exploratory factor analysis i Flashcards
They are not…
hypothesis testing – but in the wider sense “hypothesis generating”
Factor analysis is relevant in the context of
- Big data
- Personality models, e.g. Extraversion and Neuroticism, Big 5 etc
- Intelligence models and research (‘g-factor’, intelligence domains)
- Machine learning, unsupervised learning
- All kinds of technical applications, e.g. image/signal processing, neuroimaging applications
Vectors in 3D
1st number across
2nd number along
3rd number up
equation for cos of angle
x = cos(a) * l
l = hypotenuse
a = ?
a = arctan (y/x)
how strong is correlation if cos is 0 or 90
cos 0 deg = correlation of approx 1
cos 90 deg = correlation of 0
cos 180 deg = correlation of -1
latent variable
e.g a personality factor, or a physiological source in EEG/MEG
Model linking latent variables to observed variables
X = U * Y
X= observed value
U= projection of latent variables onto observed variable
Y= e.g a persoanlity factor…
For interpretating a PCA, the following outcomes/measures are crucial
the eigenvalues tell us how much variances each factor extracts
the factor loadings associated with each eigenvector represent the correlation of original variables with the new factors and help interpreting these
the factor scores are the new values of individual observations - these thus define the positions in the new coordinate system
what do factor analysis and PCA do powerfully?
find meaningful hidden patterns in vast datasets
allow reduction of very large datasets into smaller variables
find out about latent variables
what model did Eysenck (1967) base on factor analysis?
extraversion and neuroticism
what did Gary (1982) base on factor analysis?
impulsivity and anxiety - used as coordinates of eysenck’s model of extraversion & neuroticism
if correlation between 2 variables is high….
the angle between those 2 variables is smaller
how do we calculate x?
cos (angle) x length of vector
how do we calculate y?
sin (angle) x length of vector
