Factor Analysis Flashcards
What is the aim of FA
To reduce a larger set of variables into a smaller set of components
The ‘smaller set of components’ in FA aims to…
Account for most of the variance in the original variables
How is factor analysis done?
By analysing patterns of correlations between variables
Groups of variables that relate highly to each other…
Constitute a factor
What is one type of factor analysis?
Principle components analysis
Difference between PCA and FA?
FA is often used with a smaller set of variables
Idea underlying the PCA equation…
Equation that MAXIMISES the variance accounted for by a component
The second component should be ______ with the first
Uncorrelated
The second component should be uncorrelated with the first, yet still
Accounting for max amount of variance remaining
A Factor loading is…
The correlation between a variable and a component
“The correlation between a variable and a component” - What is this?
Factor loading
What would we do with factor loadings to tell us the variance this component explains over others?
Squaring and summing
Absolute loadings above >.3 are…
Salient and interpreted
Where do we find the factor loadings in SPSS?
Component matrix
The level of correlation considered worthy of a variables inclusion is usually…
> .3
You would examine the correlation matrix to see…
If there are any variables NOT strongly correlated with any other variable
Communalities are…
Proportion of variance in a variable accounted for by EXTRACTED COMPONENTS
If you were to retain all components in the analysis, you will be able to account for all the variance in the variables. Why don’t we just do this?
This not the purpose
Purpose is to explain as much variance as poss whilst using as few variables as poss
Total Variance Explained table…How many components are usually extracted?
Generally only the first few
What is an Eigenvalue?
The measure of VARIANCE accounted for by a COMPONENT
Sum of squared loadings within a component
An Eigenvalue of 1 represents the….
Variance of one variable
Eigenvalues
25 variables represents…
25 eigenvalues
What is the most popular method for choosing COMPONENTS to retain?
Eigen-value one criterion (Kaiser criterion)
What is Kaiser’s criterion recommendation?
Eigenvalue less than 1 should not be retained
Kaiser’s Criterion states that a variable less than one indicates…
That the component explains less than a variable would
How is an Eigenvalue calculate?
Sum of squared loadings within a component
Eigenvalues range between…
0-total number of components
An Eigenvalue larger than ____ is GOOD
1
An Eigenvalue larger than 1 indicates the factor…
Should be selected
A communality of ____ suggests that the variable is _______ and should be _______
< .3
Unreliable
Removed
Aside from Kaiser’s Criterion, what else can we use to decide which components to keep?
Scree plot
What does a scree plot tell us
Total variance explained by each component against its respective component
Scree plot
How do we know which components to retain
Those before last inflection point
Scree plot
The inflection point represents
The point at which the graph begins to level out
Subsequent components add little
“The point at which the graph begins to level out
Subsequent components add little”
What does this description refer to?
Inflection point
A scree plot is another way of…
Deciding which components to keep/remove
The first Factor Loading matrix SPSS will display is…
Unrotated
What is one way of visualising the clusters of variables that form the components?
Plot variables in a factor space
Our ideal result would be where each variable loads uniquely onto…
ONE COMPONENT ONLY
Our ideal result would be where each variable loads uniquely onto one component only. However, what do we often find?
Cross-loading
Two ways of solving cross-loading?
Orthogonal/oblique rotation
What is orthogonal rotation?
Where we rotate the axis to fit the data we’ve got
What is the difference between orthogonal and oblique rotation?
Oblique moves through each axes independently until they go through items
Why are orthogonal/oblique rotations used?
- Solves cross-loading
- Makes interpretation easier
6 STEPS OF FACTOR ANALYSIS
a) Matrix of Correlations B) Extract factors (Kaiser's) & Scree plot C) Examine FLs and communalities D) Do factors need rotating E) Check FLs again
A PCA can be used to solve three major problems…
a) Removing unrelated variables
b) Reducing redundancy
c) Removing multicollinearity
What is multicollinearity
Two or more variables that are highly correlated
“Two or more variables that are highly correlated “ Whats this
Multicollinearity
What does ‘redundancy’ refer to
Some of the variables are measuring the SAME UNDERLYING CONSTRUCT (not what you want)
What do we look at: SPSS
M of Correlations
Communalities
Eigenvalues
Factor loadings
Orthogonal rotation can sometimes create factors that are _______ or ________ with each other
Correlated
Uncorrelated
The proportion of variance each variable explains in the principle (extracted) components
What is this describing
Communalities
Comment on Factor Loadings
All items load highly onto the first component. Only some items load highly (both positively and negatively) onto the second factor.
Does this indicate a simple factor structure?
No - they need to be rotated
Factor loadings are the
Correlation between variable and component
“Correlation between a variable and a COMPONENT”
What is this
Factor loadings
Communalities
What is the cut-off for removal
.3
If there are 2 components making up the component matrix, this tells us…
2 components have been extracted
Orthogonal rotation keeps the axes at ______ ________, whereas Oblique does not
Right angles
How do you decide if it is complex structure when there are 3 components?
If there are items that load highly onto more than 1 component
Inspection of the commonalities revealed that the two factors accounted for (>.30)
Sufficient amount of variance in all items
Inspection of the commonalities revealed that the two factors accounted for sufficient amounts of variance in all items (>.30), indicating that
All items were reliable
The rotated factor loadings were plotted, which confirmed the clear
X factor structure
Write-up
Inspection of the FL’s indicated that all items loaded strongly (>.40) on both factors. The factor loadings were therefore
Plotted
Write-up
The unrotated factor loadings were then plotted which indicated
The factors should be subjected to rotation
Write-up
The rotated factor loadings were also plotted, which
Confirmed a clear two-factor structure
Write-up
Inspection of the commonalities revealed that the two factors accounted for
Sufficient amounts of variance in the items (>.30)
