EFA Theory Flashcards
What is EFA
a mathematical technique by which patterns of correlations can be explained by a smaller number of variables (components/factors)
What is usually assumed in an EFA
that these components (factors) are uncorrelated.
What does EFA make possible
modelling the extent to which measured variables and their co-variability can by explained by a smaller number of latent variables
What does EFA often reach the same solution as
PFC
What is EFA confirmatory to
The researchers specify a model that is then tested
What are different models compared in
Goodness of fit
What is a latent factor or variable
Not directly observed, cannot be directly measured
E.g. cognitive ability
and EFA measures different aspects of it
What is the main question of EFA
Are those aspects riven by the same underlying principles
What does EFA aim to do
Understand the structure of set of variables
Try to find a simple structure
How does an EFA try a simple structure
identify relatively independent clusters of variables – reduce large set of variables to smaller subset while keeping information
What are the pre-analysis checks of EFA
Correlation matrix
Sample size, number of items
What does EFA extraction measure
How many factors
What does ration decide
how to best view the soltion
What does naming do
Name the factors, how good was the EFA
What does the correlation matrix show
Variables that cluster together that are corelated together usually 2 up and down and right to the bottom
Why are some sample size pre-condtions needed
because correlations coefficient are less reliable for small samples
How many participants are needed per item
N (participants) / P (items): 5:1, 10:1
absolute minimum 100
How many subjects to facts
N (subjects) / M (factors): 6:1
How many items to facotrs
P (items) / M (factors) : 4:1
What are the two stats checks
Sampling adequacy and R matrix
What does the sampling adequancy do
measure the extent to which the data is suitable for EFA (is there some common variability that can explained by some factors)
What do the factors =
linear combinations of variables
What are the three commonly used ways to extract factors
K1 rule
Scree test
Parallel Analysis
What are all the three extract factors based on
Eigenvalues
What are eigenvalues
Are a measure of the variance explained by a factor (principal component
What is assumed about eigenvalues
that the more the variance that is explained the better….
What do you select with the K1 rules
Select all factors with eigenvalue totals >1
What is does the scree test plot
Plot the eigenvalues against the component number
What did Cattell argue the cut off point should be
argued that the cut off point should be before the point of inflexion
When can scree test visual test be a problem
if the plot doesn’t have a clear ‘point of inflexion
Which do you count in the scree test
Those to the left of the point of infection ignoring the point itself
What does parallel analysis do
Generate a set of ‘random’ eigenvalues given N (number of participants) and P (number of items)
What does parallel analysis extract
Extract as many factors as there are observed eigenvalues greater than the random eigenvalues
What are the two types of rotation
Orthogonal and Oblique
What do the types of rotation try and achieve
simple structure’ (the maximization of loadings on one factor while minimizing on the other factors).
What does orthogonal rotation assume
that the factors are not correlated with each other
What is the orthogonal rotation
Varimax rotation is one kind of orthogonal rotation
What does oblique ration assume
Assume that the factors are correlated with each other
What is a kind of oblique ration
Direct Oblimin rotation is one kind of oblique rotatio
What type of rotation is more difficult to justify
Oblique
Why are oblique rotations more difficult to justify
since in EFA it is assumed that the correlations between factors are all the same size (just not zero).
Where are the factors loadings found
In the component matrix
What do factor loadings do
Place factors into significance
What factor loadings are not shown
< 3
When the numbers are in both 1 and 2 of the component matrix what does that suggest
potential cross loading
What figures should be considered cross loadings
Any loading ≥.3 should be considered a potential cross-loading
What figures are not considered as cross loadings
If the difference between loading is ≥.2 the variable is regarded as not cross-loading.
Define reliability
A reliable measure consistently reflects the measured construct.
What are the tests of internal reliability
Split half test.
Cronbach’s alpha (∈[-∞, 1], α≥.7)
KR-20 (∈[0, 1], KR20≥.9
What are the tests of external reliability
test-retest: r > 0.7
What should be considered when naming factors
Theoretical considerations
Size of factor loading
Common sense
Raters
Who suggested the recapture item technique
Meehl 1971
What are the three components of variability
Unique - Specific to that variable
Common - Shared with other variables
Error – Random variability
What is communality
Proportion of variance explained by extracted factors
A measure of ‘common’ variance.
What are all communality
> .6: N≥100
What are communalties
5 & only a few factors: N∈[100, 200]
What is the commonalties for many factors
<500
How do you test an EFA
Researchers typically now move on to ‘Confirmatory Factor Analysis’ where theoretically specified models are tested directly.
How many solutions to a ration is there
Infinte
What mentality can be added to factors
Garbage In Garbage Out
