Week 11 - Factor Analysis Flashcards
What 2 aims of factor analysis used for ?
1) When looking for the underlying (predicted) structure of a set of related variables (You are specifically looking for an effect that you want to exist)
2) Trying to reduce set of variables to a single, composite variable that combine shared info in them (Variance) (More of an exploratory approach)
What does factor analysis seek to do?
Factor analysis seeks to form linear composites (sums of underlying variables)that represent the underlying structure of the correlation matrix
- Groups of highly intercorrelated items whose variance is well explained by the composite
What is main goal of factor analysis?
To start with a set of measured variables and find the smallest number of factors to account for most the variance in the measured variable and the correlations between them
Factor analysis allow to
Make statements about the patterns of intercorrelations
Typical factor analysis set up
Set of observed (questionnaire items) or conceptually related items (No Y variables)
- Does underlying structure link a subset of items?
- Subsets of variables that correlate highly with one another and low on other factors
Factor analysis is …
Geometric, based on correlations and the pattern of correlations that suggest linked items
Factors (Composites) in factor analysis should
Explain more than or two variables
Should explain systematic variance and exclude individual error as much as possible
History of factor analysis
Used in intelligence test (underlying g)
What can;t factor analysis do
Test for significance
2 reasons for doing factor analysis
1) data reduction to provide composites for further study
- empirical and technical reason
- after analysis is done we can obtain a factor as a new composite variable in our dataset
2) Investigate the underlying structure of a set of measured variables
- Give name to these variable using subjective judgement
Latent Variable
Not directly observed variable, Factor analysis uncover these
Observed Variables
Directly observed, exist in dataset already
Two Varieties of Factor Analysis
1) Principle Components factor analysis (PCA)
2) Factor analysis (Common factor model) (PAF)
Principle components factor analysis
Most basic form
Use mathematical properties of matrices (numbers)
Straight data reduction where error in original variables is not partialled out (all variance is used) (Does not ignore error in individual item)
Common factor model
First utilised for theory building - start with a set of variables and need to know how many dimensions (components) they contain
Known as exploratory factor analysis
Analyses common variance and leave out the unique variance to each individual variable