EFA Theory

Question 1

What is EFA

Answer 1

a mathematical technique by which patterns of correlations can be explained by a smaller number of variables (components/factors)

Question 2

What is usually assumed in an EFA

Answer 2

that these components (factors) are uncorrelated.

Question 3

What does EFA make possible

Answer 3

modelling the extent to which measured variables and their co-variability can by explained by a smaller number of latent variables

Question 4

What does EFA often reach the same solution as

Answer 4

PFC

Question 5

What is EFA confirmatory to

Answer 5

The researchers specify a model that is then tested

Question 6

What are different models compared in

Answer 6

Goodness of fit

Question 7

What is a latent factor or variable

Answer 7

Not directly observed, cannot be directly measured
E.g. cognitive ability
and EFA measures different aspects of it

Question 8

What is the main question of EFA

Answer 8

Are those aspects riven by the same underlying principles

Question 9

What does EFA aim to do

Answer 9

Understand the structure of set of variables

Try to find a simple structure

Question 10

How does an EFA try a simple structure

Answer 10

identify relatively independent clusters of variables – reduce large set of variables to smaller subset while keeping information

Question 11

What are the pre-analysis checks of EFA

Answer 11

Correlation matrix

Sample size, number of items

Question 12

What does EFA extraction measure

Answer 12

How many factors

Question 13

What does ration decide

Answer 13

how to best view the soltion

Question 14

What does naming do

Answer 14

Name the factors, how good was the EFA

Question 15

What does the correlation matrix show

Answer 15

Variables that cluster together that are corelated together usually 2 up and down and right to the bottom

Question 16

Why are some sample size pre-condtions needed

Answer 16

because correlations coefficient are less reliable for small samples

Question 17

How many participants are needed per item

Answer 17

N (participants) / P (items): 5:1, 10:1

absolute minimum 100

Question 18

How many subjects to facts

Answer 18

N (subjects) / M (factors): 6:1

Question 19

How many items to facotrs

Answer 19

P (items) / M (factors) : 4:1

Question 20

What are the two stats checks

Answer 20

Sampling adequacy and R matrix

Question 21

What does the sampling adequancy do

Answer 21

measure the extent to which the data is suitable for EFA (is there some common variability that can explained by some factors)

Question 22

What do the factors =

Answer 22

linear combinations of variables

Question 23

What are the three commonly used ways to extract factors

Answer 23

K1 rule
Scree test
Parallel Analysis

Question 24

What are all the three extract factors based on

Answer 24

Eigenvalues

Question 25

What are eigenvalues

Answer 25

Are a measure of the variance explained by a factor (principal component

Question 26

What is assumed about eigenvalues

Answer 26

that the more the variance that is explained the better….

Question 27

What do you select with the K1 rules

Answer 27

Select all factors with eigenvalue totals >1

Question 28

What is does the scree test plot

Answer 28

Plot the eigenvalues against the component number

Question 29

What did Cattell argue the cut off point should be

Answer 29

argued that the cut off point should be before the point of inflexion

Question 30

When can scree test visual test be a problem

Answer 30

if the plot doesn’t have a clear ‘point of inflexion

Question 31

Which do you count in the scree test

Answer 31

Those to the left of the point of infection ignoring the point itself

Question 32

What does parallel analysis do

Answer 32

Generate a set of ‘random’ eigenvalues given N (number of participants) and P (number of items)

Question 33

What does parallel analysis extract

Answer 33

Extract as many factors as there are observed eigenvalues greater than the random eigenvalues

Question 34

What are the two types of rotation

Answer 34

Orthogonal and Oblique

Question 35

What do the types of rotation try and achieve

Answer 35

simple structure’ (the maximization of loadings on one factor while minimizing on the other factors).

Question 36

What does orthogonal rotation assume

Answer 36

that the factors are not correlated with each other

Question 37

What is the orthogonal rotation

Answer 37

Varimax rotation is one kind of orthogonal rotation

Question 38

What does oblique ration assume

Answer 38

Assume that the factors are correlated with each other

Question 39

What is a kind of oblique ration

Answer 39

Direct Oblimin rotation is one kind of oblique rotatio

Question 40

What type of rotation is more difficult to justify

Answer 40

Oblique

Question 41

Why are oblique rotations more difficult to justify

Answer 41

since in EFA it is assumed that the correlations between factors are all the same size (just not zero).

Question 42

Where are the factors loadings found

Answer 42

In the component matrix

Question 43

What do factor loadings do

Answer 43

Place factors into significance

Question 44

What factor loadings are not shown

Answer 44

< 3

Question 45

When the numbers are in both 1 and 2 of the component matrix what does that suggest

Answer 45

potential cross loading

Question 46

What figures should be considered cross loadings

Answer 46

Any loading ≥.3 should be considered a potential cross-loading

Question 47

What figures are not considered as cross loadings

Answer 47

If the difference between loading is ≥.2 the variable is regarded as not cross-loading.

Question 48

Define reliability

Answer 48

A reliable measure consistently reflects the measured construct.

Question 49

What are the tests of internal reliability

Answer 49

Split half test. Cronbach’s alpha (∈[-∞, 1], α≥.7) KR-20 (∈[0, 1], KR20≥.9

Question 50

What are the tests of external reliability

Answer 50

test-retest: r > 0.7

Question 51

What should be considered when naming factors

Answer 51

Theoretical considerations Size of factor loading Common sense Raters

Question 52

Who suggested the recapture item technique

Answer 52

Meehl 1971

Question 53

What are the three components of variability

Answer 53

Unique - Specific to that variable Common - Shared with other variables Error – Random variability

Question 54

What is communality

Answer 54

Proportion of variance explained by extracted factors | A measure of ‘common’ variance.

Question 55

What are all communality

Answer 55

>.6: N≥100

Question 56

What are communalties

Answer 56

5 & only a few factors: N∈[100, 200]

Question 57

What is the commonalties for many factors

Answer 57

<500

Question 58

How do you test an EFA

Answer 58

Researchers typically now move on to ‘Confirmatory Factor Analysis’ where theoretically specified models are tested directly.

Question 59

How many solutions to a ration is there

Answer 59

Infinte

Question 60

What mentality can be added to factors

Answer 60

Garbage In Garbage Out