Yannick Kurvers 8008701
3a)
In Principal Axis Factoring (PAF) and orthogonal rotation (Varimax), the variance is well
distributed between the two principal factors, but the separation of the factors is quite strict.
This means that the factors are well separated from each other, but variables that theoretically
should be linked, such as social and political trust, may be pulled (slightly) too far apart. This
could be a drawback if the factors should actually be correlated.
In PAF with non-orthogonal rotation (Oblimin), where the factors do not necessarily have to be
independent, you see that there is a clear correlation between the two factors, which is more
realistic for variables such as trust, which are often correlated. The downside of this is that the
overlaps between the factors make interpretation a bit more difficult, as they are not
completely separated. According to Brown (20151), non-orthogonal rotations like Oblimin are
preferred when factors are expected to be correlated, which aligns with my findings where the
factors showed a clear correlation.
If Maximum Likelihood (ML) applied and orthogonal rotation (Varimax), The three extracted
factors explain the variance quite nicely. However, this exhibits a Heywood case, meaning
there are invalid values for the unique variance, which can cause reliability of the results to
decrease. Incidentally, this is not a problem with the other methods.
Finally, ML with oblimin rotation offers a solution where the three factors explain the variance
well and correlations between the factors are allowed. This offers the possibility of modelling
realistically correlated factors. However, as with the PAF with oblimin, the overlaps between
the factors can make interpretation more difficult.
In summary, the choice between these methods depends on the theory behind them. If we
think the factors are completely independent, then PAF with Varimax is probably the best
option. If we think the factors are correlated, then ML with Oblimin is the best choice, despite
the possible complications in interpreting overlaps.
3b)
Eigenvalue > 1 is used to determine the number of factors in factor analysis. Any factor that
has an eigenvalue greater than 1 is considered a useful factor that explains a significant
amount of variance in the data. This is because the eigenvalue of a factor indicates how much
variance that factor explains compared to the original variables. If the eigenvalue is greater
than 1, it means that the factor explains (provides information about) at least as much variance
as any of the original variables. If the eigenvalue is greater than 1, it means that the factor
explains (provides information about) at least as much variance as any of the original
variables.
According to Brown (2015: Ch. 2)2, an eigenvalue greater than 1 means that the factor
explains more variance than a single original variable. In other words, the factor is sufficiently
informative and contributes significantly to the structure of the data. If that value is smaller
than 1, it means that the factor explains less variance in the original variables.
The eigenvalue > 1.0 rule is a good approach because it provides an objective and easy-to-
apply method for selecting the number of factors. It prevents retaining factors that explain little
variance, which helps in reducing the complexity of the analysis.
The scree plot provides a visual way of showing how many factors are actually useful and
therefore significant. Here, the eigenvalues are exposed to the number of factors. We often
see the so-called ‘kink’. This is the transition where the eigenvalues go from a steep decline to
suddenly a much less steep decline. The scree plot helps to visually confirm the decision
based on the eigenvalue > 1.0 rule, and it is particularly useful when the eigenvalue decline is
less clear or when multiple potential "kinks" appear.
3c)
The correlation between the factor score for social trust (efa_factor1) and the manually
created social_trust scale is 0.6302, indicating a moderate positive relationship between the
two. The correlation between the factor score for political trust (efa_factor2) and the manually
created political_trust scale is 0.9964, indicating an extremely strong positive relationship. This
1
Brown (2015: Ch. 1 & 2): Skim the first chapter as it is mostly repetition from last week
and gives an overview of the book. Chapter 2 is essential. Make sure you understand the
procedure of EFA: (1) factor extraction, (2) factor selection, (3) factor rotation, and (4)
factor scores
2
Brown (2015: Ch. 1 & 2): Skim the first chapter as it is mostly repetition from last week
and gives an overview of the book. Chapter 2 is essential. Make sure you understand the
procedure of EFA: (1) factor extraction, (2) factor selection, (3) factor rotation, and (4)
factor scores
1
3a)
In Principal Axis Factoring (PAF) and orthogonal rotation (Varimax), the variance is well
distributed between the two principal factors, but the separation of the factors is quite strict.
