Overview ARM II
Factor analysis – Multiple regression analysis – Logistic regression analysis
Factor analysis
Interdependence technique whose primary purpose is to define the underlying
structure among the variables in the analysis
7 stages
1. Clarify the objectives of factor analysis
⁃ Exploratory factor analysis: you are interested in finding an underlying
structure of the data. Main purpose = generation of hypothesis
⁃ Confirmatory factor analysis: you have priori ideas about underlying
factors, derived from theory. Main purpose = hypothesis testing.
2. Designing a factor analysis, including selection of variables and
sample size
⁃ Q factor analysis: cases
⁃ R factor analysis: variables
⁃ All variables have to be of interval or ratio level
3. Assumptions of exploratory factor analysis (om de geschiktheid
van factoranalyse te testen)
⁃ N needs to be 5x as big as the amount of variables
⁃ KMO to test if there is enough variance in the data
Rule: KMO > 0.5 (the closer to
1 the better)
⁃ Bartlett’s Test of sphericity
to test if there is correlation
between the items.
Rule: Bartlett’s sign. <0.05
(this means there is at least
one correlation between the items)
4. Deriving factors and assessing overall fit: which factor model to
use and the number of factors
2 major types of extraction methods
1. Principal component analysis
Common variance + unique variance
Primary concern: we want to have a minimum number of factors that will
account for maximum variance.
2. Common factor analysis (Principal axis factoring)
Only common variance
Primary concern: identify underlying dimensions and their common
variance.
,Determining the number of factors; there are several ways to do this:
⁃ Priori determination: what factors do you expect and how many?
⁃ Eigenwaarde > 1
⁃ Scree plot aantal factoren tot aan de knik
⁃ Cumulative variance > 60%
LET OP: bij principal axis factoring (common factor analysis) kijk je bij
cumulative % van initial eigenvalues en bij principal component analysis
kijk je bij cumulative % of extraction sum of squared loadings.
Dus: axis & common is links, component is rechts kijken
5. Rotating and interpreting the factors
Due to rotation, factors become more easily interpretable
There are 2 types of rotation:
1. Orthogonal: if the axes are maintained at right angles Varimax
rotated factor matrix
When to use: assumes factors are not
correlated
2. Oblique: if the axes are not maintained at
right angles Oblimin pattern matrix
When to use: allows factors to be
correlated (desired)
If at least 1 factor in the correlation
matrix is >0.30, it is oblique! data
driven argument
But use also theory!
Deciding which items to delete:
, Variables with communality <0.20 are not sufficiently declared by the factor
analysis, so these items have a weak correlation with the factor.
To determine which items to delete and which first, you look at the rotation
tables (rotated factor matrix or pattern matrix) to see if there are cross loaders.
Cross loader if the difference between highest factor loading and second highest
factor loading is < 0.20
Delete the items with a
communality < 0.20 and
who are also cross loaders
first.
You keep deleting items
until all communalities are >
0.20 and there are no cross
loaders anymore. Each time
after deletion you again
assess if factor analysis is
still applicable through:
⁃ KMO > 0.5
⁃ Bartlett < 0.05
And you look again at the number of factors through:
⁃ Eigenvalue > 1
⁃ Cumulative variance > 60%
Then again look at the items with a communality < 0.20 and see if there are any
cross loaders.
Eventually you want a pattern matrix in which each variable loads clearly on 1
factor.
Minimal level: around 0.5
Significant: > 0.5
Desirable: > 0.7
Name the factors and describe which variables eventually load on each factor.
6. Validation of exploratory factor analysis solutions (Cronbach’s
Alpha)
For each factor you assess reliability and validity.
The reliability test is necessary to measure the consistency and repeatability of
the variables in order to say something about the construct validity. Construct
validity consists of convergent validity and discriminant validity.
Factor analysis – Multiple regression analysis – Logistic regression analysis
Factor analysis
Interdependence technique whose primary purpose is to define the underlying
structure among the variables in the analysis
7 stages
1. Clarify the objectives of factor analysis
⁃ Exploratory factor analysis: you are interested in finding an underlying
structure of the data. Main purpose = generation of hypothesis
⁃ Confirmatory factor analysis: you have priori ideas about underlying
factors, derived from theory. Main purpose = hypothesis testing.
2. Designing a factor analysis, including selection of variables and
sample size
⁃ Q factor analysis: cases
⁃ R factor analysis: variables
⁃ All variables have to be of interval or ratio level
3. Assumptions of exploratory factor analysis (om de geschiktheid
van factoranalyse te testen)
⁃ N needs to be 5x as big as the amount of variables
⁃ KMO to test if there is enough variance in the data
Rule: KMO > 0.5 (the closer to
1 the better)
⁃ Bartlett’s Test of sphericity
to test if there is correlation
between the items.
Rule: Bartlett’s sign. <0.05
(this means there is at least
one correlation between the items)
4. Deriving factors and assessing overall fit: which factor model to
use and the number of factors
2 major types of extraction methods
1. Principal component analysis
Common variance + unique variance
Primary concern: we want to have a minimum number of factors that will
account for maximum variance.
2. Common factor analysis (Principal axis factoring)
Only common variance
Primary concern: identify underlying dimensions and their common
variance.
,Determining the number of factors; there are several ways to do this:
⁃ Priori determination: what factors do you expect and how many?
⁃ Eigenwaarde > 1
⁃ Scree plot aantal factoren tot aan de knik
⁃ Cumulative variance > 60%
LET OP: bij principal axis factoring (common factor analysis) kijk je bij
cumulative % van initial eigenvalues en bij principal component analysis
kijk je bij cumulative % of extraction sum of squared loadings.
Dus: axis & common is links, component is rechts kijken
5. Rotating and interpreting the factors
Due to rotation, factors become more easily interpretable
There are 2 types of rotation:
1. Orthogonal: if the axes are maintained at right angles Varimax
rotated factor matrix
When to use: assumes factors are not
correlated
2. Oblique: if the axes are not maintained at
right angles Oblimin pattern matrix
When to use: allows factors to be
correlated (desired)
If at least 1 factor in the correlation
matrix is >0.30, it is oblique! data
driven argument
But use also theory!
Deciding which items to delete:
, Variables with communality <0.20 are not sufficiently declared by the factor
analysis, so these items have a weak correlation with the factor.
To determine which items to delete and which first, you look at the rotation
tables (rotated factor matrix or pattern matrix) to see if there are cross loaders.
Cross loader if the difference between highest factor loading and second highest
factor loading is < 0.20
Delete the items with a
communality < 0.20 and
who are also cross loaders
first.
You keep deleting items
until all communalities are >
0.20 and there are no cross
loaders anymore. Each time
after deletion you again
assess if factor analysis is
still applicable through:
⁃ KMO > 0.5
⁃ Bartlett < 0.05
And you look again at the number of factors through:
⁃ Eigenvalue > 1
⁃ Cumulative variance > 60%
Then again look at the items with a communality < 0.20 and see if there are any
cross loaders.
Eventually you want a pattern matrix in which each variable loads clearly on 1
factor.
Minimal level: around 0.5
Significant: > 0.5
Desirable: > 0.7
Name the factors and describe which variables eventually load on each factor.
6. Validation of exploratory factor analysis solutions (Cronbach’s
Alpha)
For each factor you assess reliability and validity.
The reliability test is necessary to measure the consistency and repeatability of
the variables in order to say something about the construct validity. Construct
validity consists of convergent validity and discriminant validity.
