L8 - Factor Analysis Flashcards
Purpose of the Factor-analysis
Discover the factors that influence the co-variation among multiple observed variables; reduce large set of variables to smaller set of factors.
Two categories of approaches concerning factor analysis
- factor analysis (estimation of latent variable and generalization to population)
- exploratory PCA
What are two types of factor analysis
- confirmatory
- exploratory
What is PCA about?
Summary of correlational structure in a given data set
are people in the data set objects or items?
objects
How does the model look like in factor analysis?
What are the loadings?
weight of a factor to express x
How to determine how many factors to retain
Eigenvalues
What is an Eigenvalue
Sum of the (normalized) variance that is reproduced by a specific factor.
How to decide how many factors to retain?
Put eigenvalues on y-axis and components on x-axis:
- Scree test
- Parallel analysis
What is the scree test about?
- Plot eigenvalues of factors in descending order
- determine the number of factors where the eigenvalue levels off “Elbow criterion”
What is the parallel analysis about?
- You generate a random data set with the same number of variables and objects as the empirical data set
- run PCA
- repeat many times
- plot average eigenvalue for each extracted value
–> cutt off where data and simulated data meet
The Elbow criterion is used to
identify an appropriate number of clusters and factors
What is factor loading?
The correlation of an item with a factor
e.g item 21 with factor PC1
What is communality?
Proportion of variance of a variable accounted for by the extracted factors.
What is uniqueness
1 - communality. Proportion of variance of a variable not accounted for by the extracted factors.
What facilitates interpretation of factors?
Rotation.
Here F1 and F2 better represent the data. You have a more equal distribution of variance across the PCs.
What is orthogonal rotation?
Rotated factors are uncorrelated.
What is oblique rotation?