This means that the factors are well separated from each other, but variables that theoretically
should be linked, such as social and political trust, may be pulled (slightly) too far apart. This
could be a drawback if the factors should actually be correlated.
In PAF with non-orthogonal rotation (Oblimin), where the factors do not necessarily have to be
independent, you see that there is a clear correlation between the two factors, which is more
realistic for variables such as trust, which are often correlated. The downside of this is that the
overlaps between the factors make interpretation a bit more difficult, as they are not
completely separated. According to Brown (20151), non-orthogonal rotations like Oblimin are
preferred when factors are expected to be correlated, which aligns with my findings where the
factors showed a clear correlation.
If Maximum Likelihood (ML) applied and orthogonal rotation (Varimax), The three extracted
factors explain the variance quite nicely. However, this exhibits a Heywood case, meaning
there are invalid values for the unique variance, which can cause reliability of the results to
decrease. Incidentally, this is not a problem with the other methods.
Finally, ML with oblimin rotation offers a solution where the three factors explain the variance
well and correlations between the factors are allowed. This offers the possibility of modelling
realistically correlated factors. However, as with the PAF with oblimin, the overlaps between
the factors can make interpretation more difficult.
In summary, the choice between these methods depends on the theory behind them. If we
think the factors are completely independent, then PAF with Varimax is probably the best
option. If we think the factors are correlated, then ML with Oblimin is the best choice, despite
the possible complications in interpreting overlaps.
3b)
Eigenvalue > 1 is used to determine the number of factors in factor analysis. Any factor that
has an eigenvalue greater than 1 is considered a useful factor that explains a significant
amount of variance in the data. This is because the eigenvalue of a factor indicates how much
variance that factor explains compared to the original variables. If the eigenvalue is greater
than 1, it means that the factor explains (provides information about) at least as much variance
as any of the original variables. If the eigenvalue is greater than 1, it means that the factor
explains (provides information about) at least as much variance as any of the original
variables.
According to Brown (2015: Ch. 2)2, an eigenvalue greater than 1 means that the factor
explains more variance than a single original variable. In other words, the factor is sufficiently
informative and contributes significantly to the structure of the data. If that value is smaller
than 1, it means that the factor explains less variance in the original variables.
The eigenvalue > 1.0 rule is a good approach because it provides an objective and easy-to-
apply method for selecting the number of factors. It prevents retaining factors that explain little
variance, which helps in reducing the complexity of the analysis.
The scree plot provides a visual way of showing how many factors are actually useful and
therefore significant. Here, the eigenvalues are exposed to the number of factors. We often
see the so-called ‘kink’. This is the transition where the eigenvalues go from a steep decline to
suddenly a much less steep decline. The scree plot helps to visually confirm the decision
based on the eigenvalue > 1.0 rule, and it is particularly useful when the eigenvalue decline is
less clear or when multiple potential "kinks" appear.
3c)
The correlation between the factor score for social trust (efa_factor1) and the manually
created social_trust scale is 0.6302, indicating a moderate positive relationship between the
two. The correlation between the factor score for political trust (efa_factor2) and the manually
created political_trust scale is 0.9964, indicating an extremely strong positive relationship. This
1
Brown (2015: Ch. 1 & 2): Skim the first chapter as it is mostly repetition from last week
and gives an overview of the book. Chapter 2 is essential. Make sure you understand the
procedure of EFA: (1) factor extraction, (2) factor selection, (3) factor rotation, and (4)
factor scores
2
Brown (2015: Ch. 1 & 2): Skim the first chapter as it is mostly repetition from last week
and gives an overview of the book. Chapter 2 is essential. Make sure you understand the
procedure of EFA: (1) factor extraction, (2) factor selection, (3) factor rotation, and (4)
factor scores
1
