Factor analysis Flashcards
What is factor analysis?
It is a statistical method that looks at how lots of different items correlate and determines how many theoretical constructs could most simply explain what you see.
What is principle components analysis (PCA)?
It is similar to factor analysis.
We conduct PCA rather than FA as it is less complex and is psychometrically sound. REsearch has suggested little difference in results between the two (Guadagnoli & Velicer, 1988)
*on SPSS, PCA will already be selected - it is the ‘type’ of FA we will be conducting.
What are the differences between FA and PCA?
FA uses a mathematical model from which the factors are estimated.
PCA uses the original data to derive the set of clusters of variables.
What does FA do?
It helps us determine items/behaviours relating to constructs.
It takes a lot of information and simplifies it by placing it into factors.
It examines the pattern/correlation between variables to calculate new variables (these are known as supervariables or FACTORS).
Determining the maximum amount of common variance using the smallest amount of explanatory constructs.
What are the uses of FA?
- Understanding the structure of an underlying dimension/construct.
- To construct a questionnaire: defining sub-scales and items which are not representative of the variable measured.
- To reduce a data set to a more manageable and purposeful size.
How can we determine personality via questionnaires?
Questionnaires allow us measure a variety of constructs (e.g. personality traits) within one scales.
What do the correlations between scale items tell us?
From the correlations between the scale items, we can infer something about their underlying nature (theoretical constructs).
Why would we not just do multiple correlations to ascertain which questions more closely relate to each other?
The more correlations there are, it becomes very difficult to interpret.
More correlations may lead to more type 1 errors.
Describe the output of correlations between variables.
Items should correlate if they measure the same underlying dimension. An identity matrix is the opposite (no correlation)
What does Bartlett’s test measure?
It measures whether the correlation matrix differs from an identity matrix and therefore should be significant (p < .05)
What does KMO test show?
It indicates if there is a distinct and reliable set of factors from the patterns of correlations between variables.
This will lie between 0-1; look for a value closer to 1.
How can we measure how many factors there are using the Kaiser Criterion?
In the Kaiser Criterion, the number of factors is all the factors with an Eigenvalue of above 1.
The Eigenvalue is the variance accounted for by that factor.
However, Kaiser’s should be used with caution. Criterion is only accurate with 30 variables and commonalities > .70.
How can we measure how many factors there are using the Scree Plot Test?
The Scree Plot Test lists the factors in order of eigenvalues in a graph.
The argued cut off point for ‘selected factors’ is the point of inflexion.
However this can be problematic as it is subjective where the line changes.
What is rotation?
Rotation maximises loading of each variable on one of the extracted factors and minimises loadings on the other factors.
Why can ‘un-rotated’ factors be difficult to interpret?
- Factors correlate with many variables.
2. Variable load onto many factors.
