenvector captures unique portion of data

Question 14

What are the limitations of extraction in EFA? (x2, plus explain x3, x3)

Answer 14

Is blunt instrument:
 Each factor explains as much variance as possible
 But don’t care which variables contribute to each
 Esp. for “late” factors - more constraints

Potential for complex factor structure:
 Factors could have variables with high loadings AND low
 Possiblt difficult to cleanly identify meaningful/interpretable subgroups of variables
 ie, ambiguous relationships, esp. toward last eigenvectors

Question 15

How does rotation address the limitations of extraction in EFA? (x2)

Answer 15

Simplifies factor structure

 Maximize high loadings, minimize low loadings for each factor

Question 16

How does rotation achieve its goals in EFA? (x3)

Answer 16

Eigenvectors rotated to better capture variable subsets w high loadings
Changes pattern of shared variance for that factor
Make factors interpretable, but within mathematical constraints

Question 17

What are the constraints on rotation in EFA? (x2)

Answer 17

 Number of factors must remain the same as in the Extraction stage
 Proportion of variance explained by each factor must remain the same

Question 18

How does rotation work in EFA? (x2)

Answer 18

 Increases in high loadings must be matched by decreases in low
 Eigenvalue therefore stays constant

Question 19

Where does rotation make the biggest difference in EFA? (x2)

Answer 19

Variables that loaded onto multiple factors

ie, leaves the high loadings alone :-) and sorts out ambiguity

Question 20

After rotation in EFA, it should be easier to… (x2)

Answer 20

Interpret the factor structure

Identify themes in the data

Question 21

What is an important caveat on rotation in EFA?

Answer 21

If no clear patterns of correlations among subgroups of variables (ie, rubbish/noisy data), no distinct/interpretable factors will emerge
 Communalities for variables will be low to begin with

Question 22

What are 2 possible reasons for rotation failing to reveal distinct factor pattern in EFA?

Answer 22

 No distinct constructs underlie the variables

 Variables might not be assessed properly

Question 23

What are the 5 steps in running an EFA?

Answer 23

Planning for the analysis
Decide on the number of factors to retain
Choose an extraction method
Choose a rotation method
Interpret the solution

Question 24

What are the 2 areas of consideration when Planning the Analysis in EFA?

Answer 24

Data collection

Checking assumptions

Question 25

What are 3 considerations when planning Data Collection in EFA?

Answer 25

What variables/items to asssess How many variables/items needed? (3-6/factor) How many Ps/cases needed? (2-5 times number of variables, or >50 Ps)

Question 26

What are 4 considerations when planning Checking Assumptions in EFA?

Answer 26

Interval scale? Sufficient variance in scores? Linear correlation between scores? (ideally around .30 - need relationship but not invariance/parsimony) Normal distrbution? (no outliers, skew - distort correlations)

Question 27

What are the considerations when Deciding on Number of Factors to retain in EFA? (x4)

Answer 27

Extraction aims to account for all variance But, noise? Tiny variance explained? Or only single variable? So, how many factors looking for? And, how many do you have evidence for?

Question 28

What are the primary mechanisms for Deciding on Number of Factors to retain in EFA? (x1)

Answer 28

Stopping rules

Question 29

What are the 3 Stopping Rules used to Decide on Number of Factors to retain in EFA?

Answer 29

A priori decision Kaiser's criterion Scree test

Question 30

On what basis would you use A priori Decision Stopping rule to decide on number of retained factors in EFA? (x1) Eg (x1) And this is applied by... (x1)

Answer 30

When strong evidence exists for constructs of interest, mapping new scale onto prior theory Constraining extraction to this number

Question 31

What are the pros of A priori decisions on number of factors retained in EFA? (x2)

Answer 31

* Scientifically appropriate to make a priori decisions | * Constrained analysis might reduce severity of interpretation problems

Question 32

What are the considerations of A priori decisions on number of factors retained in EFA? (x2)

Answer 32

* If existing theory is underdeveloped, exploration is limited… * Can’t address questions about number of factors underlying constructs

Question 33

How does the Kaiser's Criterion Stopping Rule enable a decision on number of factors to retain in EFA? (x3)

Answer 33

Variables are standardized, so variance = 1  If eigenvalue > 1, factor explains more variance than single variable—achieves data reduction So retain all factors > 1

Question 34

What is the pro and con to using the Kaiser's Criterion to decide on number of factors to retain in EFA? (x1)

Answer 34

Permits true exploration of the data

Question 35

How does the Scree Test facilitate the decision on how many factors to retain in EFA? (x6)

Answer 35

Calculate Scree Plot of eigenvalues of each factor Apply Discontinuity Principle: • Draw line summarizing descending part of plot • And flat part • Lines intersect at point of inflection • Retain number of factors to the left of there

Question 36

How to choose a stop rule for deciding on number of factors to retain in EFA?(x4)

Answer 36

Strong a priori ideas? Then specify number of factors Use post-hoc for true exploration - Kaiser's or Scree Potential for differing conclusions, So try all, examine consistency and interpretability