Factor Analysis Flashcards
What type of ‘multivariate analysis’ does factor analysis come under?
Analysis of INTERDEPNDENCE: aims of reducing and simplifying very large amounts of data into more manageable amounts
What is factor analysis and why is it useful?
The overall aim is turning VARIABLES into FACTORS.
A way of identifying correlations between a number of observed variables, by clumping similar variables together into underlying factors (high correlations in each factor). Can be both exploratory and confirmatory.
Very useful for complex phenomena that can’t be easily quantified and measured by one variable, but have several factors, each with their own correlating variables.
Define ‘factor’
A ‘super-variable’ with its commenness expressed by the group of variables having higher intercorrelations but low correlations with any other group (Burns & Burns).
Define ‘factor loading’
The relative connection of each of the original variables to a factor. A loading nearer -1 would be weak, 0.5 moderate, and +1 would be strong.
Give an overview of the overall steps involved (x3, with 4 alternative options)
- Correlation Matrix
- Extraction of initial orthogonal factors (PCA or PAF)
- Rotation to final factors (orthogonal or oblique)
What is the first step?
CORRELATION MATRIX:
SPSS output table to help give an understanding of what variables correlate with what and if these are significant.
Significance identified with *(95%) and **(99%)
One proposal for a reliable sample size is a minimum of 5 participants per variable, and no less than 100 per analysis.
What is the second step?
Extraction of initial orthogonal factors.
2a: Principal Components Analysis (PCA) is chosen when little is known about the variables, so it is assumed that communality is 1, all the variables have shared variance (common variance). The high loadings (correlations) are identified.
2b: Principal-axis factoring (PAF) is used instead once… Communality is no longer 1, the extraction column indicates the degree of common variance attributed to each variable after analysis is complete (often will be lower than 1)
What is the third step? Give definitions.
Rotations.
Where some variables look like they could fit in any of the factors i.e. the loadings are not clear (not highly correlated in a single factor)
- ORTHOGONAL = axes moved at right angles; produces factors that are unrelated
- OBLIQUE = axes don’t remain at 90degrees, but move together like scisors; in which factors are correlated
Define common, specific and error variance.
COMMON = variance shared by data points on 3 or more variables
SPECIFIC = variance that is unique to a variable i.e. not shared with any other variable
ERROR = fluctuations that inevitably result from measuring something
What are the assumptions of PCA and PAF? How are they different and when are they used?
Principal Components Analysis is used when little is known about the variables, and so communality is assumed to be 1.
Once the number of factors has been determined/chosen, Principal-axis Factoring can be used. Here, the different degrees of common variance are attributed. Following this, rotation can show the factor loadings.
Define communality.
The degree of common variance attributed to each variable after analysis is complete.
What are initial eigenvalues?
The amount of variance the variables account for (all have a value of 1 if using PCA)
How is the decision made when retaining/extracting factors?
We want to keep those that contribute most.
KAISER’S CRITERION = extract variables that are 1 or more
SCREE TEST = retain the factors before the inflexion point (Cattell, 1966)
