Samenvatting multivariate analyse
Lieke Brekelmans
Kennisclips
Kennisclip 1
Steps in scale construction
1. Identifying indicators
2. Study measurement direction & frequency distribution
3. Determine dimensionality using factor analysis
4. Perform reliability analysis (Cronbach’s alpha)
5. Compute scale(s)
6. (scale validation)
Factor analysis
- The statistical tool that helps us find out if there are multiple dimensions at play
- It will look at the patterns of correlations among items and then tell us whether they
hang together as one factor or whether there are multiple underlying constructs at
play
A loading belongs with a factor when it’s > 0.3. They are strong loadings.
Before any analysis, we run a descriptive statistics for relevant variables.
With the correlation matrix, we distinguish meaningful factors
- There should be at least some correlations (|> .3) between items
- All correlations should not be too hight (|> .8)
Manieren om aantal factoren te bepalen:
1. Cattell criterion:
a. Scree plot
b. Kink – 1 = aantal factoren
2. Kaiser criterion:
a. Je kijkt naar eigen values of components
b. Hoeveelheid eigen values zijn hoger dan 1 = aantal factoren
Interpreting the factors
- The stronger a factor loading, the more an item represents the underlying concept
- Strong factor loadings (+ and -) indicate groups of items and guide interpretation
How are these loadings calculated (factor extraction)
1. Principal axis factoring (PAF)
a. Based on correlation matrix
,b.
c. We are looking at the effects of the underlying factors on the statements
d. The factors can correlate with each other
e. Only loadings than 0.3 are important
f. The causal model is a model of spurious correlations between the variables:
i. A relationship between two variables that appears to be meaningful,
but is actually cased by a third factor (or by coincidence) rather than a
direct connection between the two
g. This means that a factor F is constructed such that:
i. If from the measured variables the effect of factor F is removed, the
correlation between the variables disappear as much as possible (if
you remove F, the variables won’t correlate as much anymore)
ii. The correlation between the factor and the measured variables to
which causal arrows run, is as high as possible
h. PAF is looking for those underlaying factors that could be driving those
correlations
i.
, Factor loadings
- The coordinates of the items in a space in which the factors represent the axes
o Each variable is given a point in this space
o This point indivates the position on all factors
o The coordinates are the factor loadings (as observed in a Pattern Matrix)
o
Rotation
- Rotation of the axes (factors) changes the projection of the variables onto the axes: it
maximizes the loading of a variable on one factor and minimizes it on other factors
- This allows for better interpretation of the factors
-
- Types of rotation:
1. Orthogonal rotation: factors are uncorrelated, angle remains 90 degrees
Lieke Brekelmans
Kennisclips
Kennisclip 1
Steps in scale construction
1. Identifying indicators
2. Study measurement direction & frequency distribution
3. Determine dimensionality using factor analysis
4. Perform reliability analysis (Cronbach’s alpha)
5. Compute scale(s)
6. (scale validation)
Factor analysis
- The statistical tool that helps us find out if there are multiple dimensions at play
- It will look at the patterns of correlations among items and then tell us whether they
hang together as one factor or whether there are multiple underlying constructs at
play
A loading belongs with a factor when it’s > 0.3. They are strong loadings.
Before any analysis, we run a descriptive statistics for relevant variables.
With the correlation matrix, we distinguish meaningful factors
- There should be at least some correlations (|> .3) between items
- All correlations should not be too hight (|> .8)
Manieren om aantal factoren te bepalen:
1. Cattell criterion:
a. Scree plot
b. Kink – 1 = aantal factoren
2. Kaiser criterion:
a. Je kijkt naar eigen values of components
b. Hoeveelheid eigen values zijn hoger dan 1 = aantal factoren
Interpreting the factors
- The stronger a factor loading, the more an item represents the underlying concept
- Strong factor loadings (+ and -) indicate groups of items and guide interpretation
How are these loadings calculated (factor extraction)
1. Principal axis factoring (PAF)
a. Based on correlation matrix
,b.
c. We are looking at the effects of the underlying factors on the statements
d. The factors can correlate with each other
e. Only loadings than 0.3 are important
f. The causal model is a model of spurious correlations between the variables:
i. A relationship between two variables that appears to be meaningful,
but is actually cased by a third factor (or by coincidence) rather than a
direct connection between the two
g. This means that a factor F is constructed such that:
i. If from the measured variables the effect of factor F is removed, the
correlation between the variables disappear as much as possible (if
you remove F, the variables won’t correlate as much anymore)
ii. The correlation between the factor and the measured variables to
which causal arrows run, is as high as possible
h. PAF is looking for those underlaying factors that could be driving those
correlations
i.
, Factor loadings
- The coordinates of the items in a space in which the factors represent the axes
o Each variable is given a point in this space
o This point indivates the position on all factors
o The coordinates are the factor loadings (as observed in a Pattern Matrix)
o
Rotation
- Rotation of the axes (factors) changes the projection of the variables onto the axes: it
maximizes the loading of a variable on one factor and minimizes it on other factors
- This allows for better interpretation of the factors
-
- Types of rotation:
1. Orthogonal rotation: factors are uncorrelated, angle remains 90 degrees
